One result of the work we have been considering is to dethrone mathematics from the lofty place that it has occupied since Pythagoras and Plato, and to destroy the presumption against empiricism which has been derived from it. Mathematical knowledge, it is true, is not obtained by induction from experience; our reason for believing that 2 and 2 are 4 is not that we have so often found, by observation, that one couple and another couple together make up a quartet. In this sense, mathematical knowledge is still not empirical. But it is also not a priori knowledge about the world. It is, in fact, merely verbal knowledge. '3' means '2 + 1', and '4' means '3 + 1'. Hence it follows (though the proof is long) that '4' means the same as '2 + 2'. Thus mathematical knowledge ceases to be mysterious. It is all of the same nature as the 'great truth' that there are three feet in a yard.
Blogger Comment:
From the perspective of Systemic Functional Linguistic theory, 'mathematical knowledge' is the meaning of the registers of language that realise the contextual field of mathematics. Mathematical equations are identifying clauses.
'3'
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means
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'2 + 1'
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Identified Token
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Process: relational
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Identifier Value
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'4'
|
means
|
'3 + 1'
|
Identified Token
|
Process: relational
|
Identifier Value
|
'4'
|
means
|
the same as '2 + 2'
|
Identified Token
|
Process: relational
|
Identifier Value
|
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