[lit-ideas] Re: (no subject)
- From: Robert Paul <rpaul@xxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sat, 01 Dec 2007 20:22:18 -0800
Walter wrote
‘"A. Kenny's wife was 12 years younger than him and didn't much care
what the Pope thought about celibacy in the priesthood." That statement
is either T or F, even though you may not know how to establish its
truth or falsity.’
Eric Dean says
Consider a generalized form of Walter’s apparently benign assertion:
‘Every statement is either T or F, even though you may not know how to
establish its truth or falsity.’ That is itself a statement, call it S,
so following Walter we might assert that S is either T or F, even though
we may not know how to establish its truth or falsity.
Isn't this though just the principle of non-contradiction [not-(p and
not-p)] or its cousin, the Law of the Excluded Middle ((p or not-p)?
That is, it's a law of logic, not an empirical claim that is established
by evidence of the sort evidence that would support 'There's a fly in my
soup.'
But if we do not know how to establish the truth or falsity of S, then S
might be true or it might be false. If S is true, then Walter’s
assertion about the statement about A. Kenny’s wife is true. But if S
is false, either some statements may be neither true nor false or the
truth or falsity of some statement may depend on our ability to
establish its truth or falsity.
S has the role of an axiom or theorem in logic. A disproof of it would
have to rely on the LEM or the the PNC, for these two 'principles,' as
I'll call them are essential to proofs in math and logic, and it may be
too much to ask of them that they take part in their own destruction.
Thus, before we can confidently assert that a particular statement must
be one of the two, T or F, whether or not we can demonstrate its truth
or falsity, we either need to establish that S, the generalization of
Walter’s assertion, is true, or we need an argument for the particular
statement showing that its truth or falsity is independent of our
ability to establish its truth or falsity.
Discussed above. Willing to trade arguments for a Kawasaki motorbike.
I think the goal of establishing the truth of S, the generalization of
Walter’s assertion, is forlorn. I think that not all statements are
either true or false and moreover some statements are such that their
truth or falsity is not independent of our ability to establish it.
S, insofar as it contains a necessary appeal to both LEM and PNC, was
good enough for Kurt Gödel, good enough to Russell, and good enough for
the likes of me
For example, insisting that a statement like “x does not care much about
y” is either true or false amounts to demanding we accept a false
dichotomy. The question “does x care much about y?” has (at least)
three *legitimate* answers: yes, no and maybe, where ‘maybe’ means
either that x hasn’t considered the question or is considering it but
has not reached a conclusion. Note that “I don’t know whether I don’t
much care about y” is not obviously a denial that I don’t much care
about y because my not being sure might be seen as an indication that I
don’t much care, but it is also not obviously an affirmation that I
don’t much care, since I could say, sometime later, without
contradiction, “You know, now that I think some more about it, I really
*do* care about y.” Thus the ‘maybe’ is important, and not just a place
holder for an epistemological shortfall.
S works best, of course, where predicates are well-defined and the means
of establishing them reasonably clear. And where concepts are too
blurry there will be no T or F decision. Logic, pace Lewis Carroll's
Tortoise, is patient and benign. It doesn't demand on the spot that one
come up with a precise answer to the question, 'Do you care very much
about y?'
Another example is “this shirt is blue.” Holding up a shirt of the
right purplish blue shade, you might get quite a distribution of yes and
no answers to the question of whether that statement is true. My wife
and I will split on this question with the right shade of purplish blue,
for example. On what basis would we decide that that statement is
either true or false? Isn’t the right answer here “it depends”?
'It depends on whom you ask,' is a perfectly good answer to 'which is
it?' Perfectly good in this case, that is; it is not so good an anwer
when the question is 'What's the third number in the sequence of perfect
numbers?'
Thus far, I have been arguing against the first half of S, saying that
some statements may be neither T nor F. But I also believe, denying the
other half of S, that the truth or falsity of some statements depends on
our ability to establish their truth or falsity.
And I've been suggesting that any genuine argument here must appeal to S
(by way of LEM and PNC).
To start, note that S itself is *not* like Goldbach’s conjecture (every
positive whole number is the sum of two primes) which is certainly
either true or false independently of our ability to establish its truth
or falsity. To assert that S is independently either true or false is
to claim that S is not a counter-example to itself. That is not what we
do when we assert that Goldbach’s conjecture is either true or false
independently of our ability to establish which it is, because
Goldbach’s conjecture is not potentially a counter-example of itself.
I'd say, Eric, that from the start you've been confusing a
mathematico/logico principle (or 'axiom') with empirical statements like
'K's wife was 12 years younger than K,'She didn't care much about the
Pope's views,' etc.
There is no particular reason to rule out the possibility that S may be
a counter-example to itself, absent a cogent argument to the contrary.
Indeed, there are plenty of examples in the recent history of logic to
encourage caution here. That is enough, in my book, to conclude that we
should not assume S is true unless we can demonstrate that it is.
S, he said, waving faintly from the farther shore is true by definition.
There. At last.
That does not mean we should assume that S is false, because it is
conceivable that someone can develop a demonstration that shows S to be
true and at the same time shows that its truth is entirely independent
of our ability to demonstrate its truth. It does mean, though, that in
practice we should be circumspect about accepting assertions like
Walter’s about any particular statement.
One could not come up with such a demonstration without using the
principles on which S depends.
[passsages omitted]
In other words, there are a lot of statements for which their truth or
falsity is very much dependent on whether their truth or falsity can
(and will) be established, and by whom.
No objection.
I think all this is worth sorting out because I think such assertions as
Walter’s play an important role in obscuring situations in which the
participants’ desires are what will shape the outcome more than the
objective realities. In such situations, demanding that we acknowledge
that all statements are independently either T or F amounts to demanding
that we ignore the way in which the decision makers’ personal interests
determine the outcome.
Speaking as someone who has had to decide what to do for large, complex
business systems, used in organizations ranging from a handful of people
to hundreds of thousands, in locations ranging from a single small town
to 90 countries around the world, I can say unequivocally that the
failure to recognize when we are imposing our wills on others, as
opposed to when we really are at least trying to trace the contours of
an independent reality, is one of the surest paths to failure.
It takes, however, a lot of nerve to acknowledge that that’s what we’re
doing, i.e. imposing our wills, especially in organizational settings
where the actors are accountable for objective tests of the outcomes of
their decisions. The assertion that all statements are either T or F
independent of our ability to establish their truth or falsity gives aid
and comfort to those who would evade that painful but necessary
understanding by swaddling themselves in a blanket of ostensibly
objective certainty in the present, focusing on today’s comfort rather
than the possibilities of tomorrow’s calamity.
Well, this is a lot to contend with in one day. Thanks. I hope to see
you tomorrow.
Robert Paul
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