In
metaphysics
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
, Plato's beard is a
paradox
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 u ...
ical argument dubbed by
Willard Van Orman Quine
Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century" ...
in his 1948 paper "On What There Is". The phrase came to be identified as the philosophy of understanding something based on what does not exist.
Doctrine
Quine defined
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
's beard – and his reason for naming it so – in the following words:
This is the old Platonic riddle of nonbeing. Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine
Doctrine (from la, doctrina, meaning "teaching, instruction") is a codification of beliefs or a body of teachings or instructions, taught principles or positions, as the essence of teachings in a given branch of knowledge or in a belief syste ...
might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor
Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond neces ...
.
The argument has been favored by prominent philosophers including
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, a ...
,
A. J. Ayer and
C. J. F. Williams.
Declaring that not ''p'' (¬''p'') cannot exist, one may be forced to abandon
truism A truism is a claim that is so obvious or self-evident as to be hardly worth mentioning, except as a reminder or as a rhetorical or literary device, and is the opposite of falsism.
In philosophy, a sentence which asserts incomplete truth conditio ...
s such as
negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P or \overline. It is interpreted intuitively as being true when P is false, and false ...
and ''
modus tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens' ...
''. There are also variations to Quine's original, which included its application both to singular and general terms.
Quine initially applied the doctrine to singular terms only before expanding it so that it covers general terms as well.
Karl Popper
Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the ...
stated the inverse. "Only if Plato's beard is sufficiently tough, and tangled by many entities, can it be worth our while to use Ockham's razor."
Russell's theory of "singular descriptions", which clearly show "how we might meaningfully use seeming names without supposing that there be the entities allegedly named", is supposed to "detangle" Plato's beard.
See also
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References
Further reading
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External links
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Willard Van Orman Quine
Logical paradoxes
Abstract object theory
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