[lit-ideas] Re: Philosophy Of Maths
- From: wokshevs@xxxxxx
- To: donalmcevoyuk@xxxxxxxxxxx
- Date: Tue, 17 Jun 2008 16:37:26 -0230
A very fine, clarifying account provided by Donal below, imo. The same issue
that Donal arrives at regarding mathematical knowledge is also an issue in
moral knowledge. In *Truth and Justification*, Habermas discounts realism in
the moral realm and goes the anti-realist route. (Moral judgements are
justification-immanent, not justification-transcendent like truth.) And yet,
he grants that justifiable validity claims to moral rightness - i.e., those
upon which we can agree as to their generalizability (not "universalizability"
a la Kant) under idealized epistemic conditions of symmetry and reciprocity
-possess both a moment of construction and one of discovery. Our understanding
of math may not be all that dissimilar from our understanding of morality. I
hazard the guess that Habermas would admit moral knowledge into Popper's "World
Three," on the assumption that Donal's reconstruction of Popper is accurate. Its
moral inhabitants include all actual and possible moral judgements that satisfy
epistemic conditions of generalizability as established within discourse.
Thanks to Donal for some fine informative philosophizing here.
Walter O.
MUN
Quoting Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>:
>
>
>
> --- On Sun, 15/6/08, wokshevs@xxxxxx <wokshevs@xxxxxx> wrote:
>
> > Almost makes perfect sense to me. The fact that I don't
> > know the constituents of
> > DNA does not entail there is no objective knowledge of DNA.
> > The harder part is
> > generalizing my ignorance across all cognitive beings,
> > past, present and
> > future. In what sense would "knowledge" of DNA
> > "exist" in such circumstances?
> > Surely only as a possibility. And is possible objective
> > knowledge really
> > objective "knowledge?"
>
> The most important of these interesting comments is, to me, "Surely only as a
> possibility".
>
> While one might devil's advocate Popper's views ad nauseum (and his views
> are, of course, worth this), a central problem is to address the existence of
> "objective knowledge" along a scale from 'actualised' knowledge [e.g.
> 'knowledge' (or theories) we have reason to believe were, or have been,
> encoded in W1 or 'thunk' in W2] to "objective knowledge" whose 'reality' is
> not (as yet?) encoded on W1 or W2 and so, for example, is, at best, something
> that exists in "W3.3" [i.e. the realm of "objective knowledge" that has so
> far not been encoded in W1 or W2 in any way, and in this sense has never been
> "actualised" by humans].
>
> We might then ask of this "W3.3" - is all of it humanly accessible i.e.
> capable - at least potentially - of being "actualised" by humans? Even should
> we say 'yes' to this question, we might be invited to say where on the scale
> of possibility this "potential" exists? [Clearly anything that actually
> exists must be something that could possibly exist; but the mere fact
> something could possibly exist hardly gives in itself any clue to the
> likelihood that it might, or probably does - or will, exist].
>
> Take Popper's example of the sequence of natural numbers. He seems to suggest
> that this sequence did not exist in the world before we invented it [it did
> not exist at the W1 'Big Bang' or whatever; it only came into existence
> through an interaction of human W2 grasp of the concept of enumeration and of
> feedback between W2 and W3 constructs developed from such a concept]. He
> seems to suggest, however, that while the sequence does not predate our
> invention, there are objective properties to that sequence [e.g. 'odd and
> even numbers', 'prime numbers'] that come into existence along with the
> sequence i.e. these properties are there whether we realise it or not and
> whether we encode them as such or not.
>
> But in what way are they not encoded in the enumerated sequence of natural
> numbers? If they are there to be discovered, why can't we equally say that
> the very sequence of natural numbers itself was there to be discovered i.e.
> the sequence was _there_ to be discovered (as were the primes and odd and
> even numbers contained within it) even before we invented a means to
> spotlight its existence?
>
> I write this partly because I accept the following at face value and as
> true:-
>
> > Note that to caricature a position is not necessarily to
> > demean or discount it
> > in any way. One can believe the position or idea to be
> > itself quite profound,
> > as I do in this cae, and try to gain further clarity about
> > it by exaggerating
> > some of its features within analysis.
>
> We are tottering it seems on the large issue of realism/anti-realism in the
> theory of knowledge and, in particular, of mathematical knowledge.
>
> Donal
>
>
> __________________________________________________________
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>
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