‘"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.
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.
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 ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html