Deductive reasoning

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Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false.

For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.

Psychology is interested in deductive reasoning as a psychological process, i.e. how people actually draw inferences. Logic, on the other hand, focuses on the deductive relation of logical consequence between the premises and the conclusion or how people should draw inferences. There are different ways of conceptualizing this relation. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, on the other hand, holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference. A rule of inference is a schema of drawing a conclusion from a set of premises based only on their logical form.

There are various rules of inference, like the modus ponens and the modus tollens. Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies. Rules of inference are definitory rules and contrast to strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion. Deductive reasoning contrasts with non-deductive or ampliative reasoning. For ampliative arguments, like inductive or abductive arguments, the premises offer weaker support to their conclusion: they make it more likely but they do not guarantee its truth. They make up for this drawback by being able to provide genuinely new information not already found in the premises, unlike deductive arguments.

Cognitive psychology investigates the mental processes responsible for deductive reasoning. One of its topics concerns the factors determining whether people draw valid or invalid deductive inferences. One factor is the form of the argument: for example, people are more successful for arguments of the form modus ponens than for modus tollens. Another is the content of the arguments: people are more likely to believe that an argument is valid if the claim made in its conclusion is plausible. A general finding is that people tend to perform better for realistic and concrete cases than for abstract cases. Psychological theories of deductive reasoning aim to explain these findings by providing an account of the underlying psychological processes. Mental logic theories hold that deductive reasoning is a language-like process that happens through the manipulation of representations using rules of inference. Mental model theories, on the other hand, claim that deductive reasoning involves models of possible states of the world without the medium of language or rules of inference. According to dual-process theories of reasoning, there are two qualitatively different cognitive systems responsible for reasoning.

The problem of deductive reasoning is relevant to various fields and issues. Epistemology tries to understand how justification is transferred from the belief in the premises to the belief in the conclusion in the process of deductive reasoning. Probability logic studies how the probability of the premises of an inference affects the probability of its conclusion. The controversial thesis of deductivism denies that there are other correct forms of inference besides deduction. Natural deduction is a type of proof system based on simple and self-evident rules of inference. In philosophy, the geometrical method is a way of philosophizing that starts from a small set of self-evident axioms and tries to build a comprehensive logical system using deductive reasoning.

Definition

Deductive reasoning is the psychological process of drawing deductive inferences. An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises. If the reasoning was done correctly, it results in a valid deduction: the truth of the premises ensures the truth of the conclusion. For example, in the syllogistic argument "all frogs are amphibians; no cats are amphibians; therefore, no cats are frogs" the conclusion is true because its two premises are true. But even arguments with wrong premises can be deductively valid if they obey this principle, as in "all frogs are mammals; no cats are mammals; therefore, no cats are frogs". If the premises of a valid argument are true, then it is called a sound argument.

The relation between the premises and the conclusion of a deductive argument is usually referred to as "logical consequence". According to Alfred Tarski, logical consequence has 3 essential features: it is necessary, formal, and knowable a priori. It is necessary in the sense that the premises of valid deductive arguments necessitate the conclusion: it is impossible for the premises to be true and the conclusion to be false, independent of any other circumstances. Logical consequence is formal in the sense that it depends only on the form or the syntax of the premises and the conclusion. This means that the validity of a particular argument does not depend on the specific contents of this argument. If it is valid, then any argument with the same logical form is also valid, no matter how different it is on the level of its contents. Logical consequence is knowable a priori in the sense that no empirical knowledge of the world is necessary to determine whether a deduction is valid. So it is not necessary to engage in any form of empirical investigation. Some logicians define deduction in terms of possible worlds: A deductive inference is valid if and only if, there is no possible world in which its conclusion is false while its premises are true. This means that there are no counterexamples: the conclusion is true in all such cases, not just in most cases.

It has been argued against this and similar definitions that they fail to distinguish between valid and invalid deductive reasoning, i.e. they leave it open whether there are invalid deductive inferences and how to define them. Some authors define deductive reasoning in psychological terms in order to avoid this problem. According to Mark Vorobey, whether an argument is deductive depends on the psychological state of the person making the argument: "An argument is deductive if, and only if, the author of the argument believes that the truth of the premises necessitates (guarantees) the truth of the conclusion". A similar formulation holds that the speaker claims or intends that the premises offer deductive support for their conclusion. This is sometimes categorized as a speaker-determined definition of deduction since it depends also on the speaker whether the argument in question is deductive or not. For speakerless definitions, on the other hand, only the argument itself matters independent of the speaker. One advantage of this type of formulation is that it makes it possible to distinguish between good or valid and bad or invalid deductive arguments: the argument is good if the author's belief concerning the relation between the premises and the conclusion is true, otherwise it is bad. One consequence of this approach is that deductive arguments cannot be identified by the law of inference they use. For example, an argument of the form modus ponens may be non-deductive if the author's beliefs are sufficiently confused. That brings with it an important drawback of this definition: it is difficult to apply to concrete cases since the intentions of the author are usually not explicitly stated.

Deductive reasoning is studied in logic, psychology, and the cognitive sciences. Some theorists emphasize in their definition the difference between these fields. On this view, psychology studies deductive reasoning as an empirical mental process, i.e. what happens when humans engage in reasoning. But the descriptive question of how actual reasoning happens is different from the normative question of how it should happen or what constitutes correct deductive reasoning, which is studied by logic. This is sometimes expressed by stating that, strictly speaking, logic does not study deductive reasoning but the deductive relation between premises and a conclusion known as logical consequence. But this distinction is not always precisely observed in the academic literature. One important aspect of this difference is that logic is not interested in whether the conclusion of an argument is sensible. So from the premise "the printer has ink" one may draw the unhelpful conclusion "the printer has ink and the printer has ink and the printer has ink", which has little relevance from a psychological point of view. Instead, actual reasoners usually try to remove redundant or irrelevant information and make the relevant information more explicit. The psychological study of deductive reasoning is also concerned with how good people are at drawing deductive inferences and with the factors determining their performance. Deductive inferences are found both in natural language and in formal logical systems, such as propositional logic.

Conceptions of deduction

Deductive arguments differ from non-deductive arguments in that the truth of their premises ensures the truth of their conclusion. There are two important conceptions of what this exactly means. They are referred to as the syntactic and the semantic approach. According to the syntactic approach, whether an argument is deductively valid depends only on its form, syntax, or structure. Two arguments have the same form if they use the same logical vocabulary in the same arrangement, even if their contents differ. For example, the arguments "if it rains then the street will be wet; it rains; therefore, the street will be wet" and "if the meat is not cooled then it will spoil; the meat is not cooled; therefore, it will spoil" have the same logical form: they follow the modus ponens. Their form can be expressed more abstractly as "if A then B; A; therefore B" in order to make the common syntax explicit. There are various other valid logical forms or rules of inference, like modus tollens or the disjunction elimination. The syntactic approach then holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference. One difficulty for the syntactic approach is that it is usually necessary to express the argument in a formal language in order to assess whether it is valid. But since the problem of deduction is also relevant for natural languages, this often brings with it the difficulty of translating the natural language argument into a formal language, a process that comes with various problems of its own. Another difficulty is due to the fact that the syntactic approach depends on the distinction between formal and non-formal features. While there is a wide agreement concerning the paradigmatic cases, there are also various controversial cases where it is not clear how this distinction is to be drawn.

The semantic approach suggests an alternative definition of deductive validity. It is based on the idea that the sentences constituting the premises and conclusions have to be interpreted in order to determine whether the argument is valid. This means that one ascribes semantic values to the expressions used in the sentences, such as the reference to an object for singular terms or to a truth-value for atomic sentences. The semantic approach is also referred to as the model-theoretic approach since the branch of mathematics known as model theory is often used to interpret these sentences. Usually, many different interpretations are possible, such as whether a singular term refers to one object or to another. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation where its premises are true and its conclusion is false. Some objections to the semantic approach are based on the claim that the semantics of a language cannot be expressed in the same language, i.e. that a richer metalanguage is necessary. This would imply that the semantic approach cannot provide a universal account of deduction for language as an all-encompassing medium.

Rules of inference

Deductive reasoning usually happens by applying rules of inference. A rule of inference is a way or schema of drawing a conclusion from a set of premises. This happens usually based only on the logical form of the premises. A rule of inference is valid if, when applied to true premises, the conclusion cannot be false. A particular argument is valid if it follows a valid rule of inference. Deductive arguments that do not follow a valid rule of inference are called formal fallacies: the truth of their premises does not ensure the truth of their conclusion.

In some cases, whether a rule of inference is valid depends on the logical system one is using. The dominant logical system is classical logic and the rules of inference listed here are all valid in classical logic. But so-called deviant logics provide a different account of which inferences are valid. For example, the rule of inference known as double negation elimination, i.e. that if a proposition is not not true then it is also true, is accepted in classical logic but rejected in intuitionistic logic.

Prominent rules of inference

Modus ponens

Main article: Modus ponens

Modus ponens (also known as "affirming the antecedent" or "the law of detachment") is the primary deductive rule of inference. It applies to arguments that have as first premise a conditional statement ($P\to Q$) and as second premise the antecedent ($P$) of the conditional statement. It obtains the consequent ($Q$) of the conditional statement as its conclusion. The argument form is listed below:

1. $P\to Q$  (First premise is a conditional statement)
2. $P$  (Second premise is the antecedent)
3. $Q$  (Conclusion deduced is the consequent)

In this form of deductive reasoning, the consequent ($Q$) obtains as the conclusion from the premises of a conditional statement ($P\to Q$) and its antecedent ($P$). However, the antecedent ($P$) cannot be similarly obtained as the conclusion from the premises of the conditional statement ($P\to Q$) and the consequent ($Q$). Such an argument commits the logical fallacy of affirming the consequent.

The following is an example of an argument using modus ponens:

1. If it is raining, then there are clouds in the sky.
2. It is raining.
3. Thus, there are clouds in the sky.

Modus tollens

Main article: Modus tollens

Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. It validates an argument that has as premises a conditional statement (formula) and the negation of the consequent (${\displaystyle \mathrm{\neg }Q}$) and as conclusion the negation of the antecedent ($\mathrm{\neg }P$). In contrast to modus ponens, reasoning with modus tollens goes in the opposite direction to that of the conditional. The general expression for modus tollens is the following:

1. $P\to Q$. (First premise is a conditional statement)
2. ${\displaystyle \mathrm{\neg }Q}$. (Second premise is the negation of the consequent)
3. $\mathrm{\neg }P$. (Conclusion deduced is the negation of the antecedent)

The following is an example of an argument using modus tollens:

1. If it is raining, then there are clouds in the sky.
2. There are no clouds in the sky.
3. Thus, it is not raining.

Hypothetical syllogism

Main article: hypothetical syllogism

A hypothetical syllogism is an inference that takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form:

1. $P\to Q$
2. ${\displaystyle Q\to R}$
3. Therefore, ${\displaystyle P\to R}$.

In there being a subformula in common between the two premises that does not occur in the consequence, this resembles syllogisms in term logic, although it differs in that this subformula is a proposition whereas in Aristotelian logic, this common element is a term and not a proposition.

The following is an example of an argument using a hypothetical syllogism:

1. If there had been a thunderstorm, it would have rained.
2. If it had rained, things would have gotten wet.
3. Thus, if there had been a thunderstorm, things would have gotten wet.

Fallacies

Various formal fallacies have been described. They are invalid forms of deductive reasoning. An additional aspect of them is that they appear to be valid on some occasions or on the first impression. They may thereby seduce people into accepting and committing them. One type of formal fallacy is affirming the consequent, as in "if John is a bachelor, then he is male; John is male; therefore, John is a bachelor". This is similar to the valid rule of inference named modus ponens, but the second premise and the conclusion are switched around, which is why it is invalid. A similar formal fallacy is denying the antecedent, as in "if Othello is a bachelor, then he is male; Othello is not a bachelor; therefore, Othello is not male". This is similar to the valid rule of inference called modus tollens, the difference being that the second premise and the conclusion are switched around. Other formal fallacies include affirming a disjunct, denying a conjunct, and the fallacy of the undistributed middle. All of them have in common that the truth of their premises does not ensure the truth of their conclusion. But it may still happen by coincidence that both the premises and the conclusion of formal fallacies are true.

Definitory and strategic rules

Rules of inferences are definitory rules: they determine whether an argument is deductively valid or not. But reasoners are usually not just interested in making any kind of valid argument. Instead, they often have a specific point or conclusion that they wish to prove or refute. So given a set of premises, they are faced with the problem of choosing the relevant rules of inference for their deduction to arrive at their intended conclusion. This issue belongs to the field of strategic rules: the question of which inferences need to be drawn to support one's conclusion. The distinction between definitory and strategic rules is not exclusive to logic: it is also found in various games. In chess, for example, the definitory rules state that bishops may only move diagonally while the strategic rules recommend that one should control the center and protect one's king if one intends to win. In this sense, definitory rules determine whether one plays chess or something else whereas strategic rules determine whether one is a good or a bad chess player. The same applies to deductive reasoning: to be an effective reasoner involves mastering both definitory and strategic rules.

Validity and soundness

Argument terminology

Deductive arguments are evaluated in terms of their validity and soundness.

An argument is “valid” if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises are true. An argument can be “valid” even if one or more of its premises are false.

An argument is “sound” if it is valid and the premises are true.

It is possible to have a deductive argument that is logically valid but is not sound. Fallacious arguments often take that form.

The following is an example of an argument that is “valid”, but not “sound”:

1. Everyone who eats carrots is a quarterback.
2. John eats carrots.
3. Therefore, John is a quarterback.

The example's first premise is false – there are people who eat carrots who are not quarterbacks – but the conclusion would necessarily be true, if the premises were true. In other words, it is impossible for the premises to be true and the conclusion false. Therefore, the argument is “valid”, but not “sound”. False generalizations – such as "Everyone who eats carrots is a quarterback" – are often used to make unsound arguments. The fact that there are some people who eat carrots but are not quarterbacks proves the flaw of the argument.

In this example, the first statement uses categorical reasoning, saying that all carrot-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.

Deductive reasoning can be contrasted with inductive reasoning, in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is “valid”, it is possible for the conclusion to be false (determined to be false with a counterexample or other means).

Difference from ampliative reasoning

Deductive reasoning is usually contrasted with non-deductive or ampliative reasoning. The hallmark of valid deductive inferences is that it is impossible for their premises to be true and their conclusion to be false. In this way, the premises provide the strongest possible support to their conclusion. The premises of ampliative inferences also support their conclusion. But this support is weaker: they are not necessarily truth-preserving. So even for correct ampliative arguments, it is possible that their premises are true and their conclusion is false. Two important forms of ampliative reasoning are inductive and abductive reasoning. Sometimes the term "inductive reasoning" is used in a very wide sense to cover all forms of ampliative reasoning. However, in a more strict usage, inductive reasoning is just one form of ampliative reasoning. In the narrow sense, inductive inferences are forms of statistical generalization. They are usually based on many individual observations that all show a certain pattern. These observations are then used to form a conclusion either about a yet unobserved entity or about a general law. For abductive inferences, the premises support the conclusion because the conclusion is the best explanation of why the premises are true.

The support ampliative arguments provide for their conclusion comes in degrees: some ampliative arguments are stronger than others. This is often explained in terms of probability: the premises make it more likely that the conclusion is true. Strong ampliative arguments make their conclusion very likely, but not absolutely certain. An example of ampliative reasoning is the inference from the premise "every raven in a random sample of 3200 ravens is black" to the conclusion "all ravens are black": the extensive random sample makes the conclusion very likely, but it does not exclude that there are rare exceptions. In this sense, ampliative reasoning is defeasible: it may become necessary to retract an earlier conclusion upon receiving new related information. Ampliative reasoning is very common in everyday discourse and the sciences.

An important drawback of deductive reasoning is that it does not lead to genuinely new information. This means that the conclusion only repeats information already found in the premises. Ampliative reasoning, on the other hand, goes beyond the premises by arriving at genuinely new information. One difficulty for this characterization is that it makes deductive reasoning appear useless: if deduction is uninformative, it is not clear why people would engage in it and study it. It has been suggested that this problem can be solved by distinguishing between surface and depth information. On this view, deductive reasoning is uninformative on the depth level, in contrast to ampliative reasoning. But it may still be valuable on the surface level by presenting the information in the premises in a new and sometimes surprising way.

A popular misconception of the relation between deduction and induction identifies their difference on the level of particular and general claims. On this view, deductive inferences start from general premises and draw particular conclusions, while inductive inferences start from particular premises and draw general conclusions. This idea is often motivated by seeing deduction and induction as two inverse processes that complement each other: deduction is top-down while induction is bottom-up. But this is a misconception that does not reflect how valid deduction is defined in the field of logic: a deduction is valid if it is impossible for its premises to be true while its conclusion is false, independent of whether the premises or the conclusion are particular or general. Because of this, some deductive inferences have a general conclusion and some also have particular premises.

In various fields

Cognitive psychology

Cognitive psychology studies the psychological processes responsible for deductive reasoning. It is concerned, among other things, with how good people are at drawing valid deductive inferences. This includes the study of the factors affecting their performance, their tendency to commit fallacies, and the underlying biases involved. A notable finding in this field is that the type of deductive inference has a significant impact on whether the correct conclusion is drawn. In a meta-analysis of 65 studies, for example, 97% of the subjects evaluated modus ponens inferences correctly, while the success rate for modus tollens was only 72%. On the other hand, even some fallacies like affirming the consequent or denying the antecedent were regarded as valid arguments by the majority of the subjects. An important factor for these mistakes is whether the conclusion seems initially plausible: the more believable the conclusion is, the higher the chance that a subject will mistake a fallacy for a valid argument.

An important bias is the matching bias, which is often illustrated using the Wason selection task. In an often-cited experiment by Peter Wason, 4 cards are presented to the participant. In one case, the visible sides show the symbols D, K, 3, and 7 on the different cards. The participant is told that every card has a letter on one side and a number on the other side, and that "[e]very card which has a D on one side has a 3 on the other side". Their task is to identify which cards need to be turned around in order to confirm or refute this conditional claim. The correct answer, only given by about 10%, is the cards D and 7. Many select card 3 instead, even though the conditional claim does not involve any requirements on what symbols can be found on the opposite side of card 3. But this result can be drastically changed if different symbols are used: the visible sides show "drinking a beer", "drinking a coke", "16 years of age", and "22 years of age" and the participants are asked to evaluate the claim "[i]f a person is drinking beer, then the person must be over 19 years of age". In this case, 74% of the participants identified correctly that the cards "drinking a beer" and "16 years of age" have to be turned around. These findings suggest that the deductive reasoning ability is heavily influenced by the content of the involved claims and not just by the abstract logical form of the task: the more realistic and concrete the cases are, the better the subjects tend to perform.

Another bias is called the "negative conclusion bias", which happens when one of the premises has the form of a negative material conditional, as in "If the card does not have an A on the left, then it has a 3 on the right. The card does not have a 3 on the right. Therefore, the card has an A on the left". The increased tendency to misjudge the validity of this type of argument is not present for positive material conditionals, as in "If the card has an A on the left, then it has a 3 on the right. The card does not have a 3 on the right. Therefore, the card does not have an A on the left".

Psychological theories of deductive reasoning

Various psychological theories of deductive reasoning have been proposed. These theories aim to explain how deductive reasoning works in relation to the underlying psychological processes responsible. They are often used to explain the empirical findings, such as why human reasoners are more susceptible to some types of fallacies than to others.

An important distinction is between mental logic theories, sometimes also referred to as rule theories, and mental model theories. Mental logic theories see deductive reasoning as a language-like process that happens through the manipulation of representations. This is done by applying syntactic rules of inference in a way very similar to how systems of natural deduction transform their premises to arrive at a conclusion. On this view, some deductions are simpler than others since they involve fewer inferential steps. This idea can be used, for example, to explain why humans have more difficulties with some deductions, like the modus tollens, than with others, like the modus ponens: because the more error-prone forms do not have a native rule of inference but need to be calculated by combining several inferential steps with other rules of inference. In such cases, the additional cognitive labor makes the inferences more open to error.

Mental model theories, on the other hand, hold that deductive reasoning involves models or mental representations of possible states of the world without the medium of language or rules of inference. In order to assess whether a deductive inference is valid, the reasoner mentally constructs models that are compatible with the premises of the inference. The conclusion is then tested by looking at these models and trying to find a counterexample in which the conclusion is false. The inference is valid if no such counterexample can be found. In order to reduce cognitive labor, only such models are represented in which the premises are true. Because of this, the evaluation of some forms of inference only requires the construction of very few models while for others, many different models are necessary. In the latter case, the additional cognitive labor required makes deductive reasoning more error-prone, thereby explaining the increased rate of error observed. This theory can also explain why some errors depend on the content rather than the form of the argument. For example, when the conclusion of an argument is very plausible, the subjects may lack the motivation to search for counterexamples among the constructed models.

Both mental logic theories and mental model theories assume that there is one general-purpose reasoning mechanism that applies to all forms of deductive reasoning. But there are also alternative accounts that posit various different special-purpose reasoning mechanisms for different contents and contexts. In this sense, it has been claimed that humans possess a special mechanism for permissions and obligations, specifically for detecting cheating in social exchanges. This can be used to explain why humans are often more successful in drawing valid inferences if the contents involve human behavior in relation to social norms. Another example is the so-called dual-process theory. This theory posits that there are two distinct cognitive systems responsible for reasoning. Their interrelation can be used to explain commonly observed biases in deductive reasoning. System 1 is the older system in terms of evolution. It is based on associative learning and happens fast and automatically without demanding many cognitive resources. System 2, on the other hand, is of more recent evolutionary origin. It is slow and cognitively demanding, but also more flexible and under deliberate control. The dual-process theory posits that system 1 is the default system guiding most of our everyday reasoning in a pragmatic way. But for particularly difficult problems on the logical level, system 2 is employed. System 2 is mostly responsible for deductive reasoning.

Intelligence

The ability of deductive reasoning is an important aspect of intelligence and many tests of intelligence include problems that call for deductive inferences. Because of this relation to intelligence, deduction is highly relevant to psychology and the cognitive sciences. But the subject of deductive reasoning is also pertinent to the computer sciences, for example, in the creation of artificial intelligence.

Epistemology

Deductive reasoning plays an important role in epistemology. Epistemology is concerned with the question of justification, i.e. to point out which beliefs are justified and why. Deductive inferences are able to transfer the justification of the premises onto the conclusion. So while logic is interested in the truth-preserving nature of deduction, epistemology is interested in the justification-preserving nature of deduction. There are different theories trying to explain why deductive reasoning is justification-preserving. According to reliabilism, this is the case because deductions are truth-preserving: they are reliable processes that ensure a true conclusion given the premises are true. Some theorists hold that the thinker has to have explicit awareness of the truth-preserving nature of the inference for the justification to be transferred from the premises to the conclusion. One consequence of such a view is that, for young children, this deductive transference does not take place since they lack this specific awareness.

Probability logic

Probability logic is interested in how the probability of the premises of an argument affects the probability of its conclusion. It differs from classical logic, which assumes that propositions are either true or false but does not take into consideration the probability or certainty that a proposition is true or false. The probability of the conclusion of a deductive argument cannot be calculated by figuring out the cumulative probability of the argument’s premises. Dr. Timothy McGrew, a specialist in the applications of probability theory, and Dr. Ernest W. Adams, a Professor Emeritus at UC Berkeley, pointed out that the theorem on the accumulation of uncertainty designates only a lower limit on the probability of the conclusion. So the probability of the conjunction of the argument’s premises sets only a minimum probability of the conclusion. The probability of the argument’s conclusion cannot be any lower than the probability of the conjunction of the argument’s premises. For example, if the probability of a deductive argument’s four premises is ~0.43, then it is assured that the probability of the argument’s conclusion is no less than ~0.43. It could be much higher, but it cannot drop under that lower limit.

There can be examples in which each single premise is more likely true than not and yet it would be unreasonable to accept the conjunction of the premises. Professor Henry Kyburg, who was known for his work in probability and logic, clarified that the issue here is one of closure – specifically, closure under conjunction. There are examples where it is reasonable to accept P and reasonable to accept Q without its being reasonable to accept the conjunction (P&Q). Lotteries serve as very intuitive examples of this, because in a basic non-discriminatory finite lottery with only a single winner to be drawn, it is sound to think that ticket 1 is a loser, sound to think that ticket 2 is a loser,...all the way up to the final number. However, clearly, it is irrational to accept the conjunction of these statements; the conjunction would deny the very terms of the lottery because (taken with the background knowledge) it would entail that there is no winner.

Dr. McGrew further adds that the sole method to ensure that a conclusion deductively drawn from a group of premises is more probable than not is to use premises the conjunction of which is more probable than not. This point is slightly tricky, because it can lead to a possible misunderstanding. What is being searched for is a general principle that specifies factors under which, for any logical consequence C of the group of premises, C is more probable than not. Particular consequences will differ in their probability. However, the goal is to state a condition under which this attribute is ensured, regardless of which consequence one draws, and fulfilment of that condition is required to complete the task.

This principle can be demonstrated in a moderately clear way. Suppose, for instance, the following group of premises:

{P, Q, R}

Suppose that the conjunction ((P & Q) & R) fails to be more probable than not. Then there is at least one logical consequence of the group that fails to be more probable than not – namely, that very conjunction. So it is an essential factor for the argument to “preserve plausibility” (Dr. McGrew coins this phrase to mean “guarantee, from information about the plausibility of the premises alone, that any conclusion drawn from those premises by deductive inference is itself more plausible than not”) that the conjunction of the premises be more probable than not.

History

Aristotle, a Greek philosopher, started documenting deductive reasoning in the 4th century BC. René Descartes, in his book Discourse on Method, refined the idea for the Scientific Revolution. Developing four rules to follow for proving an idea deductively, Descartes laid the foundation for the deductive portion of the scientific method. Descartes' background in geometry and mathematics influenced his ideas on the truth and reasoning, causing him to develop a system of general reasoning now used for most mathematical reasoning. Similar to postulates, Descartes believed that ideas could be self-evident and that reasoning alone must prove that observations are reliable. These ideas also lay the foundations for the ideas of rationalism.

Related concepts and theories

Deductivism

Deductivism is a philosophical position that gives primacy to deductive reasoning or arguments over their non-deductive counterparts. It is often understood as the evaluative claim that only deductive inferences are good or correct inferences. This theory would have wide-reaching consequences for various fields since it implies that the rules of deduction are "the only acceptable standard of evidence". This way, the rationality or correctness of the different forms of inductive reasoning is denied. Some forms of deductivism express this in terms of degrees of reasonableness or probability. Inductive inferences are usually seen as providing a certain degree of support for their conclusion: they make it more likely that their conclusion is true. Deductivism states that such inferences are not rational: the premises either ensure their conclusion, as in deductive reasoning, or they do not provide any support at all.

One motivation for deductivism is the problem of induction introduced by David Hume. It consists in the challenge of explaining how or whether inductive inferences based on past experiences support conclusions about future events. For example, a chicken comes to expect, based on all its past experiences, that the person entering its coop is going to feed it, until one day the person "at last wrings its neck instead". According to Karl Popper's falsificationism, deductive reasoning alone is sufficient. This is due to its truth-preserving nature: a theory can be falsified if one of its deductive consequences is false. So while inductive reasoning does not offer positive evidence for a theory, the theory still remains a viable competitor until falsified by empirical observation. In this sense, deduction alone is sufficient for discriminating between competing hypotheses about what is the case. Hypothetico-deductivism is a closely related scientific method, according to which science progresses by formulating hypotheses and then aims to falsify them by trying to make observations that run counter to their deductive consequences.

Natural deduction

The term "natural deduction" refers to a class of proof systems based on self-evident rules of inference. The first systems of natural deduction were developed by Gerhard Gentzen and Stanislaw Jaskowski in the 1930s. The core motivation was to give a simple presentation of deductive reasoning that closely mirrors how reasoning actually takes place. In this sense, natural deduction stands in contrast to other less intuitive proof systems, such as Hilbert-style deductive systems, which employ axiom schemes to express logical truths. Natural deduction, on the other hand, avoids axioms schemes by including many different rules of inference that can be used to formulate proofs. These rules of inference express how logical constants behave. They are often divided into introduction rules and elimination rules. Introduction rules specify under which conditions a logical constant may be introduced into a new sentence of the proof. For example, the introduction rule for the logical constant "$\wedge$" (and) is "${\displaystyle \frac{A,B}{(A\wedge B)}}$". It expresses that, given the premises "$A$" and "$B$" individually, one may draw the conclusion "$A\wedge B$" and thereby include it in one's proof. This way, the symbol "$\wedge$" is introduced into the proof. The removal of this symbol is governed by other rules of inference, such as the elimination rule "${\displaystyle \frac{(A\wedge B)}{A}}$", which states that one may deduce the sentence "$A$" from the premise "$(A\wedge B)$". Similar introduction and elimination rules are given for other logical constants, such as the propositional operator "$\mathrm{\neg }$", the propositional connectives "$\vee$" and "$\to$", and the quantifiers "$\mathrm{\exists }$" and "$\mathrm{\forall }$".

The focus on rules of inferences instead of axiom schemes is an important feature of natural deduction. But there is no general agreement on how natural deduction is to be defined. Some theorists hold that all proof systems with this feature are forms of natural deduction. This would include various forms of sequent calculi or tableau calculi. But other theorists use the term in a more narrow sense, for example, to refer to the proof systems developed by Gentzen and Jaskowski. Because of its simplicity, natural deduction is often used for teaching logic to students.

Geometrical method

The geometrical method is a method of philosophy based on deductive reasoning. It starts from a small set of self-evident axioms and tries to build a comprehensive logical system based only on deductive inferences from these first axioms. It was initially formulated by Baruch Spinoza and came to prominence in various rationalist philosophical systems in the modern era. It gets its name from the forms of mathematical demonstration found in traditional geometry, which are usually based on axioms, definitions, and inferred theorems. An important motivation of the geometrical method is to repudiate philosophical skepticism by grounding one's philosophical system on absolutely certain axioms. Deductive reasoning is central to this endeavor because of its necessarily truth-preserving nature. This way, the certainty initially invested only in the axioms is transferred to all parts of the philosophical system.

One recurrent criticism of philosophical systems build using the geometrical method is that their initial axioms are not as self-evident or certain as their defenders proclaim. This problem lies beyond the deductive reasoning itself, which only ensures that the conclusion is true if the premises are true, but not that the premises themselves are true. For example, Spinoza's philosophical system has been criticized this way based on objections raised against the causal axiom, i.e. that "the knowledge of an effect depends on and involves knowledge of its cause". A different criticism targets not the premises but the reasoning itself, which may at times implicitly assume premises that are themselves not self-evident.

Terror management theory

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Terror_management_theory

Terror management theory (TMT) is both a social and evolutionary psychology theory originally proposed by Jeff Greenberg, Sheldon Solomon, and Tom Pyszczynski and codified in their book The Worm at the Core: On the Role of Death in Life (2015). It proposes that a basic psychological conflict results from having a self-preservation instinct while realizing that death is inevitable and to some extent unpredictable. This conflict produces terror, which is managed through a combination of escapism and cultural beliefs that act to counter biological reality with more significant and enduring forms of meaning and value.

The most obvious examples of cultural values that assuage death anxiety are those that purport to offer literal immortality (e.g. belief in the afterlife through religion). However, TMT also argues that other cultural values – including those that are seemingly unrelated to death – offer symbolic immortality. For example, values of national identity, posterity, cultural perspectives on sex, and human superiority over animals have been linked to calming death concerns. In many cases these values are thought to offer symbolic immortality, by either a) providing the sense that one is part of something greater that will ultimately outlive the individual (e.g. country, lineage, species), or b) making one's symbolic identity superior to biological nature (i.e. you are a personality, which makes you more than a glob of cells). Because cultural values influence what is meaningful, they are foundational for self-esteem. TMT describes self-esteem as being the personal, subjective measure of how well an individual is living up to their cultural values.

Terror management theory was developed by social psychologists Greenberg, Solomon, and Pyszczynski. However, the idea of TMT originated from anthropologist Ernest Becker's 1973 Pulitzer Prize-winning work of nonfiction The Denial of Death. Becker argues most human action is taken to ignore or avoid the inevitability of death. The terror of absolute annihilation creates such a profound – albeit subconscious – anxiety in people that they spend their lives attempting to make sense of it. On large scales, societies build symbols: Laws, religious meanings, cultures, and belief systems to explain the significance of life, define what makes certain characteristics, skills, and talents extraordinary, reward others whom they find exemplify certain attributes, and punish or kill others who do not adhere to their cultural worldview. Adherence to these created "symbols" aid in relieving stresses associated with the reality of mortality. On an individual level, self-esteem provides a buffer against death-related anxiety.

Background

The idea of death, the fear of it, haunts the human animal like nothing else; it is a mainspring of human activity designed largely to avoid the fatality of death, to overcome it by denying in some way that it is the final destiny for man.

Ernest Becker, 1973

Cultural anthropologist Ernest Becker asserted in his 1973 book The Denial of Death that humans, as intelligent animals, are able to grasp the inevitability of death. They therefore spend their lives building and believing in cultural elements that illustrate how to make themselves stand out as individuals and give their lives significance and meaning. Death creates an anxiety in humans; it strikes at unexpected and random moments, and its nature is essentially unknowable, causing people to spend most of their time and energy to explain, forestall, and avoid it.

Becker expounded upon the previous writings of Sigmund Freud, Søren Kierkegaard, Norman O. Brown, and Otto Rank. According to clinical psychiatrist Morton Levitt, Becker replaces the Freudian preoccupation with sexuality with the fear of death as the primary motivation in human behavior.

People desire to think of themselves as beings of value and worth with a feeling of permanence, a concept in psychology known as self-esteem. This feeling counters the cognitive dissonance created by an individual's realization that they may be no more important than any other living thing. Becker refers to high self-esteem as heroism:

the problem of heroics is the central one of human life, that it goes deeper into human nature than anything else because it is based on organismic narcissism and on the child's need for self-esteem as the condition for his life. Society itself is a codified hero system, which means that society everywhere is a living myth of the significance of human life, a defiant creation of meaning.

The rationale behind decisions regarding one's own health can be explored through a terror management model. A 2008 research article in Psychological Review proposes a three-part model for understanding how awareness of death can ironically subvert health-promoting behaviors by redirecting one's focus towards behaviors that build self-esteem instead:

Proposition 1 suggests that conscious thoughts about death can instigate health-oriented responses aimed at removing death-related thoughts from current focal attention. Proposition 2 suggests that the unconscious resonance of death-related cognition promotes self-oriented defenses directed toward maintaining, not one's health, but a sense of meaning and self-esteem. The last proposition suggests that confrontations with the physical body may undermine symbolic defenses and thus present a previously unrecognized barrier to health promotion activities.

Evolutionary backdrop

Terror management theorists consider TMT to be compatible with the theory of evolution: Valid fears of dangerous things have an adaptive function that helped facilitate the survival of our ancestors' genes. However, generalized existential anxiety resulting from the clash between a desire for life and awareness of the inevitability of death is neither adaptive nor selected for. TMT views existential anxiety as an unfortunate byproduct of these two highly adaptive human proclivities rather than as an adaptation that the evolutionary process selected for its advantages. Just as human bipedalism confers advantages as well as disadvantages, death anxiety is an inevitable part of our intelligence and awareness of dangers.

Anxiety in response to the inevitability of death threatened to undermine adaptive functioning and therefore needed amelioration. TMT posits that humankind used the same intellectual capacities that gave rise to this problem to fashion cultural beliefs and values that provided protection against this potential anxiety. TMT considers these cultural beliefs (even unpleasant and frightening ones, such as ritual human sacrifice) when they manage potential death anxiety in a way that promotes beliefs and behaviors which facilitated the functioning and survival of the collective.

Hunter-gatherers used their emerging cognitive abilities to facilitate solving practical problems, such as basic needs for nutrition, mating, and tool-making. As these abilities evolved, an explicit awareness of death also emerged. But once this awareness materialized, the potential for terror that it created put pressure on emerging conceptions of reality. Any conceptual formation that was to be widely accepted by the group needed to provide a means of managing this terror.

Originally, the emergence of morality evolved to facilitate co-existence within groups. Together with language, morality served pragmatic functions that extended survival. The struggle to deny the finality of death co-opted and changed the function of these cultural inventions. For example, Neanderthals might have begun burying their dead as a means of avoiding unpleasant odors, disease-infested parasites, or dangerous scavengers. But during the Upper Paleolithic era, these pragmatic burial practices appear to have become imbued with layers of ritual performance and supernatural beliefs, suggested by the elaborate decoration of bodies with thousands of beads or other markers. Food and other necessities were also included within the burial chamber, indicating the potential for a belief system that included life after death. In many human cultures today, funerals are viewed primarily as cultural events, viewed through the lens of morality and language, with little thought given to the utilitarian origins of burying the dead.

Evolutionary history also indicates that "the costs of ignoring threats have outweighed the costs of ignoring opportunities for self-development." This reinforces the concept that abstract needs for individual and group self-esteem may continue to be selected for by evolution, even when they sometimes confer risks to physical health and well-being.

Self-esteem

Self-esteem lies at the heart of TMT and is a fundamental aspect of its core paradigms. TMT fundamentally seeks to elucidate the causes and consequences of a need for self-esteem. Theoretically, it draws heavily from Ernest Becker's conceptions of culture and self-esteem. TMT not only attempts to explain the concept of self-esteem, it also tries to explain why we need self-esteem. One explanation is that self-esteem is used as a coping mechanism for anxiety. It helps people control their sense of terror and nullify the realization that humans are just animals trying to manage the world around them. According to TMT, self-esteem is a sense of personal value that is created by beliefs in the validity of one's cultural worldview, and the belief that one is living up to the cultural standards created by that worldview.

Critically, Hewstone et al. (2002) have questioned the causal direction between self-esteem and death anxiety, evaluating whether one's self-esteem comes from their desire to reduce their death anxiety, or if death anxiety arises from a lack of self-esteem. In other words, an individual's suppression of death anxiety may arise from their overall need to increase their self-esteem in a positive manner.

Research has demonstrated that self-esteem can play an important role in physical health. In some cases, people may be so concerned with their physical appearance and boosting their self-esteem that they ignore problems or concerns with their own physical health. Arndt et al. (2009) conducted three studies to examine how peer perceptions and social acceptance of smokers contributes to their quitting, as well as if, and why these people continue smoking for outside reasons, even when faced with thoughts of death and anti-smoking prompts. Tanning and exercising were also looked at in the researchers' studies. The studies found that people are influenced by the situations around them. Specifically, Arndt et al. (2009) found in terms of their self-esteem and health, that participants who saw someone exercising were more likely to increase their intentions to exercise. In addition, the researchers found in study two that how participants reacted to an anti-smoking commercial was affected by their motivation for smoking and the situation which they were in. For instance, people who smoked for extrinsic reasons and were previously prompted with death reminders were more likely to be compelled by the anti-smoking message.

Self-esteem as anxiety buffer

An individual's level of self-consciousness can affect their views on life and death. To a point, increasing self-consciousness is adaptive in that it helps prevent awareness of danger. However, research has demonstrated that there may be diminishing returns from this phenomenon. Individuals with higher levels of self-consciousness sometimes have increased death cognition, and a more negative outlook on life, than those with reduced self-consciousness.

Conversely, self-esteem can work in the opposite manner. Research has confirmed that individuals with higher self-esteem, particularly in regard to their behavior, have a more positive attitude towards their life. Specifically, death cognition in the form of anti-smoking warnings weren't effective for smokers and in fact, increased their already positive attitudes towards the behavior. The reasons behind individuals' optimistic attitudes towards smoking after mortality was made salient, indicate that people use positivity as a buffer against anxiety. Continuing to hold certain beliefs even after they are shown to be flawed creates cognitive dissonance regarding current information and past behavior, and the way to alleviate this is to simply reject new information. Therefore, anxiety buffers such as self-esteem allow individuals to cope with their fears more easily. Death cognition may in fact cause negative reinforcement that leads people to further engage in dangerous behaviors (smoking in this instance) because accepting the new information would lead to a loss of self-esteem, increasing vulnerability and awareness of mortality.

Mortality salience

The mortality salience hypothesis (MS) states that if indeed one's cultural worldview, or one's self-esteem, serves a death-denying function, then threatening these constructs should produce defenses aimed at restoring psychological equanimity (i.e., returning the individual to a state of feeling invulnerable). In the MS paradigm, these "threats" are simply experiential reminders of one's own death. This can, and has, taken many different forms in a variety of study paradigms (e.g., asking participants to write about their own death; conducting the experiment near funeral homes or cemeteries; having participants watch graphic depictions of death, etc.). Like the other TMT hypotheses, the literature supporting the MS hypothesis is vast and diverse. For a meta analysis of MS research, see Burke et al. (2010).

Experimentally, the MS hypothesis has been tested in close to 200 empirical articles. After participants in an experiment are asked to write about their own death (vs. a neutral, non-death control topic, such as dental pain), and then following a brief delay (distal, worldview/self-esteem defenses work the best after a delay; see Greenberg et al. (1994) for a discussion), the participants' defenses are measured. In one early TMT study assessing the MS hypothesis, Greenberg et al. (1990) had Christian participants evaluate other Christian and Jewish students that were similar demographically, but differed in their religious affiliation. After being reminded of their death (experimental MS induction), Christian participants evaluated fellow Christians more positively, and Jewish participants more negatively, relative to the control condition. Conversely, bolstering self-esteem in these scenarios leads to less worldview defense and derogation of dissimilar others.

Mortality salience has an influence on individuals and their decisions regarding their health. Cox et al. (2009) discuss mortality salience in terms of suntanning. Specifically, the researchers found that participants who were prompted with the idea that pale was more socially attractive along with mortality reminders, tended to lean towards decisions that resulted in more protective measures from the sun. The participants were placed in two different conditions; one group of participants were given an article relating to the fear of death, while the control group received an article unrelated to death, dealing with the fear of public speaking. Additionally, they gave one group an article pertaining to the message that "bronze is beautiful," one relating to the idea that "pale is pretty," and one neutral article that did not speak of tan or pale skin tones. Finally, after introducing a delay activity, the researchers gave the participants a five-item questionnaire asking them about their future sun-tanning behaviors. The study illustrated that when tan skin was associated with attractiveness, mortality salience positively affected people's intentions to suntan; however, when pale skin was associated with attractiveness people's intentions to tan decreased.

Mortality and self-esteem on health risks

Studies have shown that mortality and self-esteem are important factors of the terror management theory. Jessop et al. (2008) study this relationship within four studies that all examine how people react when they are given information on risks, specifically, in terms of the mortality related to the risks of driving. More specifically, the researchers were exploring how participants acted in terms of self-esteem, and its impact on how mortality-related health-risk information would be received. Overall, Jessop et al. (2008) found that even when mortality is prominent, people who engage in certain behaviors to improve their self-esteem have a greater chance of continuing with these activities. Mortality and self-esteem are both factors that influence people's behaviors and decision-making regarding their health. Furthermore, individuals who are involved in behaviors and possess motivation to enhance their self-worth are less likely to be affected by the importance placed on health risks, in terms of mortality.

Self-esteem is important when mortality is made salient. It can allow people a coping mechanism, one that can cushion individuals' fears; and thus, impacting one's attitudes towards a given behavior. Individuals who have higher levels of self-esteem regarding their behavior(s) are less likely to have their attitudes, and thus their behaviors changed regardless of mortality salience or death messages. People will use their self-esteem to hide behind their fears of dying. In terms of smoking behaviors, people with higher smoking-based self-esteem are less susceptible to anti-smoking messages that relate to death; therefore, mortality salience and death warnings afford them with an even more positive outlook on their behavior, or in this instance their smoking.

In the Hansen et al. (2010) experiment the researchers manipulated mortality salience. In the experiment, Hansen et al. (2010) examined smokers' attitudes towards the behavior of smoking. Actual warning labels were utilized to create mortality salience in this specific experiment. The researchers first gave participants a questionnaire to measure their smoking-based self-esteem. Following the questionnaire, participants were randomly assigned to two different conditions; the first were given anti-smoking warning labels about death and the second control group were exposed to anti-smoking warning labels not dealing with death. Before the participants' attitudes towards smoking were taken the researchers introduced an unrelated question to provide a delay. Further research has demonstrated that delays allow mortality salience to emerge because thoughts of death become non-conscious. Finally, participants were asked questions regarding their intended future smoking behavior. However, one weakness in their conduction was that the final questionnaire addressed opinions and behavioral questions, as opposed to the participants level of persuasion regarding the different anti-smoking warning labels.

Social influences

Many people are more motivated by social pressures, rather than health risks. Specifically for younger people, mortality salience is stronger in eliciting changes of one's behavior when it brings awareness to the immediate loss of social status or position, rather than a loss, such as death that one can not imagine and feels far off. However, there are many different factors to take into consideration, such as how strongly an individual feels toward a decision, his or her level of self-esteem, and the situation around the individual. Particularly with people's smoking behaviors, self-esteem and mortality salience have different effects on individuals' decisions. In terms of the longevity of their smoking decisions, it has been seen that individuals' smoking habits are affected, in the short-term sense, when they are exposed to mortality salience that interrelates with their own self-esteem. Moreover, people who viewed social exclusion prompts were more likely to quit smoking in the long run than those who were simply shown health-effects of smoking. More specifically, it was demonstrated that when individuals had high levels of self-esteem they were more likely to quit smoking following the social pressure messages, rather than the health risk messages. In this specific instance, terror management, and specifically mortality salience is showing how people are more motivated by the social pressures and consequences in their environment, rather than consequences relating to their health. This is mostly seen in young adult smokers with higher smoking-based self-esteems who are not thinking of their future health and the less-immediate effects of smoking on their health.

Death thought accessibility

Another paradigm that TMT researchers use to get at unconscious concerns about death is what is known as the death thought accessibility (DTA) hypothesis. Essentially, the DTA hypothesis states that if individuals are motivated to avoid cognitions about death, and they avoid these cognitions by espousing a worldview or by buffering their self-esteem, then when threatened, an individual should possess more death-related cognitions (e.g., thoughts about death, and death-related stimuli) than they would when not threatened.he DTA hypothesis has its origins in work by Greenberg et al. (1994) as an extension of their earlier terror management hypotheses (i.e., the anxiety buffer hypothesis and the mortality salience hypothesis). The researchers reasoned that if, as indicated by Wegner's research on thought suppression (1994; 1997), thoughts that are purposely suppressed from conscious awareness are often brought back with ease, then following a delay death-thought cognitions should be more available to consciousness than (a) those who keep the death-thoughts in their consciousness the whole time, and (b) those who suppress the death-thoughts but are not provided a delay. That is precisely what they found. However, other psychologists have failed to replicate these findings.

In these initial studies (i.e., Greenberg et al. (2004); Arndt et al. (1997)), and in numerous subsequent DTA studies, the main measure of DTA is a word fragment task, whereby participants can complete word fragments in distinctly death-related ways (e.g., coff_ _ as coffin, not coffee) or in non death-related ways (e.g., sk_ _l as skill, not skull). If death-thoughts are indeed more available to consciousness, then it stands to reason that the word fragments should be completed in a way that is semantically related to death.

Importance of the Death Thought Accessibility hypothesis

The introduction of this hypothesis has refined TMT, and led to new avenues of research that formerly could not be assessed due to the lack of an empirically validated way of measuring death-related cognitions. Also, the differentiation between proximal (conscious, near, and threat-focused) and distal (unconscious, distant, symbolic) defenses that have been derived from DTA studies have been extremely important in understanding how people deal with their terror.

It is important to note how the DTA paradigm subtly alters, and expands, TMT as a motivational theory. Instead of solely manipulating mortality and witnessing its effects (e.g., nationalism, increased prejudice, risky sexual behavior, etc.), the DTA paradigm allows a measure of the death-related cognitions that result from various affronts to the self. Examples include threats to self-esteem and to one's worldview; the DTA paradigm can therefore assess the role of death-thoughts in self-esteem and worldview defenses. Furthermore, the DTA hypothesis lends support to TMT in that it corroborates its central hypothesis that death is uniquely problematic for human beings, and that it is fundamentally different in its effects than meaning threats (i.e., Heine et al., 2006) and that is death itself, and not uncertainty and lack of control associated with death; Fritsche et al. (2008) explore this idea.

Since its inception, the DTA hypothesis had been rapidly gaining ground in TMT investigations, and as of 2009, has been employed in over 60 published papers, with a total of more than 90 empirical studies.

Death anxiety on health promotion

How people respond to their fears and anxiety of death is investigated in TMT. Moreover, Taubman-Ben-Ari and Noy (2010) examine the idea that a person's level of self-awareness and self-consciousness should be considered in relation to their responses to their anxiety and death cognitions. The more an individual is presented with their death or death cognitions in general, the more fear and anxiety one may have; therefore, to combat said anxiety one may implement anxiety buffers.

Due to a change in people's lifestyles, in the direction of more unhealthy behaviors, the leading causes of death now, being cancer and heart disease, most definitely are related to individuals' unhealthy behaviors (though the statement is over-generalising and certainly cannot be applied to every case). Age and death anxiety both are factors that should be considered in the terror management theory, in relation to health-promoting behaviors. Age undoubtedly plays some kind of role in people's health-promoting behaviors; however, an actual age related effect on death anxiety and health-promoting behaviors has yet to be seen. Although research has demonstrated that for young adults only, when they were prompted with death related scenarios, they yielded more health-promoting behaviors, compared to those participants in their sixties. In addition, death anxiety has been found to have an effect for young adults, on their behaviors of health promotion.

Terror management health model

The terror management health model (TMHM) explores the role that death plays on one's health and behavior. Goldenberg and Arndt (2008) state that the TMHM proposes the idea that death, despite its threatening nature, is in fact instrumental and purposeful in the conditioning of one's behavior towards the direction of a longer life.

According to Goldenberg and Arndt (2008), certain health behaviors such as breast self-exams (BSEs) can consciously activate and facilitate people to think of death, especially their own death. While death can be instrumental for individuals, in some cases, when breast self-exams activate people's death thoughts an obstacle can present itself, in terms of health promotion, because of the experience of fear and threat. Abel and Kruger (2009) have suggested that the stress caused by increased awareness of mortality when celebrating one's birthday might explain the birthday effect, where mortality rates seem to spike around these days.

On the other hand, death and thoughts of death can serve as a way of empowering the self, not as threats. Researchers, Cooper et al. (2011) explored TMHM in terms of empowerment, specifically using BSEs under two conditions; when death thoughts were prompted, and when thoughts of death were non-conscious. According to TMHM, people's health decisions, when death thoughts are not conscious, should be based on their motivations to act appropriately, in terms of the self and identity. Cooper et al. (2011) found that when mortality and death thoughts were primed, women reported more empowerment feelings than those who were not prompted before performing a BSE.

Additionally, TMHM suggests that mortality awareness and self-esteem are important factors in individuals' decision making and behaviors relating to their health. TMHM explores how people will engage in behaviors, whether positive or negative, even with the heightened awareness of mortality, in the attempt to conform to society's expectations and improve their self-esteem. The TMHM is useful in understanding what motivates individuals regarding their health decisions and behaviors.

In terms of smoking behaviors and attitudes, the impact of warnings with death messages depends on:

1. The individuals' level of smoking-based self-esteem
2. The warnings' actual degree of death information

Emotion

People with low self-esteem, but not high self-esteem, have more negative emotions when reminded of death. This is believed to be because these individuals lack the very defenses that TMT argues protect people from mortality concerns (e.g., solid worldviews). In contrast, positive mood states are not impacted by death thoughts for people of low or high self-esteem.

Leadership

It has been suggested that culture provides meaning, organization, and a coherent world view that diminishes the psychological terror caused by the knowledge of eventual death. The terror management theory can help to explain why a leader's popularity can grow substantially during times of crisis. When a follower's mortality is made prominent they will tend to show a strong preference for iconic leaders. An example of this occurred when George W. Bush's approval rating jumped almost 50 percent following the September 11 attacks in the United States. As Forsyth (2009) posits, this tragedy made U.S. citizens aware of their mortality, and Bush provided an antidote to these existential concerns by promising to bring justice to the terrorist group responsible for the attacks.

Researchers Cohen et al. (2004), in their particular study on TMT, tested the preferences for different types of leaders, while reminding people of their mortality. Three different candidates were presented to participants. The three leaders were of three different types: task-oriented (emphasized setting goals, strategic planning, and structure), relationship-oriented (emphasized compassion, trust, and confidence in others), and charismatic. The participants were then placed in one of two conditions: mortality salient or control group. In the former condition the participants were asked to describe the emotions surrounding their own death, as well as the physical act of the death itself, whereas the control group were asked similar questions about an upcoming exam. The results of the study were that the charismatic leader was favored more, and the relationship-oriented leader was favored less, in the mortality-salient condition. Further research has shown that mortality salient individuals also prefer leaders who are members of the same group, as well as men rather than women (Hoyt et al. 2010). This has links to social role theory.

Religion

TMT posits that religion was created as a means for humans to cope with their own mortality. Supporting this, arguments in favor of life after death, and simply being religious, reduce the effects of mortality salience on worldview defense. Thoughts of death have also been found to increase religious beliefs. At an implicit, subconscious level, this is the case even for people who claim to be nonreligious.

Mental health

Some researchers have argued that death anxiety may play a central role in numerous mental health conditions. To test whether death anxiety causes a particular mental illness, TMT researchers use a mortality salience experiment, and examine whether reminding participants of death leads to increased prevalence of behaviors associated with that mental illness. Such studies have shown that reminders of death lead to increases in compulsive handwashing in obsessive-compulsive disorder, avoidance in spider phobias and social anxiety, and anxious behaviors in other disorders, including panic disorder and health anxiety, suggesting the role of death anxiety in these conditions according to TMT researchers.

Criticisms

Criticisms of terror management theory have been based on several lines of arguments:

• Suppression of fear and anxiety is implausible from an evolutionary point of view.
• The observed psychological responses to terrifying cues are better explained by coalitional psychology and theories of collective defense.
• The responses can be explained as fear of uncertainty and the unknown.
• The responses can be explained as search for meaning of life and mortality.
• The experimental results are difficult to replicate.

These arguments are discussed in the following sections.

Evolutionary argument

Anxiety and fear are psychological responses that have evolved because they help us avoid danger. A mechanism to suppress anxiety and fear, as postulated by TMT, is unlikely to have evolved because it would reduce the chances of survival. It is argued that TMT relies on misguided assumptions about evolved human nature originating from psychoanalytic theory. Proponents of TMT argue that it is not responses to immediate danger that are suppressed, but the thought that we are all mortal. However, critics argue that the observed responses are not only evoked by cues of essential mortality, but more generally by cues of danger or insecurity.

Coalitional psychology and collective defense as alternative explanations

TMT posits that people respond to cues about mortality by strengthening shared worldviews. Critics believe that such a worldview defense is better explained by coalitional psychology. People confronted with danger tend to build shared worldviews and a pro-normative orientation in order to garner social support and to build coalitions and alliances. Proponents of TMT argue that the coalitional psychology theory relies on limited evidence, is unable to explain the diversity of responses to mortality cues, and is unable to explain the symbolic and supernatural worldview defenses found in all cultures. The coalitional theory is supported, however, by a large statistical study finding that conservatism, traditionalism, and other responses represented by TMT theory are connected with collective danger, while individual danger has very different and often opposite effects. The observed connection with collective danger supports the coalitional theory, while it contradicts the TMT which explicitly deals with individual danger only. Similarly, another study has found that the response of system justification postulated by TMT theorists is increased by salience of terrorism, not by salience of individual mortality. Earlier experimental findings can be explained by the fact that individual danger and collective danger are seriously confounded. The findings that the observed responses are connected with collective danger rather than individual danger was predicted by regality theory. This finding is in agreement with authoritarianism theory, realistic group conflict theory, and Ronald Inglehart's theory of modernization, but not in agreement with terror management theory.

Prevalence of death

Since findings on mortality salience and worldview defense were first published, other researchers have claimed that the effects may have been obtained due to reasons other than death itself, such as anxiety, fear, or other aversive stimuli such as pain. The experimental manipulations in TMT research are likely to elicit a mixture of different types of negative emotions, including fear, anxiety, sadness, and anger.

Other studies have found effects similar to those that mortality salience results in – for example, thinking about difficult personal choices to be made, being made to respond to open-ended questions regarding uncertainty, thinking about being robbed, thinking about being socially isolated, and being told that one's life lacks meaning. While these cases exist, thoughts of death have since been compared to various aversive experimental controls, such as (but not limited to) thinking about: failure, writing a critical exam, public speaking with a considerable audience, being excluded, paralysis, dental pain, intense physical pain, etc.

With regards to the studies that found similar effects, TMT theorists have argued that in the previously mentioned studies where death was not the subject thought about, the subjects would quite easily be related to death in an individual's mind due to "linguistic or experiential connection with mortality" (p. 332). For example, being robbed invokes thoughts of violence and being unsafe in one's own home – many people have died trying to protect their property and family. A second possible explanation for these results involves the death-thought accessibility hypothesis: these threats somehow sabotage crucial anxiety-buffering aspects of an individual's worldview or self-esteem, which increases their death thought accessibility. For example, one study found increased death thought accessibility in response to thoughts of antagonistic relations with attachment figures. However, this makes it difficult or impossible to isolate the effect of mortality salience.

While many TMT theorists claim that affective responses to mortality salience are suppressed and pushed out of consciousness, later studies contradict this and show that affective responses are indeed observable.

Meaning maintenance model

The meaning maintenance model (MMM) was initially introduced as a comprehensive motivational theory that claimed to subsume TMT, with alternative explanations for TMT findings. Essentially, it posits that people automatically give meaning to things, and when those meanings are somehow disrupted, it causes anxiety. In response, people concentrate on "meaning maintenance to reestablish their sense of symbolic unity" and that such "meaning maintenance often involves the compensatory reaffirmation of alternative meaning structures". These meanings, among other things, should "provide a basis for prediction and control of our...environments, help [one] to cope with tragedy and trauma...and the symbolic cheating of death via adherence to the enduring values that these cultures provide".

While TMT regards the search for meaning as a defense mechanism, meaning management theory regards the quest for meaning as a primary motive because we are meaning-seeking and meaning-making creatures living in a world of meanings. When people are exposed to mortality salience, both TMT and meaning management theory would predict an increase in pro-culture and pro-esteem activities, but for very different reasons. The latter theory is replacing death denial by death acceptance.

TMT theorists argue that meaning management theory cannot describe why different sets of meaning are preferred by different people, and that different types of meaning have different psychological functions. TMT theorists argue that unless something is an important element of a person's anxiety-buffering worldview or self-esteem, it will not require broad meaning maintenance. TMT theorists believe that meaning management theory cannot accurately claim to be an alternative to TMT because it does not seem to be able to explain the current breadth of TMT evidence.

Offensive defensiveness

Some theorists have argued that it is not the idea of death and nonexistence that is unsettling to people, but the fact that uncertainty is involved. For example, these researchers posited that people defend themselves by altering their fear responses from uncertainty to an enthusiasm approach. Other researchers argue for distinguishing fear of death from fear of dying and, therein, posit that ultimately the fear of death has more to do with some other fear (e.g., fear of pain) or reflects uncertainty avoidance or fear of the unknown.

TMT theorists agree that uncertainty can be disconcerting in some cases and it may even result in defense responses, but note that they believe the inescapability of death and the possibility of its finality regarding one's existence is most unsettling. They also note that people actually seek out some types of uncertainty, and that being uncertain is not always very unpleasant. In contrast, there is substantial evidence that, all things being equal, uncertainty and the unknown represent fundamental fears and are only experienced as pleasant when there is sufficient contextual certainty. For example, a surprise involves uncertainty, but is only perceived as pleasant if there is sufficient certainty that the surprise will be pleasant.

Though TMT theorists acknowledge that many responses to mortality salience involve greater approaches (zealousness) towards important worldviews, they also note examples of mortality salience which resulted in the opposite, which offensive defensiveness cannot account for: when negative features of a group to which participants belong were made salient, people actively distanced themselves from that group under mortality salience.

Replication failure

In addition to the criticisms from alternative theoretical perspectives, a large-scale attempt by Many Labs 4 to replicate published findings failed to replicate the mortality salience effect on worldview defense under any condition. The test is a multi-lab replication of Study 1 of Greenberg et al. (1994). Psychologists in 21 labs across the U.S. re-executed the original experiment among a total of 2,200 participants. In response to the Many Labs 4 paper, Tom Pyszczynski (one of the founding psychologists of TMT), criticized the study for insufficient sample sizes, failure to follow the advice of researchers, and deviation from a preregistered protocol.

Popularity

Psychologist Yoel Inbar summarized the popularity of the theory:

I can not explain to people who were not around during this time - which I would say was roughly 2004 to 2008 - how much everything at the time was about terror management theory. You would go to SPSP and it seemed like half of the posters were about terror management theory. It was just everywhere. There is just an explosion of terror management theory stuff. And then it sort of receded. And now you barely see it. Which is also kind of weird. We were obsessed with this for a period of 3-5 years, then we moved on to other things.

Modal realism

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Modal_realism

Modal realism is the view propounded by philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on four tenets: possible worlds exist, possible worlds are not different in kind from the actual world, possible worlds are irreducible entities, and the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".

Extended modal realism is a form of modal realism that involves ontological commitments not just to possible worlds but also to impossible worlds. Objects are conceived as being spread out in the modal dimension, i.e. as having not just spatial and temporal parts but also modal parts. This contrasts with Lewis' modal realism according to which each object only inhabits one possible world.

Common arguments for modal realism refer to their theoretical usefulness for modal reasoning and to commonly accepted expressions in natural language that seem to imply ontological commitments to possible worlds. A common objection to modal realism is that it leads to an inflated ontology, which some think to run counter to Occam's razor. Critics of modal realism have also pointed out that it is counterintuitive to allow possible objects the same ontological status as actual objects. This line of thought has been further developed in the argument from morality by showing how an equal treatment of actual and non-actual persons would lead to highly implausible consequences for morality, culminating in the moral principle that every choice is equally permissible.

The term possible world

Main article: Possible world

The term goes back to Leibniz's theory of possible worlds, used to analyse necessity, possibility, and similar modal notions. In short: the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote. A proposition is necessary if it is true in all possible worlds, and possible if it is true in at least one.

Main tenets

At the heart of David Lewis's modal realism are six central doctrines about possible worlds:

1. Possible worlds exist – they are just as real as our world;
2. Possible worlds are the same sort of things as our world – they differ in content, not in kind;
3. Possible worlds cannot be reduced to something more basic – they are irreducible entities in their own right.
4. Actuality is indexical. When we distinguish our world from other possible worlds by claiming that it alone is actual, we mean only that it is our world.
5. Possible worlds are unified by the spatiotemporal interrelations of their parts; every world is spatiotemporally isolated from every other world.
6. Possible worlds are causally isolated from each other.

Details and alternatives

In philosophy possible worlds are usually regarded as real but abstract possibilities (i.e. platonism), or sometimes as a mere metaphor, abbreviation, or as mathematical devices, or a mere combination of propositions.

Lewis himself not only claimed to take modal realism seriously (although he did regret his choice of the expression modal realism), he also insisted that his claims should be taken literally:

By what right do we call possible worlds and their inhabitants disreputable entities, unfit for philosophical services unless they can beg redemption from philosophy of language? I know of no accusation against possibles that cannot be made with equal justice against sets. Yet few philosophical consciences scruple at set theory. Sets and possibles alike make for a crowded ontology. Sets and possibles alike raise questions we have no way to answer. [...] I propose to be equally undisturbed by these equally mysterious mysteries.

How many [possible worlds] are there? In what respects do they vary, and what is common to them all? Do they obey a nontrivial law of identity of indiscernibles? Here I am at a disadvantage compared to someone who pretends as a figure of speech to believe in possible worlds, but really does not. If worlds were creatures of my imagination, I could imagine them to be any way I liked, and I could tell you all you wished to hear simply by carrying on my imaginative creation. But as I believe that there really are other worlds, I am entitled to confess that there is much about them that I do not know, and that I do not know how to find out.

Extended modal realism

Main article: Extended modal realism

Extended modal realism, as developed by Takashi Yagisawa, differs from other versions of modal realism, such as David Lewis' views, in several important aspects. Possible worlds are conceived as points or indices of the modal dimension rather than as isolated space-time structures. Regular objects are extended not only in the spatial and the temporal dimensions but also in the modal dimension: some of their parts are modal parts, i.e. belong to non-actual worlds. The concept of modal parts is best explained in analogy to spatial and temporal parts. My hand is a spatial part of myself just as my childhood is a temporal part of myself, according to four-dimensionalism. These intuitions can be extended to the modal dimension by considering possible versions of myself which took different choices in life than I actually did. According to extended modal realism, these other selves are inhabitants of different possible worlds and are also parts of myself: modal parts.

Another difference to the Lewisian form of modal realism is that among non-actual worlds within the modal dimension are not just possible worlds but also impossible worlds. Yagisawa holds that while the notion of a world is simple, being a modal index, the notion of a possible world is composite: it is a world that is possible. Possibility can be understood in various ways: there is logical possibility, metaphysical possibility, physical possibility, etc. A world is possible if it doesn't violate the laws of the corresponding type of possibility. For example, a world is logically possible if it obeys the laws of logic or physically possible if it obeys the laws of nature. Worlds that don't obey these laws are impossible worlds. But impossible worlds and their inhabitants are just as real as possible or actual entities.

Arguments for modal realism

Reasons given by Lewis

Lewis backs modal realism for a variety of reasons. First, there doesn't seem to be a reason not to. Many abstract mathematical entities are held to exist simply because they are useful. For example, sets are useful, abstract mathematical constructs that were only conceived in the 19th century. Sets are now considered to be objects in their own right, and while this is a philosophically unintuitive idea, its usefulness in understanding the workings of mathematics makes belief in it worthwhile. The same should go for possible worlds. Since these constructs have helped us make sense of key philosophical concepts in epistemology, metaphysics, philosophy of mind, etc., their existence should be accepted on pragmatic grounds.

Lewis believes that the concept of alethic modality can be reduced to talk of real possible worlds. For example, to say "x is possible" is to say that there exists a possible world where x is true. To say "x is necessary" is to say that in all possible worlds x is true. The appeal to possible worlds provides a sort of economy with the least number of undefined primitives/axioms in our ontology.

Taking this latter point one step further, Lewis argues that modality cannot be made sense of without such a reduction. He maintains that we cannot determine that x is possible without a conception of what a real world where x holds would look like. In deciding whether it is possible for basketballs to be inside of atoms we do not simply make a linguistic determination of whether the proposition is grammatically coherent, we actually think about whether a real world would be able to sustain such a state of affairs. Thus we require a brand of modal realism if we are to use modality at all.

Argument from ways

Possible worlds are often regarded with suspicion, which is why their proponents have struggled to find arguments in their favor. An often-cited argument is called the argument from ways. It defines possible worlds as "ways how things could have been" and relies for its premises and inferences on assumptions from natural language, for example:

(1) Hillary Clinton could have won the 2016 US election.

(2) So there are other ways how things could have been.

(3) Possible worlds are ways how things could have been.

(4) So there are other possible worlds.

The central step of this argument happens at (2) where the plausible (1) is interpreted in a way that involves quantification over "ways". Many philosophers, following Willard Van Orman Quine, hold that quantification entails ontological commitments, in this case, a commitment to the existence of possible worlds. Quine himself restricted his method to scientific theories, but others have applied it also to natural language, for example, Amie L. Thomasson in her easy approach to ontology. The strength of the argument from ways depends on these assumptions and may be challenged by casting doubt on the quantifier-method of ontology or on the reliability of natural language as a guide to ontology.

Criticisms

A number of philosophers, including Lewis himself, have produced criticisms of (what some call) "extreme realism" about possible worlds.

Lewis's own critique

Lewis's own extended presentation of the theory (On the Plurality of Worlds, 1986) raises and then counters several lines of argument against it. That work introduces not only the theory, but its reception among philosophers. The many objections that continue to be published are typically variations on one or other of the lines that Lewis has already canvassed.

Here are some of the major categories of objection:

• Catastrophic counterintuitiveness. The theory does not accord with our deepest intuitions about reality. This is sometimes called "the incredulous stare", since it lacks argumentative content, and is merely an expression of the affront that the theory represents to "common sense" philosophical and pre-philosophical orthodoxy. Lewis is concerned to support the deliverances of common sense in general: "Common sense is a settled body of theory — unsystematic folk theory — which at any rate we do believe; and I presume that we are reasonable to believe it. (Most of it.)" (1986, p. 134). But most of it is not all of it (otherwise there would be no place for philosophy at all), and Lewis finds that reasonable argument and the weight of such considerations as theoretical efficiency compel us to accept modal realism. The alternatives, he argues at length, can themselves be shown to yield conclusions offensive to our modal intuitions.
• Inflated ontology. Some object that modal realism postulates vastly too many entities, compared with other theories. It is therefore, they argue, vulnerable to Occam's razor, according to which we should prefer, all things being equal, those theories that postulate the smallest number of entities. Lewis's reply is that all things are not equal, and in particular competing accounts of possible worlds themselves postulate more classes of entities, since there must be not only one real "concrete" world (the actual world), but many worlds of a different class altogether ("abstract" in some way or other).
• Too many worlds. This is perhaps a variant of the previous category, but it relies on appeals to mathematical propriety rather than Occamist principles. Some argue that Lewis's principles of "worldmaking" (means by which we might establish the existence of further worlds by recombination of parts of worlds we already think exist) are too permissive. So permissive are they, in fact, that the total number of worlds must exceed what is mathematically coherent. Lewis allows that there are difficulties and subtleties to address on this front (1986, pp. 89–90). Daniel Nolan ("Recombination unbound", Philosophical Studies, 1996, vol. 84, pp. 239–262) mounts a sustained argument against certain forms of the objection; but variations on it continue to appear.
• Island universes. On the version of his theory that Lewis strongly favours, each world is distinct from every other world by being spatially and temporally isolated from it. Some have objected that a world in which spatio-temporally isolated universes ("island universes") coexist is therefore not possible, by Lewis's theory (see for example Bigelow, John, and Pargetter, Robert, "Beyond the blank stare", Theoria, 1987, Vol. 53, pp. 97–114). Lewis's awareness of this difficulty discomforted him; but he could have replied that other means of distinguishing worlds may be available, or alternatively that sometimes there will inevitably be further surprising and counterintuitive consequences — beyond what we had thought we would be committed to at the start of our investigation. But this fact in itself is hardly surprising. Plantinga also wonders why we would think that possibility is grounded in some other multi-verse counterpart to me if we were to discover other universes. If not, then why think the same would apply to possible worlds as a whole?

Finally, some of these objections can be combined. For example, one can think that modal realism is unnecessary because multiverse theory can do all the modal work (e.g. many "worlds" interpretation of quantum mechanics).

A pervasive theme in Lewis's replies to the critics of modal realism is the use of tu quoque argument: your account would fail in just the same way that you claim mine would. A major heuristic virtue of Lewis's theory is that it is sufficiently definite for objections to gain some foothold; but these objections, once clearly articulated, can then be turned equally against other theories of the ontology and epistemology of possible worlds.

Stalnaker's response

Robert Stalnaker, while he finds some merit in Lewis's account of possible worlds, finds the position to be ultimately untenable. He himself advances a more "moderate" realism about possible worlds, which he terms actualism (since it holds that all that exists is in fact actual, and that there are no "merely possible" entities). In particular, Stalnaker does not accept Lewis's attempt to argue on the basis of a supposed analogy with the epistemological objection to mathematical Platonism that believing in possible worlds as Lewis imagines them is no less reasonable than believing in mathematical entities such as sets or functions.

Kripke's response

Saul Kripke described modal realism as "totally misguided", "wrong", and "objectionable". Kripke argued that possible worlds were not like distant countries out there to be discovered; rather, we stipulate what is true according to them. Kripke also criticized modal realism for its reliance on counterpart theory, which he regarded as untenable. Specifically, Kripke states that Lewis' modal realism implies that when we refer to possibilities regarding persons like you or me, we're not referring to you or me. Instead, we're referring to counterparts who are similar to us but not identical. This seems problematic because it seems like when, for example, we say that, 'Humphrey could have become President', we are talking about Humphrey (and we're not talking about a person that is like Humphrey). Lewis responds by saying this objection (i.e. The Humphrey Objection) wouldn't apply to modal realists who believe that the identity of persons can "overlap" in multiple worlds, even though Lewis thinks that view is problematic. Secondly, Lewis doesn't seem to share the intuition that there is any problem, as evidenced by the fact that he calls it an "alleged" intuition.

Argument from morality

The argument from morality, as initially formulated by Robert Merrihew Adams, criticizes modal realism on the grounds that modal realism has very implausible consequences for morality and should therefore be rejected. This can be seen by considering the principle of plenitude: the thesis that there is a possible world for every way things could be. The consequence of this principle is that the nature of the pluriverse, i.e. of reality in the widest sense, is fixed. This means that whatever choices human agents make, they have no impact on reality as a whole. For example, assume that during a stroll at a lake you spot a drowning child not far from the shore. You have a choice to save the child or not to. If you choose to save the child then a counterpart of you at another possible world chooses to let it drown. If you choose to let it drown then the counterpart of you at this other possible world chooses to save it. Either way, the result for these two possible worlds is the same: one child drowns and the other is saved. The only impact of your choice is to relocate a death from the actual world to another possible world. But since, according to modal realism, there is no important difference between the actual world and other possible worlds, this shouldn't matter. The consequence would be that there is no moral obligation to save the child, which is drastically at odds with common-sense morality. Worse still, this argument can be generalized to any decision, so whatever you choose in any decision would be morally permissible.

David Lewis defends moral realism against this argument by pointing out that morality, as commonly conceived, is only interested in the actual world, specifically, that the actual agent doesn't do evil. So the argument from morality would only be problematic for an odd version of utilitarianism aiming at maximizing the "sum total of good throughout the plurality of worlds". But, as Mark Heller points out, this reply doesn't explain why we are justified in morally privileging the actual world, as modal realism seems to be precisely against such a form of unequal treatment. This is not just a problem for utilitarians but for any moral theory that is sensitive to how other people are affected by one's actions in the widest sense, causally or otherwise: "the modal realist has to consider more people in moral decision making than we ordinarily do consider". Bob Fischer, speaking on Lewis' behalf, concedes that, from a modally unrestricted point of view of morality, there is no obligation to save the child from drowning. Common-sense morality, on the other hand, assumes a modally restricted point of view. This disagreement with common-sense is a cost of modal realism to be considered in an overall cost-benefit calculation, but it is no knockdown argument.