Begging the question

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In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: petitio principii) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. A question-begging inference is valid, in the sense that the conclusion is as true as the premise, but it is not a valid argument.

For example, the statement that "wool sweaters are superior to nylon jackets because wool sweaters have higher wool content" begs the question because this statement does not explain why higher wool content makes a garment superior. Begging the question is a type of circular reasoning, and often occurs in an indirect way such that the fallacy's presence is hidden, or at least not easily apparent.

The phrase "begs the question" is also commonly used to mean "prompts a question" or "raises a question".

History

Bust of Aristotle, whose Prior Analytics contained an early discussion of this fallacy

The original phrase used by Aristotle from which begging the question descends is: τὸ ἐξ ἀρχῆς (or sometimes ἐν ἀρχῇ) αἰτεῖν, "asking for the initial thing". Aristotle's intended meaning is closely tied to the type of dialectical argument he discusses in his Topics, book VIII: a formalized debate in which the defending party asserts a thesis that the attacking party must attempt to refute by asking yes-or-no questions and deducing some inconsistency between the responses and the original thesis.

In this stylized form of debate, the proposition that the answerer undertakes to defend is called "the initial thing" (τὸ ἐξ ἀρχῆς, τὸ ἐν ἀρχῇ) and one of the rules of the debate is that the questioner cannot simply ask for it (that would be trivial and uninteresting). Aristotle discusses this in Sophistical Refutations and in Prior Analytics book II, (64b, 34–65a 9, for circular reasoning see 57b, 18–59b, 1).

The stylized dialectical exchanges Aristotle discusses in the Topics included rules for scoring the debate, and one important issue was precisely the matter of asking for the initial thing—which included not just making the actual thesis adopted by the answerer into a question, but also making a question out of a sentence that was too close to that thesis (for example, PA II 16).

The term was translated into English from Latin in the 16th century. The Latin version, petitio principii, "asking for the starting point", can be interpreted in different ways. Petitio (from peto), in the post-classical context in which the phrase arose, means assuming or postulating, but in the older classical sense means petition, request or beseeching. Principii, genitive of principium, means beginning, basis or premise (of an argument). Literally petitio principii means "assuming the premise" or "assuming the original point".

The Latin phrase comes from the Greek τὸ ἐν ἀρχῇ αἰτεῖσθαι (tò en archêi aiteîsthai, "asking the original point") in Aristotle's Prior Analytics II xvi 64b28–65a26:

Begging or assuming the point at issue consists (to take the expression in its widest sense) [in] failing to demonstrate the required proposition. But there are several other ways in which this may happen; for example, if the argument has not taken syllogistic form at all, he may argue from premises which are less known or equally unknown, or he may establish the antecedent utilizing its consequents; for demonstration proceeds from what is more certain and is prior. Now begging the question is none of these. [...] If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue.... [B]egging the question is proving what is not self-evidently employing itself...either because identical predicates belong to the same subject, or because the same predicate belongs to identical subjects.

— Aristotle, Hugh Tredennick (trans.) Prior Analytics

Aristotle's distinction between apodictic science and other forms of nondemonstrative knowledge rests on an epistemology and metaphysics wherein appropriate first principles become apparent to the trained dialectician:

Aristotle's advice in S.E. 27 for resolving fallacies of Begging the Question is brief. If one realizes that one is being asked to concede the original point, one should refuse to do so, even if the point being asked is a reputable belief. On the other hand, if one fails to realize that one has conceded the point at issue and the questioner uses the concession to produce the apparent refutation, then one should turn the tables on the sophistical opponent by oneself pointing out the fallacy committed. In dialectical exchange, it is a worse mistake to be caught asking for the original point than to have inadvertently granted such a request. The answerer in such a position has failed to detect when different utterances mean the same thing. The questioner, if he did not realize he was asking the original point, has committed the same error. But if he has knowingly asked for the original point, then he reveals himself to be ontologically confused: he has mistaken what is non-self-explanatory (known through other things) to be something self-explanatory (known through itself). In pointing this out to the false reasoner, one is not just pointing out a tactical psychological misjudgment by the questioner. It is not simply that the questioner falsely thought that the original point is placed under the guise of a semantic equivalent, or a logical equivalent, or a covering universal, or divided up into exhaustive parts, would be more persuasive to the answerer. Rather, the questioner falsely thought that a non-self-explanatory fact about the world was an explanatory first principle. For Aristotle, that certain facts are self-explanatory while others are not is not a reflection solely of the cognitive abilities of humans. It is primarily a reflection of the structure of noncognitive reality. In short, a successful resolution of such a fallacy requires a firm grasp of the correct explanatory powers of things. Without a knowledge of which things are self-explanatory and which are not the reasoner is liable to find a question-begging argument persuasive.

— Scott Gregory Schreiber, Aristotle on False Reasoning: Language and the World in the Sophistical Refutations

Thomas Fowler believed that petitio principii would be more properly called petitio quæsiti, which is literally "begging the question".

Definition

To "beg the question" (also called petitio principii) is to attempt to support a claim with a premise that itself restates or presupposes the claim. It is an attempt to prove a proposition while simultaneously taking the proposition for granted.

When the fallacy involves only a single variable, it is sometimes called a hysteron proteron (Greek for "later earlier"), a rhetorical device, as in the statement:

Opium induces sleep because it has a soporific quality.

Reading this sentence, the only thing one can learn is a new word in a more classical style (soporific), for referring to a more common action (induces sleep), but it does not explain why it causes that effect. A sentence attempting to explain why opium induces sleep, or the same, why opium has soporific quality, would be the following one:

Opium induces sleep because it contains Morphine-6-glucuronide, which inhibits the brain's receptors for pain, causing a pleasurable sensation that eventually induces sleep.

A less obvious example from Fallacies and Pitfalls of Language: The Language Trap by S. Morris Engel:

Free trade will be good for this country. The reason is patently clear. Isn't it obvious that unrestricted commercial relations will bestow on all sections of this nation the benefits which result when there is an unimpeded flow of goods between countries?

This form of the fallacy may not be immediately obvious. Linguistic variations in syntax, sentence structure, and the literary device may conceal it, as may other factors involved in an argument's delivery. It may take the form of an unstated premise which is essential but not identical to the conclusion, or is "controversial or questionable for the same reasons that typically might lead someone to question the conclusion":

...[S]eldom is anyone going to simply place the conclusion word-for-word into the premises ... Rather, an arguer might use phraseology that conceals the fact that the conclusion is masquerading as a premise. The conclusion is rephrased to look different and is then placed in the premises.

— Paul Herrick

For example, one can obscure the fallacy by first making a statement in concrete terms, then attempting to pass off an identical statement, delivered in abstract terms, as evidence for the original. One could also "bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of Norman origin", as here:

To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments."

When the fallacy of begging the question is committed in more than one step, some authors dub it circulus in probando (reasoning in a circle) or, more commonly, circular reasoning.

Begging the question is not considered a formal fallacy (an argument that is defective because it uses an incorrect deductive step). Rather, it is a type of informal fallacy that is logically valid but unpersuasive, in that it fails to prove anything other than what is already assumed.

Related fallacies

Main articles: Circular reasoning, Complex question, and Ignoratio elenchi

Closely connected with begging the question is the fallacy of circular reasoning (circulus in probando), a fallacy in which the reasoner begins with the conclusion. The individual components of a circular argument can be logically valid because if the premises are true, the conclusion must be true, and does not lack relevance. However, circular reasoning is not persuasive because a listener who doubts the conclusion also doubts the premise that leads to it.

Begging the question is similar to the complex question (also known as trick question or fallacy of many questions): a question that, to be valid, requires the truth of another question that has not been established. For example, "Which color dress is Mary wearing?" may be fallacious because it presupposes that Mary is wearing a dress. Unless it has previously been established that her outfit is a dress, the question is fallacious because she could be wearing an outfit that was not a dress, such as pants and no dress.

Another related fallacy is ignoratio elenchi or irrelevant conclusion: an argument that fails to address the issue in question, but appears to do so. An example might be a situation where A and B are debating whether the law permits A to do something. If A attempts to support his position with an argument that the law ought to allow him to do the thing in question, then he is guilty of ignoratio elenchi.

Vernacular

In vernacular English, begging the question (or equivalent rephrasing thereof) often occurs in place of "raises the question", "invites the question", "suggests the question", "leaves unanswered the question" etc.. Such preface is then followed with the question, as in:

• "[...] personal letter delivery is at an all-time low... Which begs the question: are open letters the only kind the future will know?"
• "Hopewell's success begs the question: why aren't more companies doing the same?"
• "Spending the summer traveling around India is a great idea, but it does beg the question of how we can afford it."

Sometimes it is further confused with "dodging the question", an attempt to avoid it, or perhaps more often begging the question is simply used to mean leaving the question unanswered.

Colorless green ideas sleep furiously

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously

 

Approximate X-Bar representation of Colorless green ideas sleep furiously. See phrase structure rules.

Colorless green ideas sleep furiously was composed by Noam Chomsky in his 1957 book Syntactic Structures as an example of a sentence that is grammatically well-formed, but semantically nonsensical. The sentence was originally used in his 1955 thesis The Logical Structure of Linguistic Theory and in his 1956 paper "Three Models for the Description of Language". There is no obvious understandable meaning that can be derived from it, which demonstrates the distinction between syntax and semantics, and the idea that a syntactically well-formed sentence is not guaranteed to be semantically well-formed as well. As an example of a category mistake, it was used to show the inadequacy of certain probabilistic models of grammar, and the need for more structured models.

Senseless but grammatical

Chomsky wrote in his 1957 book Syntactic Structures:

1. Colorless green ideas sleep furiously.
2. *Furiously sleep ideas green colorless.^[a]

It is fair to assume that neither sentence (1) nor (2) (nor indeed any part of these sentences) had ever previously occurred in an English discourse. Hence, in any statistical model that accounts for grammaticality, these sentences will be ruled out on identical grounds as equally "remote" from English. Yet (1), though nonsensical, is grammatical, while (2) is not grammatical.

Approximate representation of "Colorless green ideas sleep furiously". See Minimalist Program.

Colorless green ideas – which functions as the subject of the sentence – is an anomalous string for at least two reasons:

• The adjective colorless can be understood as dull, uninteresting, or lacking in color, and so when it combines with the adjective green, this is nonsensical: an object cannot simultaneously lack color and have the color of green.
• In the phrase, colorless green ideas the abstract noun idea is described as being colorless and green. However, due to its abstract nature, an idea cannot have or lack color.

Sleep furiously – which functions as the predicate of the sentence – is structurally well-formed; in other words, it is grammatical. However the meaning that it expresses is peculiar, as the activity of sleeping is not generally taken to be something that can be done in a furious fashion. Nevertheless, sleep furiously is both grammatical and interpretable, though its interpretation is unusual.

Combining Colorless green ideas with sleep furiously creates a sentence that some believe to be nonsensical. On the one hand, an abstract noun like idea is taken to not have the ability to engage in an activity like sleeping. On the other hand, some think it possible for an idea to sleep.

Linguists account for the unusual nature of this sentence by distinguishing two types of selection: semantic selection (s-selection) and categorical selection (c-selection). Relative to s-selection, the sentence is semantically anomalous – senseless – for three reasons:

• The s-selection of the adjective colorless is violated because it can only describe objects that lack color.
• The s-selection of the adverb furiously is violated because it can only describe activity that is compatible with angry action, and such meanings are generally incompatible with the activity of sleeping.
• The s-selection of the verb sleep is violated because it can occur only with subjects that can engage in sleep.

However, relative to c-selection, the sentence is structurally well-formed:

• The c-selection of the adverb furiously is satisfied, as it combines with the verb sleep, satisfying the requirement that an adverb modifies a verb.
• The c-selection of the adjectives colorless and green are satisfied as they combine with noun idea, satisfying the requirement that an adjective modifies a noun.
• The c-selection of the intransitive verb sleep is satisfied as it combines with the subject colorless green ideas, satisfying the requirement that an intransitive verb combines with a subject.

This leads to the conclusion that although meaningless, the structural integrity of this sentence is high.

Attempts at meaningful interpretations

Polysemy

The mechanism of polysemy – where a word has multiple meanings – can be used to create an interpretation for an otherwise non-sensical sentence. For example, the adjectives green and colorless both have figurative meanings. Green has a wide range of figurative meanings, including "immature", "pertaining to environmental consciousness", "newly formed", and "naive". And colorless can be interpreted as "nondescript". Likewise the verb sleep can have the figurative meaning of "being in dormant state", and the adverb furiously can have the figurative meaning "to do an action violently or quickly".

• figurative meaning of colorless: nondescript
• figurative meanings of green: (i) immature; (ii) pertaining to environmental consciousness; (iii) newly formed; (iv) naive
• figurative meaning of sleep: be in a dormant mental state
• figurative meaning of furiously: to do an action quickly, vigorously, intensely, energetically or violently

When these figurative meanings are taken into account the sentence Colorless green ideas sleep furiously can have legitimate meaning, with less oblique semantics, and so is compatible with the following interpretations:

1. Colorless green ideas sleep furiously.= "Nondescript immature ideas have violent nightmares."
2. Colorless green ideas sleep furiously.= "Naive ideas which have not yet attained their full scope can cause a mind to race even while it attempts to rest"

In popular culture

Chomsky's "colorless green" inspired written works, which all try to create meaning from the semantically meaningless utterance through added context. In 1958, linguist and anthropologist Dell Hymes presented his work to show that nonsense words can develop into something meaningful when in the right sequence.

Hued ideas mock the brain,
Notions of color not yet color,
Of pure, touchless, branching pallor
Of invading, essential Green

— Dell Hymes, 1958

Russian-American linguist and literary theorist Roman Jakobson (1959) interpreted "colorless green" as a pale green, and "sleep furiously" as the wildness of "a state-like sleep, as that of inertness, torpidity, numbness." Jakobson gave the example that if "[someone's] hatred never slept, why then, cannot someone's ideas fall into sleep?" John Hollander, an American poet and literary critic, argued that the sentence operates in a vacuum as it is without context. He went on to write a poem based on that idea, entitled Coiled Alizarine that was included in his book, The Night Mirror (1971).

Curiously deep, the slumber of crimson thoughts:
While breathless, in stodgy viridian
Colorless green ideas sleep furiously.

— John Hollander, 1971

Years later, Hollander contacted Chomsky about whether the color choice of 'green' was intentional, however Chomsky denied any intentions or influences, especially the hypothesized influence from Andrew Marvell's lines from "The Garden" (1681).

"Annihilating all that's made / To a green thought in a green shade"

One of the first writers to have attempted to provide the sentence meaning through context is Chinese linguist Yuen Ren Chao (1997). Chao's poem, entitled Making Sense Out of Nonsense: The Story of My Friend Whose "Colorless Green Ideas Sleep Furiously" (after Noam Chomsky) was published in 1971. This poem attempts to explain what "colorless green ideas" are and how they are able to "sleep furiously". Chao interprets "colorless" as plain, "green" as unripened, and "sleep furiously" as putting the ideas to rest; sleeping on them overnight whilst having internal conflict with these ideas.

I have a friend who is always full of ideas, good ideas and bad ideas, fine ideas and crude ideas, old ideas and new ideas. Before putting his new ideas into practice, he usually sleeps over them to let them mature and ripen. However, when he is in a hurry, he sometimes puts his ideas into practice before they are quite ripe, in other words, while they are still green. Some of his green ideas are quite lively and colorful, but not always, some being quite plain and colorless. When he remembers that some of his colorless ideas are still too green to use, he will sleep over them, or let them sleep, as he puts it. But some of those ideas may be mutually conflicting and contradictory and when they sleep together in the same night they get into furious fights and turn the sleep into a nightmare. Thus my friend often complains that his colorless green ideas sleep furiously.

British linguist Angus McIntosh was unable to accept that Chomsky's utterance was entirely meaningless because to him, "colorless green ideas may well sleep furiously". As if to prove that the sentences are in fact meaningful, McIntosh wrote two poems influenced by Chomsky's utterance, one of which was entitled Nightmare I.

Tortured my mind's eye at its small peephole
sees through the virid glass
the endless ghostly oscillographic stream
Furiously sleep ideas green colorless
Madly awake am I at my small window

— Angus McIntosh, 1961

Stanford 1985 competition

In 1985, a literary competition was held at Stanford University in which the contestants were invited to make Chomsky's sentence meaningful using not more than 100 words of prose or 14 lines of verse. An example entry from the competition, by C. M. Street, is:

It can only be the thought of verdure to come, which prompts us in the autumn to buy these dormant white lumps of vegetable matter covered by a brown papery skin, and lovingly to plant them and care for them. It is a marvel to me that under this cover they are labouring unseen at such a rate within to give us the sudden awesome beauty of spring flowering bulbs. While winter reigns the earth reposes but these colourless green ideas sleep furiously.

Experimental usage

Research has been done by implementing this into conversations on text. Research led by Bruno Galantucci at Yeshiva University has implemented the meaningless sentence into real conversations to test reactions. They ran 30 conversations with 1 male and 1 female slipping "colorless green ideas sleep furiously" eight minutes into the conversation during silence. After the conversation, the experimenters did a post-conversation questionnaire, mainly asking if they thought the conversation was unusual. Galantucci concluded that there was a trend of insensitivity to conversational coherence.

There are two general theories that were garnered from this experiment. The first theory is that people tend to ignore the inconsistency of speech to protect the quality of the conversation. In particular, face-to-face conversation has a 33.33% lower detection rate of nonsensical sentences than online messaging. The authors further explain how humans often disregard some contents of every conversation. The second theory the authors deduced is that effective communication may be subconsciously undermined when dealing with conversational coherence. These conclusions support the idea that phatic communication plays a key role in social life.

Statistical challenges

Since the 1950s, the field has used techniques more in line with Chomsky's approach. However, this all changed in the mid-1980s, when researchers started to experiment with statistical models, convincing over 90% of the researchers in the field to switch to statistical approaches.

In 2000, Fernando Pereira of the University of Pennsylvania fitted a simple statistical Markov model to a body of newspaper text, and showed that under this model, Furiously sleep ideas green colorless is about 200,000 times less probable than Colorless green ideas sleep furiously.

This statistical model defines a similarity metric, whereby sentences which are more like those within a corpus in certain respects are assigned higher values than sentences less alike. Pereira's model assigns an ungrammatical version of the same sentence a lower probability than the syntactically well-formed structure demonstrating that statistical models can identify variations in grammaticality with minimal linguistic assumptions. However, it is not clear that the model assigns every ungrammatical sentence a lower probability than every grammatical sentence. That is, colorless green ideas sleep furiously may still be statistically more "remote" from English than some ungrammatical sentences. To this, it may be argued that no current theory of grammar is capable of distinguishing all grammatical English sentences from ungrammatical ones.

Related and similar examples

In other languages

The French syntactician Lucien Tesnière came up with the French language sentence "Le silence vertébral indispose la voile licite" ("The vertebral silence indisposes the licit sail").

In Russian schools of linguistics, the glokaya kuzdra example has similar characteristics.

In games

The game of exquisite corpse is a method for generating nonsense sentences. It was named after the first sentence generated in the game in 1925: Le cadavre exquis boira le vin nouveau (the exquisite corpse will drink the new wine).

In the popular game of "Mad Libs", a chosen player asks each other player to provide parts of speech without providing any contextual information (e.g., "Give me a proper noun", or "Give me an adjective"), and these words are inserted into pre-composed sentences with a correct grammatical structure, but in which certain words have been omitted. The humor of the game is in the generation of sentences which are grammatical but which are meaningless or have absurd or ambiguous meanings (such as 'loud sharks'). The game also tends to generate humorous double entendres.

In philosophy

There are likely earlier examples of such sentences, possibly from the philosophy of language literature, but not necessarily uncontroversial ones, given that the focus has been mostly on borderline cases. For example, followers of logical positivism hold that "metaphysical" (i.e. not empirically verifiable) statements are simply meaningless; e.g. Rudolf Carnap wrote an article where he argued that almost every sentence from Heidegger was grammatically well-formed, yet meaningless.

The philosopher Bertrand Russell used the sentence "Quadruplicity drinks procrastination" in his "An Inquiry into Meaning and Truth" from 1940, to make a similar point; W.V. Quine took issue with him on the grounds that for a sentence to be false is nothing more than for it not to be true; and since quadruplicity doesn't drink anything, the sentence is simply false, not meaningless.

Other arguably "meaningless" utterances are ones that make sense, are grammatical, but have no reference to the present state of the world, such as Russell's "The present King of France is bald" (France does not presently have a king) from "On Denoting" (also see definite description).

In literature and entertainment

Another approach is to create a syntactically-well-formed, easily parsable sentence using nonsense words; a famous such example is "The gostak distims the doshes". Lewis Carroll's Jabberwocky is also famous for using this technique, although in this case for literary purposes; similar sentences used in neuroscience experiments are called Jabberwocky sentences.

In a sketch about linguistics, British comedy duo Fry and Laurie used the nonsensical sentence "Hold the newsreader's nose squarely, waiter, or friendly milk will countermand my trousers."

The Star Trek: The Next Generation episode "Darmok" features a race that communicates entirely by referencing folklore and stories. While the vessel's universal translator correctly translates the characters and places from these stories, it fails to decipher the intended meaning, leaving Captain Picard unable to understand the alien.

Labor theory of value

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https://en.wikipedia.org/wiki/Labor_theory_of_value 

The labor theory of value (LTV) is a theory of value that argues that the economic value of a good or service is determined by the total amount of "socially necessary labor" required to produce it.

The LTV is usually associated with Marxian economics, although it originally appeared in the theories of earlier classical economists such as Adam Smith and David Ricardo, and later in anarchist economics. Smith saw the price of a commodity in terms of the labor that the purchaser must expend to buy it, which embodies the concept of how much labor a commodity, a tool for example, can save the purchaser. The LTV is central to Marxist theory, which holds that the working class is exploited under capitalism, and dissociates price and value. However, Marx did not refer to his own theory of value as a "labour theory of value".

Orthodox neoclassical economics rejects the LTV, using a theory of value based on subjective preferences.

The revival in interpretation of Marx known as the Neue Marx-Lektüre also rejects Marxian economics and the LTV, calling them "substantialist". This reading claims that the LTV is a misinterpretation of the concept of fetishism in relation to value, and that this understanding never appears in Marx's work. The school heavily emphasizes works such as Capital as explicitly being a critique of political economy, instead of a "more correct" theory.

Definitions of value and labor

When speaking in terms of a labor theory of value, "value", without any qualifying adjective should theoretically refer to the amount of labor necessary to produce a marketable commodity, including the labor necessary to develop any real capital used in the production. Both David Ricardo and Karl Marx tried to quantify and embody all labor components in order to develop a theory of the real price, or natural price of a commodity. The labor theory of value as presented by Adam Smith did not require the quantification of past labor, nor did it deal with the labor needed to create the tools (capital) that might be used in producing a commodity. Smith's theory of value was very similar to the later utility theories in that Smith proclaimed that a commodity was worth whatever labor it would command in others (value in trade) or whatever labor it would "save" the self (value in use), or both. However, this "value" is subject to supply and demand at a particular time:

The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it. What every thing is really worth to the man who has acquired it, and who wants to dispose of it or exchange it for something else, is the toil and trouble which it can save to himself, and which it can impose upon other people. (Wealth of Nations Book 1, chapter V)

Smith's theory of price has nothing to do with the past labor spent in producing a commodity. It speaks only of the labor that can be "commanded" or "saved" at present. If there is no use for a buggy whip, then the item is economically worthless in trade or in use, regardless of all the labor spent in creating it.

Distinctions of economically pertinent labor

Value "in use" is the usefulness of this commodity, its utility. A classical paradox often comes up when considering this type of value. In the words of Adam Smith:

The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called "value in use"; the other, "value in exchange." The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it (Wealth of Nations Book 1, chapter IV).

Value "in exchange" is the relative proportion with which this commodity exchanges for another commodity (in other words, its price in the case of money). It is relative to labor as explained by Adam Smith:

The value of any commodity, [...] to the person who possesses it, and who means not to use or consume it himself, but to exchange it for other commodities, is equal to the quantity of labour which it enables him to purchase or command. Labour, therefore, is the real measure of the exchangeable value of all commodities (Wealth of Nations Book 1, chapter V).

Value (without qualification) is the labor embodied in a commodity under a given structure of production. Marx defined the value of the commodity by this third definition. In his terms, value is the 'socially necessary abstract labor' embodied in a commodity. To David Ricardo and other classical economists, this definition serves as a measure of "real cost", "absolute value", or a "measure of value" invariable under changes in distribution and technology.

Ricardo, other classical economists and Marx began their expositions with the assumption that value in exchange was equal to or proportional to this labor value. They thought this was a good assumption from which to explore the dynamics of development in capitalist societies. Other supporters of the labor theory of value used the word "value" in the second sense to represent "exchange value".

Labor process

Since the term "value" is understood in the LTV as denoting something created by labor, and its "magnitude" as something proportional to the quantity of labor performed, it is important to explain how the labor process both preserves value and adds new value in the commodities it creates.

The value of a commodity increases in proportion to the duration and intensity of labor performed on average for its production. Part of what the LTV means by "socially necessary" is that the value only increases in proportion to this labor as it is performed with average skill and average productivity. So though workers may labor with greater skill or more productivity than others, these more skillful and more productive workers thus produce more value through the production of greater quantities of the finished commodity. Each unit still bears the same value as all the others of the same class of commodity. By working sloppily, unskilled workers may drag down the average skill of labor, thus increasing the average labor time necessary for the production of each unit commodity. But these unskillful workers cannot hope to sell the result of their labor process at a higher price (as opposed to value) simply because they have spent more time than other workers producing the same kind of commodities.

However, production not only involves labor, but also certain means of labor: tools, materials, power plants and so on. These means of labor—also known as means of production—are often the product of another labor process as well. So the labor process inevitably involves these means of production that already enter the process with a certain amount of value. Labor also requires other means of production that are not produced with labor and therefore bear no value: such as sunlight, air, uncultivated land, unextracted minerals, etc. While useful, even crucial to the production process, these bring no value to that process. In terms of means of production resulting from another labor process, LTV treats the magnitude of value of these produced means of production as constant throughout the labor process. Due to the constancy of their value, these means of production are referred to, in this light, as constant capital.

Consider for example workers who take coffee beans, use a roaster to roast them, and then use a brewer to brew and dispense a fresh cup of coffee. In performing this labor, these workers add value to the coffee beans and water that comprise the material ingredients of a cup of coffee. The worker also transfers the value of constant capital—the value of the beans; some specific depreciated value of the roaster and the brewer; and the value of the cup—to the value of the final cup of coffee. Again, on average, the worker can transfer no more than the value of these means of labor previously possessed to the finished cup of coffee. So the value of coffee produced in a day equals the sum of both the value of the means of labor—this constant capital—and the value newly added by the worker in proportion to the duration and intensity of their work.

Often this is expressed mathematically as:

${\displaystyle c+L=W}$,

where

• ${\displaystyle c}$ is the constant capital of materials used in a period plus the depreciated portion of tools and plant used in the process. (A period is typically a day, week, year, or a single turnover: meaning the time required to complete one batch of coffee, for example.)
• ${\displaystyle L}$ is the quantity of labor time (average skill and productivity) performed in producing the finished commodities during the period
• ${\displaystyle W}$ is the value (or think "worth") of the product of the period (${\displaystyle w}$ comes from the German word for value: wert)

Note: if the product resulting from the labor process is homogeneous (all similar in quality and traits, for example, all cups of coffee) then the value of the period's product can be divided by the total number of items (use-values or ${\displaystyle v_u}$) produced to derive the unit value of each item. ${\displaystyle \begin{array}{c}{w}_i=\frac{W}{\sum v_u}\end{array}}$ where ${\displaystyle \begin{array}{c}\sum v_u\end{array}}$ is the total items produced.

The LTV further divides the value added during the period of production, ${\displaystyle L}$, into two parts. The first part is the portion of the process when the workers add value equivalent to the wages they are paid. For example, if the period in question is one week and these workers collectively are paid $1,000, then the time necessary to add $1,000 to—while preserving the value of—constant capital is considered the necessary labor portion of the period (or week): denoted ${\displaystyle NL}$. The remaining period is considered the surplus labor portion of the week: or ${\displaystyle SL}$. The value used to purchase labor-power, for example, the $1,000 paid in wages to these workers for the week, is called variable capital (${\displaystyle v}$). This is because in contrast to the constant capital expended on means of production, variable capital can add value in the labor process. The amount it adds depends on the duration, intensity, productivity and skill of the labor-power purchased: in this sense, the buyer of labor-power has purchased a commodity of variable use. Finally, the value added during the portion of the period when surplus labor is performed is called surplus value (${\displaystyle s}$). From the variables defined above, we find two other common expressions for the value produced during a given period:

${\displaystyle c+v+s=W}$

and

${\displaystyle c+NL+SL=W}$

The first form of the equation expresses the value resulting from production, focusing on the costs ${\displaystyle c+v}$ and the surplus value appropriated in the process of production, ${\displaystyle s}$. The second form of the equation focuses on the value of production in terms of the values added by the labor performed during the process ${\displaystyle NL+SL}$.

Relation between values and prices

One issue facing the LTV is the relationship between value quantities on one hand and prices on the other. If a commodity's value is not the same as its price, and therefore the magnitudes of each likely differ, then what is the relation between the two, if any? Various LTV schools of thought provide different answers to this question. For example, some argue that value in the sense of the amount of labor embodied in a good acts as a center of gravity for price.

However, most economists would say that cases where pricing is given as approximately equal to the value of the labour embodied, are in fact only special cases. In General Theory pricing most usually fluctuates. The standard formulation is that prices normally include a level of income for "capital" and "land". These incomes are known as "profit" and "rent" respectively. Yet Marx made the point that value cannot be placed upon labour as a commodity, because capital is a constant, whereas profit is a variable, not an income; thus explaining the importance of profit in relation to pricing variables.

In Book 1, chapter VI, Adam Smith writes:

The real value of all the different component parts of price, it must be observed, is measured by the quantity of labour which they can, each of them, purchase or command. Labour measures the value not only of that part of price which resolves itself into labour, but of that which resolves itself into rent, and of that which resolves itself into profit.

The final sentence explains how Smith sees value of a product as relative to labor of buyer or consumer, as opposite to Marx who sees the value of a product being proportional to labor of laborer or producer. And we value things, price them, based on how much labor we can avoid or command, and we can command labor not only in a simple way but also by trading things for a profit.

The demonstration of the relation between commodities' unit values and their respective prices is known in Marxian terminology as the transformation problem or the transformation of values into prices of production. The transformation problem has probably generated the greatest bulk of debate about the LTV. The problem with transformation is to find an algorithm where the magnitude of value added by labor, in proportion to its duration and intensity, is sufficiently accounted for after this value is distributed through prices that reflect an equal rate of return on capital advanced. If there is an additional magnitude of value or a loss of value after transformation, then the relation between values (proportional to labor) and prices (proportional to total capital advanced) is incomplete. Various solutions and impossibility theorems have been offered for the transformation, but the debate has not reached any clear resolution.

LTV does not deny the role of supply and demand influencing price, since the price of a commodity is something other than its value. In Value, Price and Profit (1865), Karl Marx quotes Adam Smith and sums up:

It suffices to say that if supply and demand equilibrate each other, the market prices of commodities will correspond with their natural prices, that is to say, with their values as determined by the respective quantities of labor required for their production.

The LTV seeks to explain the level of this equilibrium. This could be explained by a cost of production argument—pointing out that all costs are ultimately labor costs, but this does not account for profit, and it is vulnerable to the charge of tautology in that it explains prices by prices. Marx later called this "Smith's adding up theory of value".

Smith argues that labor values are the natural measure of exchange for direct producers like hunters and fishermen. Marx, on the other hand, uses a measurement analogy, arguing that for commodities to be comparable they must have a common element or substance by which to measure them, and that labor is a common substance of what Marx eventually calls commodity-values.

History

Origins

The labor theory of value has developed over many centuries. It had no single originator, but rather many different thinkers arrived at the same conclusion independently. Aristotle is claimed to hold to this view. Some writers trace its origin to Thomas Aquinas. In his Summa Theologiae (1265–1274) he expresses the view that "value can, does and should increase in relation to the amount of labor which has been expended in the improvement of commodities." Scholars such as Joseph Schumpeter have cited Ibn Khaldun, who in his Muqaddimah (1377), described labor as the source of value, necessary for all earnings and capital accumulation. He argued that even if earning "results from something other than a craft, the value of the resulting profit and acquired (capital) must (also) include the value of the labor by which it was obtained. Without labor, it would not have been acquired." Scholars have also pointed to Sir William Petty's Treatise of Taxes of 1662 and to John Locke's labor theory of property, set out in the Second Treatise on Government (1689), which sees labor as the ultimate source of economic value. Karl Marx himself credited Benjamin Franklin in his 1729 essay entitled "A Modest Enquiry into the Nature and Necessity of a Paper Currency" as being "one of the first" to advance the theory.

Adam Smith accepted the theory for pre-capitalist societies but saw a flaw in its application to contemporary capitalism. He pointed out that if the "labor embodied" in a product equaled the "labor commanded" (i.e. the amount of labor that could be purchased by selling it), then profit was impossible. David Ricardo (seconded by Marx) responded to this paradox by arguing that Smith had confused labor with wages. "Labor commanded", he argued, would always be more than the labor needed to sustain itself (wages). The value of labor, in this view, covered not just the value of wages (what Marx called the value of labor power), but the value of the entire product created by labor.

Ricardo's theory was a predecessor of the modern theory that equilibrium prices are determined solely by production costs associated with Neo-Ricardianism.

Based on the discrepancy between the wages of labor and the value of the product, the "Ricardian socialists"—Charles Hall, Thomas Hodgskin, John Gray, and John Francis Bray, and Percy Ravenstone—applied Ricardo's theory to develop theories of exploitation.

Marx expanded on these ideas, arguing that workers work for a part of each day adding the value required to cover their wages, while the remainder of their labor is performed for the enrichment of the capitalist. The LTV and the accompanying theory of exploitation became central to his economic thought.

19th century American individualist anarchists based their economics on the LTV, with their particular interpretation of it being called "Cost the limit of price". They, as well as contemporary individualist anarchists in that tradition, hold that it is unethical to charge a higher price for a commodity than the amount of labor required to produce it. Hence, they propose that trade should be facilitated by using notes backed by labor.

Adam Smith and David Ricardo

Adam Smith held that, in a primitive society, the amount of labor put into producing a good determined its exchange value, with exchange value meaning, in this case, the amount of labor a good can purchase. However, according to Smith, in a more advanced society the market price is no longer proportional to labor cost since the value of the good now includes compensation for the owner of the means of production: "The whole produce of labour does not always belong to the labourer. He must in most cases share it with the owner of the stock which employs him." According to Whitaker, Smith is claiming that the 'real value' of such a commodity produced in advanced society is measured by the labor which that commodity will command in exchange but "[Smith] disowns what is naturally thought of as the genuine classical labor theory of value, that labor-cost regulates market-value. This theory was Ricardo's, and really his alone."

Classical economist David Ricardo's labor theory of value holds that the value of a good (how much of another good or service it exchanges for in the market) is proportional to how much labor was required to produce it, including the labor required to produce the raw materials and machinery used in the process. David Ricardo stated it as, "The value of a commodity, or the quantity of any other commodity for which it will exchange, depends on the relative quantity of labour which is necessary for its production, and not on the greater or less compensation which is paid for that labour." In this connection Ricardo seeks to differentiate the quantity of labour necessary to produce a commodity from the wages paid to the laborers for its production. Therefore, wages did not always increase with the price of a commodity. However, Ricardo was troubled with some deviations in prices from proportionality with the labor required to produce them. For example, he said "I cannot get over the difficulty of the wine, which is kept in the cellar for three or four years [i.e., while constantly increasing in exchange value], or that of the oak tree, which perhaps originally had not 2 s. expended on it in the way of labour, and yet comes to be worth £100." (Quoted in Whitaker) Of course, a capitalist economy stabilizes this discrepancy until the value added to aged wine is equal to the cost of storage. If anyone can hold onto a bottle for four years and become rich, that would make it hard to find freshly corked wine. There is also the theory that adding to the price of a luxury product increases its exchange-value by mere prestige.

The labor theory as an explanation for value contrasts with the subjective theory of value, which says that value of a good is not determined by how much labor was put into it but by its usefulness in satisfying a want and its scarcity. Ricardo's labor theory of value is not a normative theory, as are some later forms of the labor theory, such as claims that it is immoral for an individual to be paid less for his labor than the total revenue that comes from the sales of all the goods he produces.

It is arguable to what extent these classical theorists held the labor theory of value as it is commonly defined. For instance, David Ricardo theorized that prices are determined by the amount of labor but found exceptions for which the labor theory could not account. In a letter, he wrote: "I am not satisfied with the explanation I have given of the principles which regulate value." Adam Smith theorized that the labor theory of value holds true only in the "early and rude state of society" but not in a modern economy where owners of capital are compensated by profit. As a result, "Smith ends up making little use of a labor theory of value."

Anarchism

See also: Anarchist economics and Cost the limit of price

 

Sample labor for labor note for the Cincinnati Time Store. Scanned from Equitable Commerce (1846) by Josiah Warren

Pierre Joseph Proudhon's mutualism and American individualist anarchists such as Josiah Warren, Lysander Spooner and Benjamin Tucker adopted the labor theory of value of classical economics and used it to criticize capitalism while favoring a non-capitalist market system.

Warren is widely regarded as the first American anarchist, and the four-page weekly paper he edited during 1833, The Peaceful Revolutionist, was the first anarchist periodical published. Cost the limit of price was a maxim coined by Warren, indicating a (prescriptive) version of the labor theory of value. Warren maintained that the just compensation for labor (or for its product) could only be an equivalent amount of labor (or a product embodying an equivalent amount). Thus, profit, rent, and interest were considered unjust economic arrangements. In keeping with the tradition of Adam Smith's The Wealth of Nations, the "cost" of labor is considered to be the subjective cost; i.e., the amount of suffering involved in it. He put his theories to the test by establishing an experimental "labor for labor store" called the Cincinnati Time Store at the corner of 5th and Elm Streets in what is now downtown Cincinnati, where trade was facilitated by notes backed by a promise to perform labor. "All the goods offered for sale in Warren's store were offered at the same price the merchant himself had paid for them, plus a small surcharge, in the neighborhood of 4 to 7 percent, to cover store overhead." The store stayed open for three years; after it closed, Warren could pursue establishing colonies based on Mutualism. These included "Utopia" and "Modern Times". Warren said that Stephen Pearl Andrews' The Science of Society, published in 1852, was the most lucid and complete exposition of Warren's own theories.

Mutualism is an economic theory and anarchist school of thought that advocates a society where each person might possess a means of production, either individually or collectively, with trade representing equivalent amounts of labor in the free market. Integral to the scheme was the establishment of a mutual-credit bank that would lend to producers at a minimal interest rate, just high enough to cover administration. Mutualism is based on a labor theory of value that holds that when labor or its product is sold, in exchange, it ought to receive goods or services embodying "the amount of labor necessary to produce an article of exactly similar and equal utility". Mutualism originated from the writings of philosopher Pierre-Joseph Proudhon.

Collectivist anarchism as defended by Mikhail Bakunin defended a form of labor theory of value when it advocated a system where "all necessaries for production are owned in common by the labour groups and the free communes ... based on the distribution of goods according to the labour contributed".

Karl Marx

Contrary to popular belief Marx never used the term "Labor theory of value" in any of his works but used the term Law of value, Marx opposed "ascribing a supernatural creative power to labor", arguing as such:

Labor is not the source of all wealth. Nature is just as much a source of use values (and it is surely of such that material wealth consists!) as labor, which is itself only the manifestation of a force of nature, human labor power.

Here, Marx was distinguishing between exchange value (the subject of the LTV) and use value. Marx used the concept of "socially necessary labor time" to introduce a social perspective distinct from his predecessors and neoclassical economics. Whereas most economists start with the individual's perspective, Marx started with the perspective of society as a whole. "Social production" involves a complicated and interconnected division of labor of a wide variety of people who depend on each other for their survival and prosperity. "Abstract" labor refers to a characteristic of commodity-producing labor that is shared by all different kinds of heterogeneous (concrete) types of labor. That is, the concept abstracts from the particular characteristics of all of the labor and is akin to average labor.

"Socially necessary" labor refers to the quantity required to produce a commodity "in a given state of society, under certain social average conditions or production, with a given social average intensity, and average skill of the labor employed." That is, the value of a product is determined more by societal standards than by individual conditions. This explains why technological breakthroughs lower the price of commodities and put less advanced producers out of business. Finally, it is not labor per se that creates value, but labor power sold by free wage workers to capitalists. Another distinction is between productive and unproductive labor. Only wage workers of productive sectors of the economy produce value. According to Marx an increase in productiveness of the laborer does not affect the value of a commodity, but rather, increases the surplus value realized by the capitalist. Therefore, decreasing the cost of production does not decrease the value of a commodity, but allows the capitalist to produce more and increases the opportunity to earn a greater profit or surplus value, as long as there is demand for the additional units of production.

Criticism

Main article: Criticisms of the labour theory of value

The Marxist labor theory of value has been criticised on several counts. Some argue that it predicts that profits will be higher in labor-intensive industries than in capital-intensive industries, which would be contradicted by measured empirical data inherent in quantitative analysis. This is sometimes referred to as the "Great Contradiction". In volume 3 of Capital, Marx explains why profits are not distributed according to which industries are the most labor-intensive and why this is consistent with his theory. Whether or not this is consistent with the labor theory of value as presented in volume 1 has been a topic of debate. According to Marx, surplus value is extracted by the capitalist class as a whole and then distributed according to the amount of total capital, not just the variable component. In the example given earlier, of making a cup of coffee, the constant capital involved in production is the coffee beans themselves, and the variable capital is the value added by the coffee maker. The value added by the coffee maker is dependent on its technological capabilities, and the coffee maker can only add so much total value to cups of coffee over its lifespan. The amount of value added to the product is thus the amortization of the value of the coffeemaker. We can also note that not all products have equal proportions of value added by amortized capital. Capital intensive industries such as finance may have a large contribution of capital, while labor-intensive industries like traditional agriculture would have a relatively small one. Critics argue that this turns the LTV into a macroeconomic theory, when it was supposed to explain the exchange ratios of individual commodities in terms of their relation to their labour ratios (making it a microeconomic theory), yet Marx was now maintaining that these ratios must diverge from their labour ratios. Critics thus held that Marx's proposed solution to the "great contradiction" was not so much a solution as it was sidestepping the issue.

Steve Keen argues that Marx's idea that only labor can produce value rests on the idea that as capital depreciates over its use, then this is transferring its exchange-value to the product. Keen argues that it is not clear why the value of the machine should depreciate at the same rate it is lost. Keen uses an analogy with labor: If workers receive a subsistence wage and the working day exhausts the capacity to labor, it could be argued that the worker has "depreciated" by the amount equivalent to the subsistence wage. However this depreciation is not the limit of value a worker can add in a day (indeed this is critical to Marx's idea that labor is fundamentally exploited). If it were, then the production of a surplus would be impossible. According to Keen, a machine could have a use-value greater than its exchange-value, meaning it could, along with labor, be a source of surplus. Keen claims that Marx almost reached such a conclusion in the Grundrisse but never developed it any further. Keen further observes that while Marx insisted that the contribution of machines to production is solely their use-value and not their exchange-value, he routinely treated the use-value and exchange-value of a machine as identical, despite the fact that this would contradict his claim that the two were unrelated. Marxists respond by arguing that use-value and exchange-value are incommensurable magnitudes; to claim that a machine can add "more use-value" than it is worth in value-terms is a category error. According to Marx, a machine by definition cannot be a source of human labor. Keen responds by arguing that the labor theory of value only works if the use-value and exchange-value of a machine are identical, as Marx argued that machines cannot create surplus value since as their use-value depreciates along with their exchange-value; they simply transfer it to the new product but create no new value in the process. Keen's machinery argument can also be applied to slavery based modes of production, which also profit from extracting more use value from the laborers than they return to laborers.

In their work Capital as Power, Shimshon Bichler and Jonathan Nitzan argue that while Marxists have claimed to produce empirical evidence of the labor theory of value via numerous studies which show consistent correlations between values and prices, these studies do not actually provide evidence for it and are inadequate. According to the authors, these studies attempt to prove the LTV by showing that there is a positive correlation between market prices and labor values. However, the authors argue that these studies measure prices by looking at the price of total output (the unit price of a commodity multiplied by its total quantity) and do these for several sectors of the economy, estimate their total price and value from official statistics and measured for several years. However, Bichler and Nitzan argue that this method has statistical implications as correlations measured this way also reflect the co-variations of the associated quantities of unit values and prices. This means that the unit price and unit value of each sector are multiplied by the same value, which means that the greater the variability of output across different sectors, the tighter the correlation. This means that the overall correlation is substantially larger than the underlying correlation between unit values and unit prices; when sectors are controlled for their size, the correlations often drop to insignificant levels. Furthermore, the authors argue that the studies do not seem to actually attempt to measure the correlation between value and price. The authors argue that, according to Marx, the value of a commodity indicates the abstract labor time required for its production; however Marxists have been unable to identify a way to measure a unit (elementary particle) of abstract labor (indeed the authors argue that most have given up and little progress has been made beyond Marx's original work) due to numerous difficulties. This means assumptions must be made and according to the authors, these involve circular reasoning:

The most important of these assumptions are that the value of labour power is proportionate to the actual wage rate, that the ratio of variable capital to surplus value is given by the price ratio of wages to profit, and occasionally also that the value of the depreciated constant capital is equal to a fraction of the capital’s money price. In other words, the researcher assumes precisely what the labour theory of value is supposed to demonstrate.

Bichler and Nitzan argue that this amounts to converting prices into values and then determining if they correlate, which the authors argue proves nothing since the studies are simply correlating prices with themselves. Paul Cockshott disagreed with Bichler and Nitzan's arguments, arguing that it was possible to measure abstract labour time using wage bills and data on working hours, while also arguing Bichler and Nitzan's claims that the true value-price correlations should be much lower actually relied on poor statistical analysis itself. Most Marxists, however, reject Bichler and Nitzan's interpretation of Marx, arguing that their assertion that individual commodities can have values, rather than prices of production, misunderstands Marx's work. For example, Fred Moseley argues Marx understood "value" to be a "macro-monetary" variable (the total amount of labor added in a given year plus the depreciation of fixed capital in that year), which is then concretized at the level of individual prices of production, meaning that "individual values" of commodities do not exist.

The theory can also be sometimes found in non-Marxist traditions. For instance, mutualist theorist Kevin Carson's Studies in Mutualist Political Economy opens with an attempt to integrate marginalist critiques into the labor theory of value.

Additionally, economist Joseph Schumpeter pointed out a couple of issues he believed undermined the validity of the labor theory of value. Firstly he wrote that labor theory of value failed to take into account the intrinsic differences in labor quality between individuals (a difference that, he believed, could not be properly encapsulated through the use of a value multiplier). Furthermore, he claims that labor theory of value, both in its Marxist and Ricardian formulations, would entail that labor be the sole input in an economy alongside all labor being homogenous in nature, a thesis which Schumpeter dismisses as unrealistic and one that could be resolved by Marginalism anyway. Schumpeter goes on to divert his attention towards the supposed self-contradictory nature of how labor theory of value allows for the justification of the Marxian exploitation thesis, highlighting that labor itself could not be valued since it was not itself produced by any labor and that the accumulation of surplus value described by Marx could not occur in a static, perfectly competitive market. Thus, although giving Marx the credit for seeing the need for change inherent in capitalist markets, Schumpeter nonetheless concludes that labor theory of value and its consequences remain problematic theories.

Some post-Keynesian economists have been highly critical of the labor theory of value. Joan Robinson, who herself was considered an expert on the writings of Karl Marx, wrote that the labor theory of value was largely a tautology and "a typical example of the way metaphysical ideas operate". The well-known Marxian economist Roman Rosdolsky replied to Robinson's claims at length, arguing that Robinson failed to understand key components of Marx's theory; for instance, Robinson argued that "Marx's theory, as we have seen, rests on the assumption of a constant rate of exploitation", but as Rosdolsky points out, there is a great deal of contrary evidence.

In ecological economics, the labor theory of value has been criticized, where it is argued that labor is in fact energy over time. Such arguments generally fail to recognize that Marx is inquiring into social relations among human beings, which cannot be reduced to the expenditure of energy, just as democracy cannot be reduced to the expenditure of energy that a voter makes in getting to the polling place. However, echoing Joan Robinson, Alf Hornborg, an environmental historian, argues that both the reliance on "energy theory of value" and "labor theory of value" are problematic as they propose that use-values (or material wealth) are more "real" than exchange-values (or cultural wealth)—yet, use-values are culturally determined. For Hornborg, any Marxist argument that claims uneven wealth is due to the "exploitation" or "underpayment" of use-values is actually a tautological contradiction, since it must necessarily quantify "underpayment" in terms of exchange-value. The alternative would be to conceptualize unequal exchange as "an asymmetric net transfer of material inputs in production (e.g., embodied labor, energy, land, and water), rather than in terms of an underpayment of material inputs or an asymmetric transfer of 'value'". In other words, uneven exchange is characterised by incommensurability, namely: the unequal transfer of material inputs; competing value-judgements of the worth of labor, fuel, and raw materials; differing availability of industrial technologies; and the off-loading of environmental burdens on those with less resources.