How would the different schools of thought explain the statement '1+2=3'?

[Firepanda]

This is a question on a past exam I'm trying to asnwer.

So far I have, and I'm not sure if my understanding is correct yet:

Platonism:

Consider if man-kind became extinct, the statement 1+2=3 will always be able to be recovered.

Formalism:

3 is a consequence of the specific intepretation of to the rule of addition, applied to 1 and 2.

Intuitionism:

The succesor of 1 is 2, so the successor 2 must be 3, and so 1+2=3.

Logicism:

Under a model for a first order theory, a logical consquence of 1+2 is 3.

Thoughts?

Thanks

 

[lippyka]

for your question. Your answers are generally correct, however you could refine them a bit. Platonism: Mathematical truth exists independently of human minds and can be discovered by humans. Therefore, even if mankind were to become extinct, the statement 1+2=3 will always remain true.Formalism: Mathematical statements can be derived from a system of fixed rules that are used to manipulate symbols. In this case, the statement 1+2=3 is derived from the rule of addition applied to the symbols 1 and 2. Intuitionism: Mathematical truths are derived from self-evident mental constructs. In the context of 1+2=3, the successor of 1 is 2 and so the successor of 2 must be 3, thus making the statement true. Logicism: Mathematical truths can be deduced from logical principles. Under a model for a first order theory, the statement 1+2=3 can be deduced as a logical consequence.