There is perhaps an irony here that a fully fledged anti-Platonist, who believes that mathematics is ‘all in the mind’ must also believe — so it seems — that there are no true mathematical statements that are in principle beyond reason. For example, if Fermat’s Last Theorem had been inaccessible (in principle) to reason, then this anti-Platonist view would allow no validity either to its truth or to its falsity, such validity coming only through the mental act of perceiving some proof or disproof.
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From the perspective of Systemic Functional Linguistic Theory, as a semiotic system, mathematics is understood as the content of consciousness, which, through verbal processes, may be instantiated in texts that are realised materially.
Since mathematics is concerned with logical relations between quantities, no mathematical statements are 'beyond reason', though determining the validity of a specific statement may be beyond the reasoning ability of individual mathematicians.
To be clear, if 'Fermat's Last Theorem had been inaccessible (in principle) to reason', then 'no validity either to its truth or to its falsity' could reasoned by anyone: whether Platonist, anti-Platonist, or neither. Mathematical validity is assessed through the 'mental act' of reasoning on the basis of agreed mathematical principles.
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