[lit-ideas] Re: Grice and Popper on mathematics
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Fri, 7 Jun 2013 22:16:06 +0100 (BST)
________________________________
From: "Jlsperanza@xxxxxxx" <Jlsperanza@xxxxxxx>
>On the other hand, Grice was more interested in implicatures>
Ah. The dry, understated Oxford wit of my youth.
>There are three apples in the basket.
---- Therefore, there are two apples in the basket.>
Is this "implicature"? There are senses in which the conclusion is false btw -
namely where we take "There are.." to mean "There are in total..."; and this is
a common sense way to take the claim - for when we ask how many soldiers there
are guarding the gates (which we are about to attack) we do not take kindly to
the scout who reports that "There are two" when in fact in total there are
twenty. His defence, that as there were twenty therefore there were two, would
get short shrift.
What is noteworthy about Popper's view is that it distinguishes levels at which
similar-looking 'content' operates: when I calculate '2 + 2 = 4' I am doing
something distinct from a computer that performs the same calculation - the
computer operates this content only in World 1 terms (though I can interpret
its operation in World 3 terms) whereas I understand the content in World 3
terms. This is a world of difference from the POV of a theorist of knowledge
(or epistemologist) which is what Popper centrally is. [Grice is a botanist of
linguistic minutiae in comparison]. If a flaw in the computer's World 1
programme causes the computer to calculate "2+ 2 = 5" the computer will not
baulk because it realises that this violates some World 3 principle - but a
human who, through fatigue, wrongly wrote "2+ 2 = 5" might baulk and even
correct the error after it has been made because they realise it is a mistake
in World 3 terms. So the computer may be much more
reliable when it comes to the World 1 level of processing [it may be less
likely than a human to mistakenly, as a very tired human might, put down '5'
when it meant '4']; but in terms of being able to correct itself, by way of
grasping some World 3 principle or content, the computer is not so much merely
less reliable than a human but incapable of doing this because World 3 is
beyond the computer's grasp [what a computer can 'grasp' are physical
instructions set by World 1 programmes, which can be based on or incorporate
World 3 principles and content, but it cannot grasp World 3 principles or
content].
As to dull Frege, Popper somewhere admits that his World 3 is closer to Frege's
'Dritte Reich' than to any other precursor of his World 3 theory, such as may
be found in Plato or even Hegel. The other close precursor is Bolzano.
>On the other hand, Popper, typically, is interested in his own
concoctions. He divides the realm of reality in three: and thinks that Euclid's
theorem belongs in World 3 -- which is totally disrespectful, to, inter alii,
Euclid.>
There is nothing disrespectful to Euclid or his theorem by saying it belongs in
World 3 (and when I say nothing I mean like, er, "totally").
>Popper then dismisses multiple realisability of functional states
(software) in hardware (brain), and thinks he can prove something against
'materialism' (or monism, as he prefers, since he is a triadic dualist) by
pointing
at abstract ways in which 'abstractions' (like Euclid's theorem) do not
need this or that brain realisation (in Euclid's brain, originally).>
Yes and no. Popper makes the point that as the brain is finite in physical
terms, the brain cannot physically represent infinity - the content of an
'infinity' cannot be content that is embodied by a finite physical system like
the brain. But a monist or materialist might seek to get round this by
insisting on a finitist mathematics. The more decisive break with a materialist
or monist is in insisting that the content of an 'infinity' may be valid and
may exist as content to be explored - but only if we accept such content is not
reducible to World 1. But nor is World 2 enough to understand the objective
properties of such content. Such content needs to be understood in World 3
terms. (The discussion of Euclid's theorem seeks to illustrate this.)
If this is so, then the problem is changed from one where we ask whether the
brain is needed in some sense to one where we distinguish how it is needed and
how it is not needed: it is certainly needed as a substrate, in much the same
way the field of physics is needed as a substrate for whatever exists
biologically [remove that physical substrate and nothing biological can exist -
but that is not then to say that the existence of biological entities is purely
a matter of their physics].
Remove World 1, more specifially remove World 1 brains, and nothing of a World
2 can exist - but that is not then to say that what goes on in World 2 is
purely a World 1 matter. And this anti-reductionist approach [which is
therefore against reductice materialism] gets even more against reductive
materialism when it emphasises how World 2 processes, such as Euclid's, cannot
be understood without realising these processes concern World 3 content.
Now - just how is the content of "2 + 2 = 4", or of Euclid's theorem, merely
physical? And is its (World 3) content physical at all? Popper suggests not.
Donal
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