Saturday, December 20, 2014

Philosophical Grammar 91


91. A search for a particular thing (e.g. my stick) is a particular kind of search, and differs from a search for something else because of what one does (says, thinks) while searching, not because of what one finds. – Contrast looking for the trisection of the angle.



presumably one will do something while searching – whatever one is searching for –
and therefore the details of what one does – says – thinks etc.– could be said to distinguish one search from another

on the other hand – in so far as any search does involve doing something while searching  – and if the details of what one does while searching – are regarded as unimportant – one search is the same as another

‘ “You were looking for him? You can’t even have known if he was there!” (Contrast looking for the trisection of the angle.)’?

I’m not sure there is a contrast here –

trisecting an angle – it can be done in the special case – pi/radians (90 degrees)

you can trisect an arbitrary angle if you cheat by using a measuring ruler instead of a plain straight edge

but to play by the rules you aren’t allowed any marks on the straight edge at all – it must be blank

the problem of trisection in the general case was a mathematical problem since the Greeks

in 1837 the French mathematician Pierre Wantzel proved it was impossible

he showed that the two problems of trisecting an angel and of solving a cubic equation are equivalent –

and he showed that only a very few cubic equations can be solved using the straight-edge-and-compass method –

he deduced that most angles cannot be trisected

so is it too much of a stretch to say that looking for the trisection of the angle – is the same as ‘looking for him’ – you can’t have known if it was there?

this argument works if Wantzel’s argument stands –

that is if his thinking and proof are not put to question – and if no alternative view is forthcoming

regardless of that – this issue – like any issue in mathematics –is open to question – open to doubt –

the bottom line is that when you search for anything – you propose a state of affairs –

any such proposal is uncertain –

and in the event that what you propose comes about – this does not change the logical status of the proposal –

and further – the event – or more correctly – the description of it –

is open to question – open to doubt



© greg t. charlton. 2014