![Trivialisme en logique symbolique](https://upload.wikimedia.org/wikipedia/commons/3/3a/Trivialisme_en_logique_symbolique.svg)
Trivialism is the
logical theory
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element \phi\in T of a deductively closed theory T is ...
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 no ...
) 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
* Tr ...
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 phil ...
's
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 sa ...
. 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. Some ...
, 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 pe ...
.
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" syste ...
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; p ...
,
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
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" syste ...
.
Overview
Etymology
Trivialism, as a term, is derived from the
Latin
Latin (, or , ) is a classical language belonging to the 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 the power of the ...
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 the ...
'', 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 premises ...
, 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 Gottfried W ...
that needs to be completely represented. Thus, literally, the trivialist theory is something expressed in the simplest possible way.
Theory
In
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 w ...
(∀).
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 idea ...
:
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 bicondi ...
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 world
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional logic, intensional and mod ...
s, 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 co ...
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
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 phil ...
's
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 sa ...
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 ...
in
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" syste ...
and
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 ...
.
Arguments for trivialism
There are theoretical arguments for trivialism argued from the position of a
devil's advocate
The (Latin for Devil's advocate) is a former official position within the Catholic Church, the Promoter of the Faith: one who "argued against the canonization ( sainthood) of a candidate in order to uncover any character flaws or misrepresent ...
:
Argument from possibilism
Paul Kabay has argued for trivialism in "On the Plenitude of Truth" from the following:
Above, possibilism (
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; p ...
; 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 trut ...
,
Curry's paradox
Curry's paradox is a paradox in which an arbitrary claim ''F'' is proved from the mere existence of a sentence ''C'' that says of itself "If ''C'', then ''F''", requiring only a few apparently innocuous logical deduction rules. Since ''F'' is arbi ...
, and 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 co ...
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 reject ...
(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 E ...
—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 Gre ...
, 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 suspend ...
of
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 take i ...
, 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
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 pe ...
.
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 Renai ...
, 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 ...
is
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 forked ...
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
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 ...
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
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 ...
:
: (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 Ivan ...
): 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.
See also
*
Discordianism
Discordianism is a religion, philosophy, or paradigm centered on Eris, a.k.a. Discordia, the Goddess of chaos. Discordianism uses archetypes or ideals associated with her. It was founded after the 1963 publication of its "holy book," the ''Pri ...
*
Doublethink
Doublethink is a process of indoctrination in which subjects are expected to simultaneously accept two conflicting beliefs as truth, often at odds with their own memory or sense of reality. Doublethink is related to, but differs from, hypocrisy. ...
*
Factual relativism
Factual relativism (also called epistemic relativism, epistemological relativism, alethic relativism or cognitive relativism) argues that truth itself is relative. This form of relativism has its own particular problem, regardless of whether one i ...
*
Fatalism
Fatalism is a family of related philosophical doctrines that stress the subjugation of all events or actions to fate or destiny, and is commonly associated with the consequent attitude of resignation in the face of future events which are thou ...
*
Anekantavada
( hi, अनेकान्तवाद, "many-sidedness") is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects.
According to Jainism, ...
*
Syādvāda
( hi, अनेकान्तवाद, "many-sidedness") is the Jain doctrine about metaphysical truths that emerged in ancient India. It states that the ultimate truth and reality is complex and has multiple aspects.
According to Jainism, ...
*
Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradic ...
*
Laws of thought
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally th ...
*
Monism
Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., existence. Various kinds of monism can be distinguished:
* Priority monism states that all existing things go back to a source that is distinct from them; e.g., i ...
*
Moral relativism
Moral relativism or ethical relativism (often reformulated as relativist ethics or relativist morality) is used to describe several philosophical positions concerned with the differences in moral judgments across different peoples and cultures. ...
*
Principle of bivalence
In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called ...
References
Further reading
*
*
{{Philosophy topics
Concepts in logic
Metaphysical theories
Non-classical logic
Philosophical movements
Theories of deduction
Theories of truth