Principle of sufficient reason

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

The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhauer and Sir William Hamilton, 9th Baronet.

History

The modern formulation of the principle is usually attributed to early Enlightenment philosopher Gottfried Leibniz. Leibniz formulated it, but was not an originator. The idea was conceived of and utilized by various philosophers who preceded him, including Anaximander, Parmenides, Archimedes, Plato and Aristotle, Cicero, Avicenna, Thomas Aquinas, and Spinoza. One often pointed to is in Anselm of Canterbury: his phrase quia Deus nihil sine ratione facit and the formulation of the ontological argument for the existence of God. A clearer connection is with the cosmological argument for the existence of God. The principle can be seen in both Thomas Aquinas and William of Ockham.

Notably, the post-Kantian philosopher Arthur Schopenhauer elaborated the principle, and used it as the foundation of his system. Some philosophers have associated the principle of sufficient reason with "ex nihilo nihil fit". William Hamilton identified the laws of inference modus ponens with the "law of Sufficient Reason, or of Reason and Consequent" and modus tollens with its contrapositive expression.

Formulation

The principle has a variety of expressions, all of which are perhaps best summarized by the following:

• For every entity X, if X exists, then there is a sufficient explanation for why X exists.
• For every event E, if E occurs, then there is a sufficient explanation for why E occurs.
• For every proposition P, if P is true, then there is a sufficient explanation for why P is true.

A sufficient explanation may be understood either in terms of reasons or causes, for like many philosophers of the period, Leibniz did not carefully distinguish between the two. The resulting principle is very different, however, depending on which interpretation is given (see Payne's summary of Schopenhauer's Fourfold Root).

It is an open question whether the principle of sufficient reason can be applied to axioms within a logic construction like a mathematical or a physical theory, because axioms are propositions accepted as having no justification possible within the system. The principle declares that all propositions considered to be true within a system should be deducible from the set axioms at the base of the construction. However, Gödel has shown that for every sufficiently expressive deductive system a proposition exists that can neither be proved nor disproved (see Gödel's incompleteness theorems).

Leibniz's view

Leibniz identified two kinds of truth, necessary and contingent truths. And he claimed that all truths are based upon two principles: (1) non-contradiction, and (2) sufficient reason. In the Monadology, he says,

Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us (paragraphs 31 and 32).

Necessary truths can be derived from the law of identity (and the principle of non-contradiction): "Necessary truths are those that can be demonstrated through an analysis of terms, so that in the end they become identities, just as in Algebra an equation expressing an identity ultimately results from the substitution of values [for variables]. That is, necessary truths depend upon the principle of contradiction." The sufficient reason for a necessary truth is that its negation is a contradiction.

Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true. Even these contingent truths, according to Leibniz, can only exist on the basis of sufficient reasons. Since the sufficient reasons for contingent truths are largely unknown to humans, Leibniz made appeal to infinitary sufficient reasons, to which God uniquely has access:

In contingent truths, even though the predicate is in the subject, this can never be demonstrated, nor can a proposition ever be reduced to an equality or to an identity, but the resolution proceeds to infinity, God alone seeing, not the end of the resolution, of course, which does not exist, but the connection of the terms or the containment of the predicate in the subject, since he sees whatever is in the series.

Without this qualification, the principle can be seen as a description of a certain notion of closed system, in which there is no 'outside' to provide unexplained events with causes. It is also in tension with the paradox of Buridan's ass, because although the facts supposed in the paradox would present a counterexample to the claim that all contingent truths are determined by sufficient reasons, the key premise of the paradox must be rejected when one considers Leibniz's typical infinitary conception of the world.

In consequence of this, the case also of Buridan's ass between two meadows, impelled equally towards both of them, is a fiction that cannot occur in the universe....For the universe cannot be halved by a plane drawn through the middle of the ass, which is cut vertically through its length, so that all is equal and alike on both sides.....Neither the parts of the universe nor the viscera of the animal are alike nor are they evenly placed on both sides of this vertical plane. There will therefore always be many things in the ass and outside the ass, although they be not apparent to us, which will determine him to go on one side rather than the other. And although man is free, and the ass is not, nevertheless for the same reason it must be true that in man likewise the case of a perfect equipoise between two courses is impossible. (Theodicy, pg. 150)

Leibniz also used the principle of sufficient reason to refute the idea of absolute space:

I say then, that if space is an absolute being, there would be something for which it would be impossible there should be a sufficient reason. Which is against my axiom. And I prove it thus. Space is something absolutely uniform; and without the things placed in it, one point in space does not absolutely differ in any respect whatsoever from another point of space. Now from hence it follows, (supposing space to be something in itself, beside the order of bodies among themselves,) that 'tis impossible that there should be a reason why God, preserving the same situation of bodies among themselves, should have placed them in space after one particular manner, and not otherwise; why everything was not placed the quite contrary way, for instance, by changing East into West.

As a law of thought

The principle was one of the four recognised laws of thought, that held a place in European pedagogy of logic and reasoning (and, to some extent, philosophy in general) in the 18th and 19th centuries. It was influential in the thinking of Leo Tolstoy, amongst others, in the elevated form that history could not be accepted as random.

A sufficient reason is sometimes described as the coincidence of every single thing that is needed for the occurrence of an effect (i.e. of the so-called necessary conditions). Such view could perhaps be also applied to indeterministic systems, as long as randomness is in a way incorporated in the preconditions.

Hamilton's fourth law: "Infer nothing without ground or reason"

Here is how Hamilton, circa 1837–1838, expressed his "fourth law" in his LECT. V. LOGIC. 60–61:

"I now go on to the fourth law.

"Par. XVII. Law of Sufficient Reason, or of Reason and Consequent:

"XVII. The thinking of an object, as actually characterized by positive or by negative attributes, is not left to the caprice of Understanding – the faculty of thought; but that faculty must be necessitated to this or that determinate act of thinking by a knowledge of something different from, and independent of; the process of thinking itself. This condition of our understanding is expressed by the law, as it is called, of Sufficient Reason (principium Rationis Sufficientis); but it is more properly denominated the law of Reason and Consequent (principium Rationis et Consecutionis). That knowledge by which the mind is necessitated to affirm or posit something else, is called the logical reason ground, or antecedent; that something else which the mind is necessitated to affirm or posit, is called the logical consequent; and the relation between the reason and consequent, is called the logical connection or consequence. This law is expressed in the formula – Infer nothing without a ground or reason.¹

"Relations between Reason and Consequent: The relations between Reason and Consequent, when comprehended in a pure thought, are the following:

1. When a reason is explicitly or implicitly given, then there must exist a consequent; and, vice versa, when a consequent is given, there must also exist a reason.

¹ See Schulze, Logik, §19, and Krug, Logik, §20, – ED.

"2. Where there is no reason there can be no consequent; and, vice versa, where there is no consequent (either implicitly or explicitly) there can be no reason. That is, the concepts of reason and of consequent, as reciprocally relative, involve and suppose each other.

"The logical significance of this law: The logical significance of the law of Reason and Consequent lies in this, – That in virtue of it, thought is constituted into a series of acts all indissolubly connected; each necessarily inferring the other. Thus it is that the distinction and opposition of possible, actual and necessary matter, which has been introduced into Logic, is a doctrine wholly extraneous to this science."

Schopenhauer's Four Forms

Main article: On the Fourfold Root of the Principle of Sufficient Reason

According to Schopenhauer's On the Fourfold Root of the Principle of Sufficient Reason, there are four distinct forms of the principle.

First Form: The Principle of Sufficient Reason of Becoming (principium rationis sufficientis fiendi); appears as the law of causality in the understanding.

Second Form: The Principle of Sufficient Reason of Knowing (principium rationis sufficientis cognoscendi); asserts that if a judgment is to express a piece of knowledge, it must have a sufficient ground or reason, in which case it receives the predicate true.

Third Form: The Principle of Sufficient Reason of Being (principium rationis sufficientis essendi); the law whereby the parts of space and time determine one another as regards those relations. Example in arithmetic: Each number presupposes the preceding numbers as grounds or reasons of its being; "I can reach ten only by going through all the preceding numbers; and only by virtue of this insight into the ground of being, do I know that where there are ten, so are there eight, six, four."

"Now just as the subjective correlative to the first class of representations is the understanding, that to the second the faculty of reason, and that to the third pure sensibility, so is the subjective correlative to this fourth class found to be the inner sense, or generally self-consciousness."

Fourth Form: The Principle of Sufficient Reason of Acting (principium rationis sufficientis agendi); briefly known as the law of motivation. "Any judgment that does not follow its previously existing ground or reason" or any state that cannot be explained away as falling under the three previous headings "must be produced by an act of will which has a motive." As his proposition in 43 states, "Motivation is causality seen from within."

Proposed proofs of universal validity

See also: Free will § Views of causality

Several proofs have been prepared in order to demonstrate that the universe is at bottom causal, i.e. works in accord with the principle in question; perhaps not in every single case (randomness might still play a part here and there), but that causality must be the way it works at least in general, in most of what we see; and that our minds are aware of the principle even before any experience. A famous argument or proof as proposed by Immanuel Kant from the form of Time, temporal ordering of events and "directionality" of time.

Arthur Schopenhauer provides a proof of the a priori nature of the concept of causality by demonstrating how all perception depends on causality and the intellect. However, he also claims that "to seek a proof for the principle of sufficient reason in particular is especially absurd and is evidence of a want of reflection," and that he who does this "finds himself involved in that circle of demanding a proof for the right to demand a proof."

Once it is agreed (e.g. from a kind of an "arrow of time") that causal interconnections, as a form of principle of sufficient reason, indeed must in general exist everywhere in the universe (at least in the large scale), backwards causality in general might then be precluded using a form of the paradox of free will (i.e. an event that has a future source might cause us to remove that source quick enough and thus causality would not work).

Chandra Wickramasinghe

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

 

Chandra Wickramasinghe MBE
Chandra Wickramasinghe at the University of Buckingham
Born	20 January 1939 (age 83) Colombo, British Ceylon
Citizenship	British
Alma mater	Royal College, Colombo University of Ceylon (BSc) Cambridge University (PhD, ScD)
Known for	Organic composition of cosmic dust
Awards	Fellow of Jesus College, Cambridge University (1963–1973) Vidya Jyothi (1992)
Scientific career
Fields	Astrobiology Astronomy Mathematics
Institutions	Cambridge University University College Cardiff University of Cardiff University of Buckingham University of Ruhuna
Doctoral advisor	Fred Hoyle

Nalin Chandra Wickramasinghe MBE (born 20 January 1939) is a Sri Lankan-born British mathematician, astronomer and astrobiologist of Sinhalese ethnicity. His research interests include the interstellar medium, infrared astronomy, light scattering theory, applications of solid-state physics to astronomy, the early Solar System, comets, astrochemistry, the origin of life and astrobiology. A student and collaborator of Fred Hoyle, the pair worked jointly for over 40 years as influential proponents of panspermia. In 1974 they proposed the hypothesis that some dust in interstellar space was largely organic, later proven to be correct.

Wickramasinghe has advanced numerous fringe claims, including the argument that various outbreaks of illnesses on Earth are of extraterrestrial origins, including the 1918 flu pandemic and certain outbreaks of polio and mad cow disease. For the 1918 flu pandemic they hypothesised that cometary dust brought the virus to Earth simultaneously at multiple locations—a view almost universally dismissed by experts on this pandemic. Claims connecting terrestrial disease and extraterrestrial pathogens have been rejected by the scientific community.

Wickramasinghe has written more than 30 books about astrophysics and related topics; he has made appearances on radio, television and film, and he writes online blogs and articles. He has appeared on BBC Horizon, UK Channel 5 and the History Channel. He appeared on the 2013 Discovery Channel program "Red Rain". He has an association with Daisaku Ikeda, president of the Buddhist sect Soka Gakkai International, that led to the publication of a dialogue with him, first in Japanese and later in English, on the topic of Space and Eternal Life.

Education and career

Wickramasinghe studied at Royal College, Colombo, the University of Ceylon (where he graduated in 1960 with a BSc First Class Honours in mathematics), and at Trinity College and Jesus College, Cambridge, where he obtained his PhD and ScD degrees. Following his education, Wickramasinghe was a Fellow of Jesus College, Cambridge from 1963 to 1973, until he became professor of applied mathematics and astronomy at University College Cardiff. Wickramasinghe was a consultant and advisor to the President of Sri Lanka from 1982 to 1984, and played a key role in founding the Institute of Fundamental Studies in Sri Lanka.

After fifteen years at University College Cardiff, Wickramasinghe took an equivalent position in the University of Cardiff, a post he held from 1990 until 2006. After retirement in 2006, he incubated the Cardiff Center for Astrobiology as a special project reporting to the President of the University. In 2011 the project closed down, losing its funding in a series of UK educational cut backs. After this event, Wickramasinghe was offered the opportunity to move to the University of Buckingham as Director of the Buckingham Centre for Astrobiology, University of Buckingham where he has been since 2011. He maintains his part-time position as a UK Professor at Cardiff University. In 2015 he was elected Visiting scholar, Churchill College, Cambridge, England 2015/16.

He is a co-founder and board member of the Institute for the Study of Panspermia and Astroeconomics, set up in Japan in 2014, and the Editor-in-Chief of the Journal of Astrobiology & Outreach. He was a Visiting By-Fellow, Churchill College, Cambridge, England 2015/16; Professor and Director of the Buckingham Centre for Astrobiology at the University of Buckingham, a post he has held since 2011; Affiliated Visiting Professor, University of Peradeniya, Sri Lanka; and a board member and research director at the Institute for the Study of Panspermia and Astroeconomics, Ogaki-City, Gifu, Japan.

In 2017, Professor Chandra Wickramasinghe was appointed Adjunct Professor in the Department of Physics, at the University of Ruhuna, Matara, Sri Lanka.

Research

In 1960 he commenced work in Cambridge on his PhD degree under the supervision of Fred Hoyle, and published his first scientific paper "On Graphite Particles as Interstellar Grains” in Monthly Notices of the Royal Astronomical Society in 1962. He was awarded a PhD degree in Mathematics in 1963 and was elected a Fellow of Jesus College Cambridge in the same year. In the following year he was appointed a Staff Member of the Institute of Astronomy, Cambridge. Here he continued to work on the nature of interstellar dust, publishing many papers in this field, that led to a consideration of carbon-containing grains as well as the older silicate models.

Wickramasinghe published the first definitive book on Interstellar Grains in 1967. He has made many contributions to this field, publishing over 350 papers in peer-reviewed journals, over 75 of which are in Nature. Hoyle and Wickramasinghe further proposed a radical kind of panspermia that included the claim that extraterrestrial life forms enter the Earth's atmosphere and were possibly responsible for epidemic outbreaks, new diseases, and genetic novelty that Hoyle and Wickramasinghe contended was necessary for macroevolution.

Chandra Wickramasinghe had the longest-running collaboration with Fred Hoyle. Their publications on books and papers arguing for panspermia and a cosmic hypothesis of life are controversial and, in particular detail, essentially contra the scientific consensus in both astrophysics and biology. Several claims made by Hoyle and Wickramasinghe between 1977 and 1981, such as a report of having detected interstellar cellulose, were criticised by one author as pseudoscience. Phil Plait has described Wickramasinghe as a "fringe scientist" who "jumps on everything, with little or no evidence, and says it’s from outer space".

Organic molecules in space

In 1974 Wickramasinghe first proposed the hypothesis that some dust in interstellar space was largely organic, and followed this up with other research confirming the hypothesis. Wickramasinghe also proposed and confirmed the existence of polymeric compounds based on the molecule formaldehyde (H₂CO). Fred Hoyle and Wickramasinghe later proposed the identification of bicyclic aromatic compounds from an analysis of the ultraviolet extinction absorption at 2175A., thus demonstrating the existence of polycyclic aromatic hydrocarbon molecules in space.

Hoyle–Wickramasinghe model of panspermia

Throughout his career, Wickramasinghe, along with his collaborator Fred Hoyle, has advanced the panspermia hypothesis, that proposes that life on Earth is, at least in part, of extraterrestrial origin. The Hoyle–Wickramasinghe model of panspermia include the assumptions that dormant viruses and desiccated DNA and RNA can survive unprotected in space; that small bodies such as asteroids and comets can protect the "seeds of life", including DNA and RNA, living, fossilized, or dormant life, cellular or non-cellular; and that the collisions of asteroids, comets, and moons have the potential to spread these "seeds of life" throughout an individual star system and then onward to others. The most contentious issue around the Hoyle–Wickramasinghe model of the panspermia hypothesis is the corollary of their first two propositions that viruses and bacteria continue to enter the Earth's atmosphere from space, and are hence responsible for many major epidemics throughout history.

Towards the end of their collaboration, Wickramasinghe and Hoyle hypothesised that abiogenesis occurred close to the Galactic Center before panspermia carried life throughout the Milky Way, and stated a belief that such a process could occur in many galaxies throughout the Universe.

Scientists in North America, Europe, Russia, and Japan are testing many aspects of panspermia. (Further information at Panspermia#Research in outer space.)

Detection of living cells in the stratosphere

An image of a clump of microorganisms from 41 km fluorescing on application of a carbocyanine dye (indicating viability) is shown in the left panel, and scanning electron microscope image of a similar clump is shown on the right panel.

On 20 January 2001 the Indian Space Research Organisation (ISRO) conducted a balloon flight from Hyderabad, India to collect stratospheric dust from a height of 41 km (135,000 ft) with a view to testing for the presence of living cells. The collaborators on this project included a team of UK scientists led by Wickramasinghe. In a paper presented at a SPIE conference in San Diego in 2002 the detection of evidence for viable microorganisms from 41 km above the Earth's surface was presented. However, the experiment did not present evidence as to whether the findings are incoming microbes from space rather than microbes carried up to 41 km from the surface of the Earth.

In 2005 the ISRO group carried out a second stratospheric sampling experiment from 41 km altitude and reported the isolation of three new species of bacteria including one that they named Janibacter hoylei sp.nov. in honour of Fred Hoyle. However, these facts do not prove that bacteria on Earth originated in the cosmic environment. Samplings of the stratosphere have also been carried out by Yang et al. (2005, 2009). During the experiment strains of highly radiation-resistant Deinococcus bacterium were detected at heights up to 35 km. Nevertheless, these authors have abstained from linking these discoveries to panspermia. Wickramasinghe was also involved in coordinating analyses of the red rain in Kerala in collaborations with Godfrey Louis.

Extraterrestrial pathogens

Hoyle and Wickramasinghe have advanced the argument that various outbreaks of illnesses on Earth are of extraterrestrial origins, including the 1918 flu pandemic and certain outbreaks of polio and mad cow disease. For the 1918 flu pandemic they hypothesised that cometary dust brought the virus to Earth simultaneously at multiple locations—a view almost universally dismissed by external experts on this pandemic.

On 24 May 2003 The Lancet published a letter from Wickramasinghe, jointly signed by Milton Wainwright and Jayant Narlikar, in which they hypothesised that the virus that causes severe acute respiratory syndrome (SARS) could be extraterrestrial in origin instead of originating from chickens. The Lancet subsequently published three responses to this letter, showing that the hypothesis was not evidence-based, and casting doubts on the quality of the experiments referenced by Wickramasinghe in his letter. Claims connecting terrestrial disease and extraterrestrial pathogens have been rejected by the scientific community.

In 2020, Wickramasinghe and colleagues published a paper claiming that Severe acute respiratory syndrome coronavirus 2, the virus responsible for the COVID-19 pandemic was also of extraterrestrial origin, the claim was criticised for lacking evidence.

Polonnaruwa

Main article: Polonnaruwa (meteorite)

On 29 December 2012 a green fireball was observed in Polonnaruwa Province, Sri Lanka. It disintegrated into fragments that fell to the Earth near the villages of Aralaganwila and Dimbulagala and in a rice field near Dalukkane. Rock samples were submitted to the Medical Research Institute of the Ministry of Health in Colombo.

The rocks were sent to the University of Cardiff in Wales for analysis, where Chandra Wickramasinghe's team analyzed them and claimed that they contained extraterrestrial diatoms. From January to March 2013, five papers were published in the fringe Journal of Cosmology outlining various results from teams in the United Kingdom, United States and Germany. However, independent experts in meteoritics stated that the object analyzed by Wickramasinghe's team was of terrestrial origin, a fulgurite created by lightning strikes on Earth. Experts in diatoms complemented the statement, saying that the organisms found in the rock represented a wide range of extant terrestrial taxa, confirming their earthly origin.

Wickramasinghe and collaborators responded, using X-ray diffraction, oxygen isotope analysis, and scanning electron microscope observations, in a March 2013 paper asserting that the rocks they found were indeed meteorites, instead of being created by lightning strikes on Earth as stated by scientists from the University of Peradeniya. However, these claims were also criticised again not providing evidence that the rocks were actually meteorites.

Cephalopod alien origin

In 2018, Wickramasinghe and over 30 other authors published a paper in Progress in Biophysics and Molecular Biology entitled "Cause of Cambrian Explosion - Terrestrial or Cosmic?" which argued in favour of panspermia as the origin of the Cambrian explosion, and posited that cephalopods are alien lifeforms that originated from frozen eggs that were transported to earth via meteor. The claims gained widespread press coverage. Virologist Karin Mölling, in a companion commentary published in the same journal, stated that the claims "cannot be taken seriously".

Participation in the creation-evolution debate

Wickramasinghe and his mentor Fred Hoyle have also used their data to argue in favor of cosmic ancestry, and against the idea of life emerging from inanimate objects by abiogenesis.

Once again the Universe gives the appearance of being biologically constructed, and on this occasion on a truly vast scale. Once again those who consider such thoughts to be too outlandish to be taken seriously will continue to do so. While we ourselves shall continue to take the view that those who believe they can match the complexities of the Universe by simple experiments in their laboratories will continue to be disappointed.

Wickramasinghe attempts to present scientific evidence to support the notion of cosmic ancestry and "the possibility of high intelligence in the Universe and of many increasing levels of intelligence converging toward a God as an ideal limit."

During the 1981 scientific creationist trial in Arkansas, Wickramasinghe was the only scientist testifying for the defense, which in turn was supporting creationism. In addition, he wrote that the Archaeopteryx fossil finding is a forgery, a charge that the scientific community considers an "absurd" and "ignorant" statement.

Honours and awards

• Commonwealth Scholar at Trinity College, Cambridge, 1960-1963
• Powell Prize for English Verse, Trinity College, 1961
• Vidya Jyothi from the President of Sri Lanka, 1992
• Honorary DLitt, Sōka University (Japan), 1996
• Doctor of Science (honoris causa), University of Ruhuna, Sri Lanka, 2004
• Visiting By-Fellowship, visiting scholar, Churchill College, Cambridge, England 2015/16
• Ada Derana Sri Lankan of the Year 2017 - Global Scientist

Wickramasinghe was appointed Member of the Order of the British Empire (MBE) in the 2022 New Year Honours for services to science, astronomy and astrobiology.

Books

• Interstellar Grains (Chapman & Hall, London, 1967)
• Light Scattering Functions for Small Particles with Applications in Astronomy (Wiley, New York, 1973)
• Solid-State Astrophysics (ed. with D.J. Morgan) (D. Reidel, Boston, 1975)
• Interstellar Matter (with F.D. Khan & P.G. Mezger) (Swiss Society of Astronomy and Astrophysics, 1974)
• The Cosmic Laboratory (University College of Cardiff, 1975)
• Lifecloud: The Origin of Life in the Universe (with Fred Hoyle) (J.M. Dent, London, 1978)
• Diseases from Space (with Fred Hoyle) (J.M. Dent, London, 1979)
• Origin of Life (with Fred Hoyle) (University College Cardiff Press, 1979)
• Space Travellers: The Bringers of Life (with Fred Hoyle) (University College Cardiff Press, 1981)
• Evolution from Space (with Fred Hoyle) (J.M. Dent, London, 1981) ISBN 978-0-460-04535-3
• Is Life an Astronomical Phenomenon? (University College Cardiff Press, 1982) ISBN 9780906449493
• Why Neo-Darwinism Does Not Work (with Fred Hoyle) (University College Cardiff Press, 1982) ISBN 9780906449509
• Proofs that Life is Cosmic (with Fred Hoyle) (Institute of Fundamental Studies, Sri Lanka, Memoirs no.1, 1982)
• From Grains to Bacteria (with Fred Hoyle) (University College Cardiff Press, 1984) ISBN 9780906449646
• Fundamental Studies and the Future of Science (ed.) (University College Cardiff Press, 1984) ISBN 9780906449578
• Living Comets (with Fred Hoyle) (University College Cardiff Press, 1985) ISBN 9780906449790
• Archaeopteryx, the Primordial Bird (with Fred Hoyle) (Christopher Davies, Swansea, 1986) ISBN 9780715406656
• The Theory of Cosmic Grains (with Fred Hoyle) (Kluwer, Dordrecht, 1991) ISBN 9780792311898
• Life on Mars? The Case for a Cosmic Heritage (with Fred Hoyle) (Clinical Press, Bristol, 1997) ISBN 9781854570413
• Astronomical Origins of Life: Steps towards Panspermia (with Fred Hoyle) (Kluwer, Dordrecht, 2000) ISBN 9780792360810
• Cosmic Dragons: Life and Death on Our Planet (Souvenir Press, London, 2001) ISBN 9780285636064
• Fred Hoyle’s Universe (ed. with G. Burbidge and J. Narlikar) (Kluwer, Dordrecht, 2003) ISBN 9781402014154
• A Journey with Fred Hoyle (World Scientific, Singapore, 2005) ISBN 9789812565792
• Comets and the Origin of Life (with J. Wickramasinghe and W. Napier) (World Scientific, Hackensack NJ, 2010) ISBN 9789812814005
• A Journey with Fred Hoyle, Second Edition (World Scientific, Singapore, April 2013) ISBN 9789814436120
• The search for our cosmic ancestry, World Scientific, New Jersey 2015, ISBN 978-981-461696-6.
• Walker, Theodore; Wickramasinghe, Chandra (2015). The Big Bang and God: An Astro-Theology. Palgrave Macmillan US. doi:10.1057/9781137535030. ISBN 978-1-349-57419-3.

Articles

• Hoyle, F. and Wickramasinghe, N.C., 1962. On graphite particles as interstellar grains, Mon.Not.Roy.Astr.Soc. 124, 417-433
• Hoyle, F.; Wickramasinghe, N.C. (1969). "Interstellar Grains". Nature. 223 (5205): 450–462. Bibcode:1969Natur.223..459H. doi:10.1038/223459a0.
• Wickramasinghe, N.C., 1974. Formaldehyde polymers in interstellar space, Nature 252, 462-463
• Wickramasinghe, N.C.; Hoyle, F.; Brooks, J.; Shaw, G. (1977). "Prebiotic polymers and infrared spectra of galactic sources". Nature. 269 (5630): 674–676. Bibcode:1977Natur.269..674W. doi:10.1038/269674a0.
• Hoyle, F. and Wickramasinghe, N.C., 1977. Identification of the λ2,200A interstellar absorption feature, Nature 270, 323-324
• F., Hoyle; N. C., Wickramasinghe (1976-11-04). "Primitive grain clumps and organic compounds in carbonaceous chondrites" (PDF). Nature. 264 (5581): 45–46. Bibcode:1976Natur.264...45H. doi:10.1038/264045a0. Retrieved 2013-01-18.
• Hoyle, F. and Wickramasinghe, N.C., 1977. Polysaccharides and infrared spectra of galactic sources, Nature 268, 610-612
• Hoyle, F.; Wickramasinghe, N.C. (1979). "On the nature of interstellar grains". Astrophysics and Space Science. 66: 77–90. Bibcode:1999Ap&SS.268..249H. doi:10.1023/A:1002462602776.
• Hoyle, F.; Wickramasinghe, N.C. (1979). "Biochemical chromophores and the interstellar extinction at ultraviolet wavelengths". Astrophysics and Space Science. 65 (1): 241–244. Bibcode:1979Ap&SS..65..241H. doi:10.1007/BF00643503.
• Hoyle, F.; Wickramasinghe, N.C.; Al-Mufti, S.; et al. (1982). "Infrared spectroscopy over the 2.9-3.9μm waveband in biochemistry and astronomy". Astrophysics and Space Science. 83: 405–409. Bibcode:1999Ap&SS.268..161H. doi:10.1023/A:1002417307802.
• Hoyle, F.; Wickramasinghe, N.C.; Al-Mufti, S. (1982). "Organo-siliceous biomolecules and the infrared spectrum of the Trapezium nebula". Astrophysics and Space Science. 86 (1): 63–69. Bibcode:1982Ap&SS..86...63H. doi:10.1007/BF00651830.
• Hoyle, F.; Wickramasinghe, N.C. (1983). "Bacterial life in space". Nature. 306 (5942): 420. Bibcode:1983Natur.306..420H. doi:10.1038/306420a0. PMID 6646221.
• Hoyle, F. and Wickramasinghe, N.C., 1986. The case for life as a cosmic phenomenon, Nature 322, 509-511
• Hoyle, F. and Wickramasinghe, N.C., 1990. Influenza – evidence against contagion, Journal of the Royal Society of Medicine 83. 258-261
• Napier, W.M.; Wickramasinghe, J.T; Wickramasinghe, N.C. (2007). "The origin of life in comets". International Journal of Astrobiology. 6 (4): 321–323. Bibcode:2007IJAsB...6..321N. doi:10.1017/S1473550407003941.
• Rauf, K.; Wickramasinghe, C. (2010). "Evidence for biodegradation products in the interstellar medium". International Journal of Astrobiology. 9 (1): 29–34. Bibcode:2010IJAsB...9...29R. CiteSeerX 10.1.1.643.9541. doi:10.1017/S1473550409990334.
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Paradox

From Wikipedia, the free encyclopedia

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

This apparently impossible object, located in Gotschuchen, Austria, projects into a Penrose triangle.

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.

In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, cannot be easily resolved by making foundational changes in a logical system.

Examples outside logic include the ship of Theseus from philosophy, a paradox that questions whether a ship repaired over time by replacing each and all of its wooden parts, one at a time, would remain the same ship. Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.

In common usage, the word "paradox" often refers to statements that are ironic or unexpected, such as "the paradox that standing is more tiring than walking".

Introduction

See also: List of paradoxes

Common themes in paradoxes include self-reference, infinite regress, circular definitions, and confusion or equivocation between different levels of abstraction.

Patrick Hughes outlines three laws of the paradox:

Self-reference

An example is the statement "This statement is false", a form of the liar paradox. The statement is referring to itself. Another example of self-reference is the question of whether the barber shaves himself in the barber paradox. Yet another example involves the question "Is the answer to this question 'No'?"

Contradiction

"This statement is false"; the statement cannot be false and true at the same time. Another example of contradiction is if a man talking to a genie wishes that wishes couldn't come true. This contradicts itself because if the genie grants his wish, he did not grant his wish, and if he refuses to grant his wish, then he did indeed grant his wish, therefore making it impossible either to grant or not grant his wish without leading to a contradiction.

Vicious circularity, or infinite regress

"This statement is false"; if the statement is true, then the statement is false, thereby making the statement true. Another example of vicious circularity is the following group of statements:

"The following sentence is true."

"The previous sentence is false."

Other paradoxes involve false statements and half-truths ("impossible is not in my vocabulary") or rely on a hasty assumption. (A father and his son are in a car crash; the father is killed and the boy is rushed to the hospital. The doctor says, "I can't operate on this boy. He's my son." There is no paradox if the boy's mother is a surgeon.)

Paradoxes that are not based on a hidden error generally occur at the fringes of context or language, and require extending the context or language in order to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. "This sentence is false" is an example of the well-known liar paradox: it is a sentence that cannot be consistently interpreted as either true or false, because if it is known to be false, then it can be inferred that it must be true, and if it is known to be true, then it can be inferred that it must be false. Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory.

Thought-experiments can also yield interesting paradoxes. The grandfather paradox, for example, would arise if a time-traveler were to kill his own grandfather before his mother or father had been conceived, thereby preventing his own birth. This is a specific example of the more general observation of the butterfly effect, or that a time-traveller's interaction with the past—however slight—would entail making changes that would, in turn, change the future in which the time-travel was yet to occur, and would thus change the circumstances of the time-travel itself.

Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of a time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one that leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to.

Quine's classification

See also: Veridicality

W. V. O. Quine (1962) distinguished between three classes of paradoxes:

According to Quine's classification of paradoxes:

• A veridical paradox produces a result that appears absurd, but is demonstrated to be true nonetheless. The paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays had he been born on a leap day. Likewise, Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people. Monty Hall paradox (or equivalently Three Prisoners problem) demonstrates that a decision that has an intuitive fifty–fifty chance is in fact heavily biased towards making a decision that, given the intuitive conclusion, the player would be unlikely to make. In 20th-century science, Hilbert's paradox of the Grand Hotel, Schrödinger's cat, Wigner's friend or Ugly duckling theorem are famously vivid examples of a theory being taken to a logical but paradoxical end.
• A falsidical paradox establishes a result that not only appears false but actually is false, due to a fallacy in the demonstration. The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples of this, often relying on a hidden division by zero. Another example is the inductive form of the horse paradox, which falsely generalises from true specific statements. Zeno's paradoxes are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start. Therefore, falsidical paradoxes can be classified as fallacious arguments.
• A paradox that is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling–Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.

A fourth kind, which may be alternatively interpreted as a special case of the third kind, has sometimes been described since Quine's work:

• A paradox that is both true and false at the same time and in the same sense is called a dialetheia. In Western logics, it is often assumed, following Aristotle, that no dialetheia exist, but they are sometimes accepted in Eastern traditions (e.g. in the Mohists, the Gongsun Longzi, and in Zen) and in paraconsistent logics. It would be mere equivocation or a matter of degree, for example, to both affirm and deny that "John is here" when John is halfway through the door, but it is self-contradictory simultaneously to affirm and deny the event.

Ramsey's classification

Frank Ramsey drew a distinction between logical paradoxes and semantic paradoxes, with Russell’s paradox belonging to the former category, and the liar paradox and Grelling’s paradoxes to the latter. Ramsey introduced the by-now standard distinction between logical and semantical contradictions. Logical contradictions involve mathematical or logical terms like class and number, and hence show that our logic or mathematics is problematic. Semantical contradictions involve, besides purely logical terms, notions like thought, language, and symbolism, which, according to Ramsey, are empirical (not formal) terms. Hence these contradictions are due to faulty ideas about thought or language, and they properly belong to epistemology.

In philosophy

A taste for paradox is central to the philosophies of Laozi, Zeno of Elea, Zhuangzi, Heraclitus, Bhartrhari, Meister Eckhart, Hegel, Kierkegaard, Nietzsche, and G.K. Chesterton, among many others. Søren Kierkegaard, for example, writes in the Philosophical Fragments that:

But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of the understanding to will the collision, although in one way or another the collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think.

In medicine

A paradoxical reaction to a drug is the opposite of what one would expect, such as becoming agitated by a sedative or sedated by a stimulant. Some are common and are used regularly in medicine, such as the use of stimulants such as Adderall and Ritalin in the treatment of attention deficit hyperactivity disorder (also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a benzodiazepine.

In the smoker's paradox, cigarette smoking, despite its proven harms, has a surprising inverse correlation with the epidemiological incidence of certain diseases.