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Re: Philosophy general debate
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Daniel,
I use the term 'lemma' as a helpful proposition which is useful in proving a
larger theorem. This is how I use the term as a mathematician, and my
mathematics lecturers use the term. Its use outside of mathematics is slightly
different. This is what Boolos says:
"Different words, however, are used for different kinds of results. The most
important general results are dignified with the title of 'theorem'. Lesser
results are called 'lemmas' if they are steps on the way to a theorem,
'corollaries' if they follow directly upon some theorem, and 'propositions' if
they are free-standing. In contrast to all these, 'examples' are particular
rather than general." -- Boolos, Jeffrey, Burgess 'Computability and Logic'
Fourth Edition.
(I have just come home from my uni house and this was luckily one of the three
books I took back with me!)
I shall try and respond to the rest of your e-mail when I get time.
Andrew
> To reply to this message or start a new topic please email: BUPS-DIS@bups.org
>
>
> Hi,
>
> By presupposition, all I mean is what must be in place before someone can
> accept a starting proposition. I think that the form we are dealing here is
> as with Moore's proof of the external world (and the fault is the same).
> Here's a version of Moore's proof:
>
> 1) If I have hands, then there is an external world.
>
> 2) Here is a hand [raises left hand], here is another hand[raises right] -
> I have hands.
>
> Therefore:
>
> 3) There is an external world.
>
> The fault with this appears to me (obviously I didn't think of this first!)
> that in order to accept (2) we already have to be convinced of (3).
> Although the argument is formally valid, it fails to be cogent because it
> can't force us to believe anything new. The notion of presuppositions that
> I have used helps to explain why this happens...
>
> One does not - usually - have to claim explicitly that there is an external
> world before we point at things and claim them to be present. However, it
> is clear that if there is not an external world, then there are no hands.
> So if someone denies that there is an external world, they cannot
> reasonably accept that there are hands. Therefore, the claim that there are
> hands cannot come to bear on the issue, because it (the issue) has to be
> decided antecedently - even if it seems bloody obvious to *us*. I would
> call the external world proposition (3) a presupposition of the hands
> proposition (2).
>
> I've seen this form presented as involving an implicit disjunction before
> the explicit argument:
>
> 0) Either there is an external world OR there is not an external world.
>
> The contention (that I support) is that in order to move from (0) to (2),
> we must already come down on the side of the affirmative disjunct, and so
> choose (perhaps because of a really good argument) BEFORE WE START whether
> to accept the proposed conclusion of the argument - we cannot be convinced
> of anything NEW. That's a presupposition. (I'm sorry for the UPPER CASE,
> but my email doesn't let me use italics - sometimes I use '*...*' and
> sometimes capitals for emphasis - i'm not angry!). Accepting the premise
> requires preacceptence of the conclusion, because of the implicit
> presuppositions of the argument - that's why it can be called implicit
> question-begging, but if that title annoys anybody the fact still seems to
> remain that arguments of the form disussed are NOT COGENT and can ONLY
> CONVINCE THE CONVERTED.
>
> I think that Andrew (B) is with me on what I mean by 'presupposition'. But
> the key word in his query is 'refute'. Of course if one refutes the
> presuppositions of an argument then you've gone along way to refuting the
> argument (though perhaps we might find a completely different set of
> presuppositions to support the same explicit argument - I don't know) - but
> what i'm saying is that an argument shouldn't try to prove it's own
> presuppositions by smuggling them in with an innocent-looking premise. Of
> course, i've explained the idea of a single presupposition and Andrew uses
> the idea of the whole set - but I think that, for present purposes, we're
> in tune.
>
> I won't apply this to the tree example yet, perhaps it's obvious. Perhaps
> people could say what they think about what i've said using Moore's proof.
> With regard to calling the tree-sceptic a semantic-sceptic, all I meant to
> refer to was his apparent doubt regarding the meaning of tree and plant
> (assuming that what it is to be a tree involves being a plant, by virtue of
> the ACTUAL meanings). That's another term I have no problem with dropping,
> and of course how things have meaning is a whole new kettle of elephants.
>
> Cheers,
> Daniel
>
> P.S. I've always been a bit confused as to how to use the word 'lemma'. By
> my current understanding I might have used it to describe the proposition
> that would affirm the left hand side of the disjunction above. I'd really
> like to be told by someone who knows absolutely and for sure.
>
>
>
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>
--
Andrew Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900
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