Trivialism is the logical theory that all

statements Statement or statements may refer to: Common uses *Statement (computer science), the smallest standalone element of an imperative programming language *Statement (logic), declarative sentence that is either true or false *Statement, a declarative ...

(also known as

propositions In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the ...

) are

true True most commonly refers to truth, the state of being in congruence with fact or reality. True may also refer to: Places * True, West Virginia, an unincorporated community in the United States * True, Wisconsin, a town in the United States * ...

and that all

contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...

s of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance with this, a trivialist is a person who believes everything is true. In

classical logic Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class ...

, trivialism is in direct violation of

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...

law of noncontradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the s ...

. In

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...

, trivialism is considered by some to be the complete opposite of

skepticism Skepticism, also spelled scepticism, is a questioning attitude or doubt toward knowledge claims that are seen as mere belief or dogma. For example, if a person is skeptical about claims made by their government about an ongoing war then the p ...

Paraconsistent logic A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" syst ...

s may use "the law of non-triviality" to abstain from trivialism in logical practices that involve

true contradiction Dialetheism (from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true ...

s. Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as

modal realism Modal realism is the view propounded by philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on the following tenets: possible worlds exist; ...

dialetheism Dialetheism (from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true ...

and paraconsistent logics.

Overview

Etymology

Trivialism, as a term, is derived from the

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

word ''trivialis,'' meaning commonplace, in turn derived from the ''

trivium The trivium is the lower division of the seven liberal arts and comprises grammar, logic, and rhetoric. The trivium is implicit in ''De nuptiis Philologiae et Mercurii'' ("On the Marriage of Philology and Mercury") by Martianus Capella, but t ...

'', the three introductory educational topics (grammar, logic, and rhetoric) expected to be learned by all freemen. In

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

, from this meaning, a "trivial" theory is something regarded as defective in the face of a complex

phenomenon A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfrie ...

that needs to be completely represented. Thus, literally, the trivialist theory is something expressed in the simplest possible way.

Theory

symbolic logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

, trivialism may be expressed as the following: The above would be read as "given any proposition, it is a true proposition" through

universal quantification In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other ...

(∀). A claim of trivialism may always apply its fundamental truth, otherwise known as a

truth predicate In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or i ...

: The above would be read as a "proposition

if and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bic ...

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.

Taxonomy of trivialisms

Luis Estrada-González in "Models of Possibilism 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: * (T0) Minimal trivialism: At some world, all propositions have a designated value. * (T1) Pluralist trivialism: In some worlds, all propositions have a designated value. * (T2) Actualist trivialism: In the actual world, all propositions have a designated value. * (T3) Absolute trivialism: In all worlds, all propositions have a designated value.

Arguments against trivialism

The consensus among the majority of philosophers is descriptively a denial of trivialism, termed as non-trivialism or anti-trivialism. This is due to it being unable to produce a sound argument through the

principle of explosion In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a ...

and it being considered an

absurdity An absurdity is a state or condition of being extremely unreasonable, meaningless or unsound in reason so as to be irrational or not taken seriously. "Absurd" is an adjective used to describe an absurdity, e.g., "Tyler and the boys laughed at ...

(

reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical arguments'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absu ...

Aristotle

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."

Priest

Graham Priest Graham Priest (born 1948) is Distinguished Professor of Philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne, where he was Boyce Gibson Professor of Philosophy and also at the University of St Andr ...

considers trivialism untenable: "a substantial case can be made for ialetheism belief in rivialism though, would appear to be grounds for certifiable insanity". He formulated the "law of non-triviality" as a replacement for the

law of non-contradiction In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the sa ...

paraconsistent logic A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" syst ...

and

Arguments for trivialism

There are theoretical arguments for trivialism argued from the position of a devil's advocate:

Argument from possibilism

Paul Kabay has argued for trivialism in "On the Plenitude of Truth" from the following: Above, possibilism (

; related to

possible worlds Possible Worlds may refer to: * Possible worlds, concept in philosophy * ''Possible Worlds'' (play), 1990 play by John Mighton ** ''Possible Worlds'' (film), 2000 film by Robert Lepage, based on the play * Possible Worlds (studio) * ''Possible Wo ...

) is the oft-debated theory that every proposition is possible. With this assumed to be true, trivialism can be assumed to be true as well according to Kabay.

Paradoxes

The

liar's paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth ...

, Curry's paradox, and the

all can be asserted as valid and not required to be resolved and used to defend trivialism.

Philosophical implications

Comparison to skepticism

In Paul Kabay's comparison of trivialism to schools of

philosophical skepticism Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even rej ...

(in "On the Plenitude of Truth")—such as

Pyrrhonism Pyrrhonism is a school of philosophical skepticism founded by Pyrrho in the fourth century BCE. It is best known through the surviving works of Sextus Empiricus, writing in the late second century or early third century CE. History Pyrrho of ...

—who seek to attain a form of

ataraxia ''Ataraxia'' (Greek: ἀταραξία, from ("a-", negation) and ''tarachē'' "disturbance, trouble"; hence, "unperturbedness", generally translated as "imperturbability", " equanimity", or "tranquility") is a Greek term first used in Ancient ...

, 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 Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspende ...

belief A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to tak ...

, 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

. 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.

Impossibility of action

It 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." Due to their suspension of determination upon striking equipollence between claims, the Pyrrhonist has also remained subject to apraxia charges.

Advocates

Paul 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". Kabay also mentions a fifteenth century Roman Catholic cardinal,

Nicholas of Cusa Nicholas of Cusa (1401 – 11 August 1464), also referred to as Nicholas of Kues and Nicolaus Cusanus (), was a German Catholic cardinal, philosopher, theologian, jurist, mathematician, and astronomer. One of the first German proponents of Re ...

, 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. 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. Kabay also mentions Hegel as a philosopher whose views resemble trivialism, quoting Hegel as stating in ''The Science of Logic'' "everything is inherently contradictory."

Azzouni

Jody Azzouni is a purported advocate of trivialism in his article ''The Strengthened Liar'' by claiming that

natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...

trivial Trivia is information and data that are considered to be of little value. It can be contrasted with general knowledge and common sense. Latin Etymology The ancient Romans used the word ''triviae'' to describe where one road split or fork ...

and inconsistent through the existence of the

liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth ...

("This sentence is false"), and claiming that natural language has developed without central direction. Azzouni implies that every sentence in any natural language is true. "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."

Anaxagoras

The Greek philosopher

Anaxagoras Anaxagoras (; grc-gre, Ἀναξαγόρας, ''Anaxagóras'', "lord of the assembly"; 500 – 428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, ...

is suggested as a possible trivialist by

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."

Anti-trivialism

Luis Estrada-González in "Models of Possibilism and Trivialism" lists eight types of anti-trivialism (or non-trivialism) through the use of

: : (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 Nihilism (; ) is a philosophy, or family of views within philosophy, that rejects generally accepted or fundamental aspects of human existence, such as objective truth, knowledge, morality, values, or meaning. The term was popularized by I ...

): 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.