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Single Idea 6424

[filed under theme 6. Mathematics / C. Sources of Mathematics / 7. Formalism ]

Full Idea

The Formalists, led by Hilbert, maintain that arithmetic symbols are merely marks on paper, devoid of meaning, and that arithmetic consists of certain arbitrary rules, like the rules of chess, by which these marks can be manipulated.

Gist of Idea

Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess

Source

Bertrand Russell (My Philosophical Development [1959], Ch.10)

Book Ref

Russell,Bertrand: 'My Philosophical Development' [Routledge 1993], p.82

A Reaction

I just don't believe that maths is arbitrary, and this view pushes me into the arms of the empiricists, who say maths is far more likely to arise from experience than from arbitrary convention. The key to maths is patterns.

The 23 ideas from 'My Philosophical Development'

6420 Only by analysing is progress possible in philosophy [Russell]
6419 In 1899-1900 I adopted the philosophy of logical atomism [Russell]
6426 Intuitionism says propositions are only true or false if there is a method of showing it [Russell]
7528 Leibniz bases everything on subject/predicate and substance/property propositions [Russell]
6423 We tried to define all of pure maths using logical premisses and concepts [Russell]
6424 Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
6425 Formalism can't apply numbers to reality, so it is an evasion [Russell]
6427 Unverifiable propositions about the remote past are still either true or false [Russell]
6431 Empiricists seem unclear what they mean by 'experience' [Russell]
6432 Analysis gives new knowledge, without destroying what we already have [Russell]
6430 In epistemology we should emphasis the continuity between animal and human minds [Russell]
6434 Facts are everything, except simples; they are either relations or qualities [Russell]
6433 Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell]
6435 You can believe the meaning of a sentence without thinking of the words [Russell]
6440 Universals can't just be words, because words themselves are universals [Russell]
6436 I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
6438 Complex things can be known, but not simple things [Russell]
6437 The theory of types makes 'Socrates and killing are two' illegitimate [Russell]
6439 Names are meaningless unless there is an object which they designate [Russell]
6442 Truth belongs to beliefs, not to propositions and sentences [Russell]
6441 Pragmatism judges by effects, but I judge truth by causes [Russell]
6443 Surprise is a criterion of error [Russell]
6444 True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell]