[lit-ideas] Re: The Educational Value of Slips of the Whatever
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Mon, 28 Sep 2009 11:19:15 +0000 (GMT)
Apologies for being dilatory. I was hoping something more would have developed
by way of response than this, which I could and perhaps should have posted last
week.
> Yes; but this doesn't mean that validity is problematic
> independently of the factual claims that make up a putative
> valid argument. There's some confusion about this throughout
> Donal and Richard's interesting exchange. I hope I've added
> to it.
>
> Robert Paul
It is true my post confused, or - more precisely - conflated, validity and
soundness. That is because this distinction does not affect the substance of
the POV proposed in the relevant posts.
(1) From 'p and q' (are true) we can validly deduce 'q' is true.
(2) But whether 'p and q' are true is another issue.
The POV proposed is that both the validity of the deduction at (1) and the
truth of 'p and q' at (2) are fallible claims. This is so even if we accept
that the deduction at (1) is valid and is much "less" 'controvertible' than the
issue at (2) (in some sense).
The issue at (2) might be described as the question of the truth of given
propositions; the issue at (1) might be described as the question of the
logical connections between given propositions. That we can make mistakes in
relation to either issue is the POV proposed.
This I think is P's POV, but in his published books it is not asserted in terms
and indeed his thought on these issues evolved: in _LdF_ P appears to take a
stance that chimes with positivistic and indeed Tractarian attitudes, namely
that rational discussion is confined to scientific questions and cannot take
place in relation to metaphysical questions; he also seemed prepared to give a
privileged position to logic and maths in relation to the issue of proofs. This
was not central to the logic that underpins _LdF_ and so Popper could modify
this stance without modifying his falsificationist analysis of the logic of
research. His later position is, explicitly, that rational discussion of a kind
can take place in relation to metaphysical questions, albeit it is on a
somewhat different plane to the kind of rational discussion that can take place
in relation to questions that can be tested by observation. P also, I guess, no
longer assumes (if he ever did)
that logic or maths are 'privileged' in the sense of being fields where what
is asserted is beyond the realms of what might _possibly_ be mistaken. His
fallibilism is thus more explicitly thorough-going.
This POV does not strike many as that plausible in relation to a deduction such
as at (1): for how could such a deduction possibly be mistaken? But the
plausubility of this POV is not best illustrated by (1) but by the following
kinds of considerations:-
(a) how our 'logical thinking' is learned and corrigible in practice (which is
not to deny that some of our 'logical thinking' has an innate basis, as indeed
does our ability to see patterns of a mathematical kind);
(b) the evolution of logic and maths as a subjects with a history, a history
that is crucially one of the correction of mistakes; a history of proposed
'proofs' and of refutations. (Nb. P's view is not the same as Lakatos' in
"Proofs and Refutation" imo).
(c) the validity of the deduction at (1), as with the validity of any
deduction, arises from there being no counter-example where the premisses, if
true, lead to a false conclusion using the deductive inference asserted; just
as the validity of an empirical universal generalisation depends on the
non-existence of any counter-example, so the validity of a logical inference
depends on the non-existence of a counter-example; it is clearer in maths,
where disproofs of alleged proofs are easier to come by than a disproof of the
inference at (1), but even in deductive logic the possibility of a
counter-example to a posited 'inference' cannot ever be wholly discounted - for
the range that the inference covers extends beyond any finite set of examples
that might be given where the inference holds.
There are two technical aspects that P worked on in relation to these kinds of
question which I know of but little about, and here mention: one is 'natural
deduction' and the other is 'logic without assumptions' - his papers on these
have not been published in his books.
RP wrote:
>An argument is
> valid if and only if its premises could not jointly be true
> and its conclusion false. 'Even if your premises were true,
> I wouldn't have to accept your conclusion.' I've never heard
> of the notion of validity itself being question. The
> underpinnings of a formal system, the stopping places,
> cannot themselves be supported in the way that the
> particular deductive moves they themselves support are by
> them supported. But this doesn't mean there's some doubt as
> to whether arguments of the form 'if p, then q, p, therefore
> q,' are valid or not.
My understanding (which may be mistaken) is that, for P there is "some doubt"
always - not in the subjective sense of feeling uncertain (after all, we can
subjectively feel completely certain of what is objectively false) but in the
objective sense that any assertion - including one of the logical connect
between given propositions - has (as P puts it in "All Life Is
Problem-Solving") a "_moment of uncertainty_". Put another way:- any assertion,
including those as to the validity of deductive inferences, is possibly or
potentially mistaken.
Donal
--- On Mon, 21/9/09, Robert Paul <rpaul@xxxxxxxx> wrote:
> From: Robert Paul <rpaul@xxxxxxxx>
> Subject: [lit-ideas] Re: The Educational Value of Slips of the Whatever
> To: lit-ideas@xxxxxxxxxxxxx
> Date: Monday, 21 September, 2009, 4:21 AM
> Donal wrote (some time ago now)
>
> > More philosophically fundamental is P’s point that
> “winning” or the degree of acceptance of an argument are
> [historical] _facts_, and from these facts we cannot
> _deduce_ the _validity_ of what argument is “winning”.
> We may guess, one way or another, but we cannot _deduce_.
> This is enough to show there is a logical gap between
> “winning” and “validity”.
>
> If winning means 'acceptance,' I'd have thought that the
> history of ideas from Aristotle's celestial mechanics to the
> acceptance of phlogiston as necessary for combustion would
> have shown this. That people accept and propose invalid
> arguments isn't really news.
>
> > When assessing “validity” we look for critical
> grounds, for what actually ‘supports’ (non-inductively,
> of course) the argument or theory under consideration. The
> answer is that whether an argument is genuinely valid is
> always a guess of some sort. Even if some of these guesses
> seem incontestable, the history of ideas is littered with
> the supposedly incontestable that was then overturned, and,
> perhaps more important philosophically, logically these
> guesses cannot be demonstrated – even deduction itself,
> surely that most sound of guesses, cannot be deduced
> deductively without the argument being fatally circular.
>
> If for some, deciding whether an argument is valid amounts
> to a guess, a hunch, or a wild surmise, this would be an
> interesting fact about those who proceed this way, not about
> how validity is determined. I don't know what 'deduction
> itself' is supposed to mean: although validity is predicated
> of deductive arguments in 'formal' logic, validity itself is
> a simple notion that applies everywhere. >
> What happens when we worry about what lies behind the
> axioms of a system is illustrated by Lewis Carroll's 'What
> the Tortoise said to Achilles'
>
> http://www.mathacademy.com/pr/prime/articles/carroll/index.asp
>
> > In truth we may often accept an argument _because it
> is valid_, but it would be wrong to conclude that because we
> accept it the argument therefore is valid.
>
> Right. Was Richard questioning this?
>
> Richard himself now appears appears
>
> >> Perhaps valid arguments may be proposed for
> questions like "Is it better to get up early or late in the
> morning?" Popper, I assume, however, is more interested in
> questions of fact like "Is the universe expanding?" And for
> that there are good and less good arguments, but no "valid"
> arguments. The validity of arguments about facts can only be
> judged by Laplace's Demon or a similarly omniscient entity.
>
> Laplace's Demon is invoked to support one simple-minded
> version of determinism: suppose that such a demon knew
> everything (whatever that might mean) about the past and
> present states of the universe. The supposition is that such
> an omniscient creature would then be able to predict all of
> its future states. This creature's knowledge would help it
> to construct sound arguments, not merely 'valid' ones about
> 'facts,' and surely its the soundness of arguments that's
> here being confused with validity. A sound argument is a
> valid argument whose premises are true (however their truth
> is determined), and surely such truth-supporting facts are
> essential to determining whether an argument in, say,
> physics (where 'arguments' are perhaps more rightly called
> explanations). Validity all by itself is not enough.
>
> > P would agree, I think, with this last sentence
> provided we understand “judged” to mean “conclusively
> judged”. But we can, and do, make provisional judgments
> about such facts. Even whether "Is it better to get up early
> or late in the morning?". This question too, insofar as we
> treat it as a question fact, cannot be conclusively but only
> provisionally judged. Even where there are only "good and
> less good arguments" [getting-up-early being a case in
> point; science in general and metaphysics in particular
> being even more crucial cases] we may still speak of
> validity, and even make judgments as to validity, albeit in
> a non-conclusive sense.
>
> The Reed Institute
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