词条 | Trivialism |
释义 |
In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is considered by some to be the complete opposite of skepticism. Paraconsistent logics may use "the law of non-triviality" to abstain from trivialism in logical practices that involve true contradictions. Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as modal realism, dialetheism and paraconsistent logics. OverviewEtymologyTrivialism, as a term, is derived from the Latin word trivialis, meaning something that can be found everywhere. From this, "trivial" was used to suggest something was introductory or simple. In logic, from this meaning, a "trivial" theory is something regarded as defective in the face of a complex phenomenon that needs to be completely represented. Thus, literally, the trivialist theory is something expressed in the simplest possible way.[3] TheoryIn symbolic logic, trivialism may be expressed as the following:[3] {{block indent|}}The above would be read as "given any proposition, it is a true proposition" through universal quantification (∀). A claim of trivialism may always apply its fundamental truth, otherwise known as a truth predicate: {{block indent|}}The above would be read as a "proposition if and only if a true proposition", meaning that all propositions are believed to be inherently proven as true. Without consistent use of this concept, a claim of advocating trivialism may not be seen as genuine and complete trivialism; as to claim a proposition is true but deny it as probably true may be considered inconsistent with the assumed theory.[3] Taxonomy of trivialismsLuis Estrada-González in "Models of Possiblism and Trivialism" lists four types of trivialism through the concept of possible worlds, with a "world" being a possibility and "the actual world" being reality. It is theorized a trivialist simply designates a value to all propositions in equivalence to seeing all propositions and their negations as true. This taxonomy is used to demonstrate the different strengths and plausibility of trivialism in this context:
Arguments against trivialismThe consensus among the majority of philosophers is descriptively a denial of trivialism, termed as non-trivialism or anti-trivialism.[4] This is due to it being unable to produce a sound argument through the principle of explosion and it being considered an absurdity (reductio ad absurdum).[2][3] AristotleAristotle's law of noncontradiction and other arguments are considered to be against trivialism. Luis Estrada-González in "Models of Possiblism and Trivialism" has interpreted Aristotle's Metaphysics Book IV as such: "A family of arguments between 1008a26 and 1007b12 of the form 'If trivialism is right, then X is the case, but if X is the case then all things are one. But it is impossible that all things are one, so trivialism is impossible.' ... these Aristotelian considerations are the seeds of virtually all subsequent suspicions against trivialism: Trivialism has to be rejected because it identifies what should not be identified, and is undesirable from a logical point of view because it identifies what is not identical, namely, truth and falsehood."[4]PriestIt is implicitly claimed by Graham Priest, a professor of philosophy, that a position for trivialism is unsubstantial: "a substantial case can be made for [dialetheism]; belief in [trivialism], though, would appear to be grounds for certifiable insanity".[5] He has coined his rejection of trivialism "the law of non-triviality" as a replacement for the law of non-contradiction in paraconsistent logic and dialetheism.[12] Arguments for trivialismThere are theoretical arguments for trivialism argued from the position of a devil's advocate: Argument from possibilismPaul Kabay has argued for trivialism in "On the Plenitude of Truth" from the following: {{quote|
Above, possibilism (modal realism; related to possible worlds) is the barely accepted theory that every proposition is possible. With this assumed to be true, trivialism can be assumed to be true as well according to Kabay. ParadoxesThe liar's paradox, Curry's paradox, and the principle of explosion all can be asserted as valid and not required to be resolved and used to defend trivialism.[2][3] Philosophical implicationsComparison to skepticismIn Paul Kabay's comparison of trivialism to schools of philosophical skepticism (in "On the Plenitude of Truth")—such as Pyrrhonism—who seek to attain a form of ataraxia, or state of imperturbability; it is purported the figurative trivialist inherently attains this state. This is claimed to be justified by the figurative trivialist seeing every state of affairs being true, even in a state of anxiety. Once universally accepted as true, the trivialist is free from any further anxieties regarding whether any state of affairs is true. Kabay compares the Pyrrhonian skeptic to the figurative trivialist and claims that as the skeptic reportedly attains a state of imperturbability through a suspension of belief, the trivialist may attain such a state through an abundance of belief. In this case—and according to independent claims by Graham Priest—trivialism is considered the complete opposite of skepticism.[2][3][6] However, insofar as the trivialist affirms all states of affairs as universally true, the Pyrrhonist neither affirms nor denies the truth (or falsity) of such affairs.[7] Impossibility of actionIt is asserted by both Priest and Kabay that it is impossible for a trivialist to truly choose and thus act. Priest argues this by the following in Doubt Truth to Be a Liar: "One cannot intend to act in such a way as to bring about some state of affairs, s, if one believes s already to hold. Conversely, if one acts with the purpose of bringing s about, one cannot believe that s already obtains."[8][9] Ironically, due to their suspension of determination upon striking equipollence between claims, the Pyrrhonist has also remained subject to apraxia charges.[10][11][12] AdvocatesPaul Kabay, an Australian philosopher, in his book A Defense of Trivialism has argued that various philosophers in history have held views resembling trivialism, although he stops short of calling them trivialists. He mentions various pre-Socratic Greek philosophers as philosophers holding views resembling trivialism. He mentions that Aristotle in his book Metaphysics appears to suggest that Heraclitus and Anaxagoras advocated trivialism. He quotes Anaxagoras as saying that all things are one. Kabay also suggests Heraclitus' ideas are similar to trivialism because Heraclitus believed in a union of opposites, shown in such quotes as "the way up and down is the same".[13] Kabay also mentions a fifteen century Roman Catholic cardinal Nicholas of Cusa, stating that what Cusa wrote in De Docta Ignorantia is interpreted as stating that God contained every fact, which Kabay argues would result in trivialism, but Kabay admits that mainstream Cusa scholars would not agree with interpreting Cusa as a trivialist.[14] Kabay also mentions Spinoza as a philosopher whose views resemble trivialism. Kabay argues Spinoza was a trivialist because Spinoza believed everything was made of one substance which had infinite attributes.[15] Kabay also mentions Hegel as a philosophers whose views resemble trivialism, quoting Hegel as stating in The Science of Logic "everything is inherently contradictory."[16] AzzouniJody Azzouni is a purported advocate of trivialism in his article The Strengthened Liar by claiming that natural language is trivial and inconsistent through the existence of the liar paradox ("This sentence is false"), and claiming that natural language has developed without central direction. It is heavily implied by Azzouni that every sentence in any natural language is true.[17][18][19]AnaxagorasThe Greek philosopher Anaxagoras is suggested as a possible trivialist by Graham Priest in his 2005 book Doubt Truth to Be a Liar. Priest writes, "He held that, at least at one time, everything was all mixed up so that no predicate applied to any one thing more than a contrary predicate."[8] Anti-trivialismLuis Estrada-González in "Models of Possiblism and Trivialism" lists eight types of anti-trivialism (or non-trivialism) through the use of possible worlds: (AT0) Actualist minimal anti-trivialism: In the actual world, some propositions do not have a value of true or false. (AT1) Actualist absolute anti-trivialism: In the actual world, all propositions do not have a value of true or false. (AT2) Minimal anti-trivialism: In some worlds, some propositions do not have a value of true or false. (AT3) Pointed anti-trivialism (or minimal logical nihilism): In some worlds, every proposition does not have a value of true or false. (AT4) Distributed anti-trivialism: In every world, some propositions do not have a value of true or false. (AT5) Strong anti-trivialism: Some propositions do not have a value of true or false in every world. (AT6) Super anti-trivialism (or moderate logical nihilism): All propositions do not have a value of true or false at some world. (AT7) Absolute anti-trivialism (or maximal logical nihilism): All propositions do not have a value of true or false in every world.[4] See also{{Portal|Logic|Philosophy}}
References1. ^{{cite book|editor1-first=Dov M.|editor1-last=Gabbay|editor2-first=John|editor2-last=Woods|title=The Many Valued and Nonmonotonic Turn in Logic|chapter-url=https://books.google.com/books?id=3TNj1ZkP3qEC&pg=PA131|year=2007|publisher=Elsevier|isbn=978-0-444-51623-7|page=131|first=Graham|last=Priest|chapter=Paraconsistency and Dialetheism}} 2. ^1 2 3 4 {{cite book|author=Paul Kabay|title=On the Plenitude of Truth. A Defense of Trivialism|year=2010|publisher=Lambert Academic Publishing|isbn=978-3-8383-5102-5}} 3. ^1 2 3 4 5 {{cite web|last=Kabay|first=Paul|title=A defense of trivialism|url=http://repository.unimelb.edu.au/10187/5734|work=PhD thesis, School of Philosophy, Anthropology, and Social Inquiry|page=29|publisher=The University of Melbourne, Research Collections (UMER)|accessdate=20 May 2014}} 4. ^1 2 3 4 {{cite journal|last=Estrada-González|first=Luis|title=Models of Possibilism and Trivialism|journal=Logic and Logical Philosophy|volume=21|pages=175–205|url=http://wydawnictwoumk.pl/czasopisma/index.php/LLP/article/view/791}} 5. ^{{cite journal|last=Priest|first=Graham|title=Perceiving contradictions|journal=Australasian Journal of Philosophy|date=1999|volume= 77|issue =4|page= 443|doi=10.1080/00048409912349211}} 6. ^{{cite journal |last1=Priest |first1=G. |title=Could everything be true? |doi=10.1080/00048400012349471 |journal=Australasian Journal of Philosophy |volume=78 |issue=2 |pages=189–195 |year=2000}} 7. ^Empiricus, S. (2000). Sextus Empiricus: Outlines of Scepticism. Cambridge University Press. "Suspension of judgement is a standstill of intellect, owing to which we neither reject nor posit anything" (p. 5). 8. ^1 2 {{cite book|last=Priest|first=Graham|title=Doubt truth to be a liar|date=2008|publisher=Oxford University Press|location=Oxford|isbn=978-0199238514|pages=69–71|edition=1st pbk.}} 9. ^{{cite web|last=Kabay|first=Paul|title=Interpreting the Divyadhvani: On Why the Digambara Sect Is Right about the Nature of the Kevalin|url=http://philpapers.org/rec/KABITD|work=The Australasian Philosophy of Religion Association Conference|accessdate=23 May 2014}} 10. ^Comesaña, J. (2012). Can Contemporary Semantics Help the Pyrrhonian Get a Life?. In Pyrrhonism in Ancient, Modern, and Contemporary Philosophy (pp. 217-240). Springer Netherlands. 11. ^Wieland, J. W. (2012) Can Pyrrhonists act normally? Philosophical Explorations: An International Journal for the Philosophy of Mind and Action 15(3):277-289. 12. ^Burnyeat, M. (1980). Can the sceptic live his scepticism?. In M. Schofield, M. Burnyeat, and J. Barnes (eds.), Doubt and Dogmatism (pp. 20-53). Cambridge University Press. 13. ^Kabay, P.D. (2008) A Defense of Trivialism. Phd Thesis, School of Philosophy, Anthropology, and Social Inquiry, The University of Melbourne pages 32–35 14. ^Kabay, pages 36–37 15. ^Kabay, pages 37–40 16. ^Kabay, pages 40–41. [https://minerva-access.unimelb.edu.au/bitstream/handle/11343/35203/117801_A%20Defense%20of%20Trivialismelectronic.pdf?sequence=1 A Defense of Trivialism] 17. ^{{cite web|last=Kabay|first=Paul|title=A defense of trivialism|url=http://repository.unimelb.edu.au/10187/5734|work=PhD thesis, School of Philosophy, Anthropology, and Social Inquiry|page=42|quote=...According to Azzouni, natural language is trivial, that is to say, every sentence in natural language is true...And, of course, trivialism follows straightforwardly from the triviality of natural language: after all, 'trivialism is true' is a sentence in natural language...|publisher=The University of Melbourne, Research Collections (UMER)|accessdate=21 May 2014}} 18. ^{{cite journal |last1=Bueno |first1=O. V. |title=Troubles with Trivialism |doi=10.1080/00201740701698670 |journal=Inquiry |volume=50 |issue=6 |pages=655–667 |year=2007}} 19. ^{{cite journal|last=Azzouni|first=Jody|title=The Strengthened Liar, the Expressive Strength of Natural Languages, and Regimentation|journal=The Philosophical Forum |date=2003|volume=34|issue=3–4|page=342|url=http://philpapers.org/rec/AZZTSL|accessdate=21 May 2014}} Further reading{{Wikiquote}}{{Commons}}
6 : Concepts in logic|Metaphysical theories|Non-classical logic|Philosophical movements|Theories of deduction|Theories of truth |
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