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Single Idea 6425

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

Full Idea

Formalism is perfectly adequate for doing sums, but not for the application of number, such as the simple statement 'there are three men in this room', so it must be regarded as an unsatisfactory evasion.

Gist of Idea

Formalism can't apply numbers to reality, so it is an evasion

Source

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

Book Ref

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


A Reaction

This seems to me a powerful and simple objection. The foundation of arithmetic is that there are three men in the room, not that one plus two is three. Three men and three ties make a pattern, which we call 'three'.

Related Idea

Idea 9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]


The 23 ideas from 'My Philosophical Development'

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