[hist-analytic] Comments on Aune's ETK Chpt. 2
Baynesr at comcast.net
Baynesr at comcast.net
Fri Oct 16 13:47:41 EDT 2009
Here are a few comments on the second chapter of Bruce's book. I'm not finished with the chapter, yet. These are off the top of my head and by no means my final view. Hopefully a couple will be of some interest to someone. Disregard the comments on Kripke as Bruce and I are discussing them and these have been covered.
Bruce says (p. 38) that I learn some a priori truths from my teachers. But I think this can be misleading. I do not learn the truth of an a priori proposition from having a sentence which expresses it uttered by one of my teachers. Knowing amount to more than being told, even if by a usually reliable informant. If I am told that the theory of types is consistent, this is nothing I’ve learned. To do that I have to march myself like a soldier through the proof with comprehension.
Bruce cites in a footnote Kaplan to the effect that ‘I am here now’ is analytic. (p. 39) This is certainly nothing that Kant would say. Being here now does not belong to the *concept* of myself. The concept is one thing; I am another. The concept corresponding to my self, and thus, the unity of apperception is unrlelated to whatever place ‘here’ may refer to. Now if it refers to wherever I AM, this is not a place subject to rigid designation. There are no terms usable for the purpose of "fixing" the reference of ‘here’. Since it cannot be fixed, being part of my concept is an absurd proposal. This of course assumes rigid designation, which I may question at some future time. I know of nothing that would suggest that either Kaplan or Kripke have read Kant, let alone understood Kant’s theory of "reference." Bruce, also, says that we can know on the basis of the authority of someone who tells us that something is true. (p. 38) Knowing that what I’m told is true is different? How does knowing that what I’m told is true differ from knowing something because I am told? There is a big difference here. I can’t know the truth of the Booga Booga religion because some Boogan Boogan tells me it’s true. It has to BE true and I have to have other means of knowing this in order to count it as knowledge than being told.
Bruce says that Kripke has an argument against Kant’s view that knowledge of the length of the meter stick in Paris is a priori. I can’t think of a reason for thinking Kant would agree. Kripke himself argues that the meter stick in Paris can be known to be a meter long because we can measure it. This would be Kant’s position too, in my opinion. I see no reason for believing that Kant would hold that *knowledge* of the length of a meter stick is a priori. Remember Kripke’s argument is based, mainly, on using a ruler; and this is directed specifically against Wittgenstein, whose views on the a priori must be distinguished from Wittgenstein. Moreover, even in the case of Wittgenstein the point is not that the fact that the meter stick is a meter is a priori, rather Wittgenstein’s point is that we can’t say that the meter stick is a meter long, nor that it is not. This cannot be taken as an assertion about what the length of the meter stick is; let alone that it is a priori. Kant is a lot tougher nut to crack than hitting it with a rubber hammer, which I think Kripke is doing, if Bruce is right in his characterization of Kripke’s actual position. Most all of Kripke’s references to Kant he owes to others, and there is little reason to believe that Kripke would read anyone as "old fashioned" as Kant. Moreover, Bruce cites pp. 97-105 as the place where Kripke refutes Kant, but there is no mention of Kant, nor do I believe the position being attacked has been shown to be attributable to Kant. Reading Kant is, always, helpful; perhaps some citations from the "old guy" himself might prove useful.
I won’t discuss rigid designation in any detail here, but I have a slight problem with Bruce’s characterization of Kripke’s argument, the one he describes as taking place in Kripke (1972, pp. 97-105). The way Bruce describes it (Aune p. 41) it seems that because we know Franklin was necessarily Franklin that we "therefore" know the necessity of Franklin’s being the person who invented (discovered?) bifocals. Now from (x)(x=x) it follows that, given that Franklin is in our domain of objects, that Franklin is Franklin, but it does not follow that Franklin discovered bifocals. If a def. des. Is a rigid designator then if two such designators designate the same thing in this world, it can be argued that they will designate the same thing in any world, since a rigid designator by definition designates the same thing in all worlds. That may be a better way of expressing it, but I’ll check it out. The problem is there IS a step that goes unmentioned: if two designators designate whatever they do in this world in all possible worlds, and they designate the same object in this world, then they designate the same thing in all worlds. But what if I should deny this!
Suppose I say, that just because two designators designate the same thing in this world, and those designators are rigid, WHY should I believe they designate the same thing in all worlds? Now it may seem obvious. But it also seems obvious that if ‘p’ then ‘p or q’, but even here I rely on truth tables to justify my point. What do I appeal to in order to justify the INFERENCE to the conclusion that the two designators designate the same thing in all worlds, and that that they do do so is necessary a posteriori. It may be obvious, but do we rely on intuition, definition, or do we revert to some theorems in one of many of the modal systems where rigidity doesn’t ever really enter? Now a couple of trivial points. Just as an aside, the meaning of ‘same’ in ‘designates the same thing in this world’ may not mean what it does in ‘designates the same thing in all worlds’. This is a complex issue; the answer isn’t obvious to how we go about ensuring identity of meaning. But let’s pass on this.
First, Aune cites Nicod’s system using the Sheffer stroke. Trivial point: The pagination is given as p. 26 in Kneale and Kneale, but it is in fact p. 526. Second, he says that ‘if…then’ is indicated with a horseshoe. This is sometimes the case, but if I’m not mistaken ‘if…then..’ is generally distinguished from ‘implies’ and it is ‘implies’ that gets the horseshoe. If there is a doubt take a look at Russell’s Principles of Mathematics 1903 "Implication and Formal Implication." It’s an old book, but I can’t recall a case where ‘if…then…’ gets the horseshoe, but maybe. Any examples? Reichenbach did do this occasionally. It Is not uncommon to think of entailment is just a bracketed expression where the primary operator is material implication, but where outside the left bracket we have a necessity operator. Here there is no need to make a distinction. As for Nicod’s axiom, Bruce says it is hardly self evident. I would say that once you understand it is self-evident. Some people find the axioms of Riemannian geometry difficult to believe but easy to understand. This is a sort of complementary case.
Aune seems to hold it against rationalists that they have not "supported their conviction that all logical truths can be derived from self-evident axioms…" p. 46 However, at one point Russell made this claim and he was a "dangerous" empiricist who was proven to be wrong by an idealist and, probably a Kantian, Godel. In addition, it was by rational means that undecidabiliy was proven, not empirical means; I think this strengthens the rationalist’s case. I can’t recall a rationalist since Godel who has, actually, made this claim on the basis of axiomatic systems, which no longer have the "punch" they used to. It is one thing to say: "Give me any sentence of logic you care to and I will show it is valid, if it is valid." It is another thing to say "I can show you that all valid sentences of logic are valid."
Bruce has gone "hog wild" over the necessary a posteriori, something I reject in toto. He suggests that modus ponens is an example; but setting aside my own rejection what is it that brings him to this conclusion. I’m not sure the text makes this clear. Maybe this could be clarified. If Bruce can show it is a valid argument form, I don’t see how it can be a posteriori, but some clarification might be in order.
Aune in his attack on rationalism draws attention to religious devotees who lob off people’s heads, for example, in order illustrate, I believe, the fallibility of moral appeal to ethical intuitions. He notes that various cultures believe in different things and all this may be just a matter of social perspective. He notes that there are non-Euclidean geometries that dispel the certainty over certain axiomatic systems, thereby showing that which system we adopt is relative to our interests, such as figuring out the nature of physical space. But I find this approach, if not unconvincing at some level. A bit disturbing. What if anything makes it wrong to lob off someone’s head for some moral reason, empirical or otherwise? Aune seems to embrace utilitarianism without mentioning its flaws. It appears that outside of, possibly, narrow cultural centrism (this cannot be dismissed on Aune’s principles), there is nothing wrong with lobbing of people’s heads. Maybe one day we will discover it was all for the best. If a person does not believe that there is a fact of the matter in ethics, then the grumble seems to be that pain is bad. But what sort of pain; and what’s so bad about pain if there are arguments, utilitarian arguments that may support lobbing off heads for, allegedly, screwy religious reasons combined with reflections on the pain of infidelity? Anyway, I think jumping back to ethics from Riemann doesn’t really advance the issue. I think there are some things that are immoral. There are some act so horrendous that no adjustment for context and culture can obviate their validity. Yep, I’m an ethical absolutist in a sense.
I find myself writing a lot about Aune. Here’s why. I never turn a page without having had two ideas I’ve never had before. So, while my strong disagreement with him on some issues should be taken along with the fact that his work is provocative in the way that the last 500 page ‘jingle’ on the so and so puzzle is not; "outsiders" will know what I mean.
Aune has an argument the rule ‘~(p & ~p)’ is cannot be self-evident because it is false on certain assumptions. We have a sentence in a sphere (‘The sentence in the rectangle is true’) and another sentence in a rectangle (‘The sentence in the circle is false’). From these two we derive the contradiction ‘(p & ~p)’. He seems to believe this is a counterexample to the "law" ‘(p)~(p & ~p)’ because we have it that (Ep)(p & ~p). I don’t get this, actually. By the truth tables ‘(p & ~p)’ is false, so the law is not refuted. As for the derivation, what it shows is that one of the two statements (or both), either the one in the rectangle is false or the one in the circle is false. Which one is it? Why the one in the circle, of course! Just kidding. All kidding aside, here I think we will have trouble with the identifying the referent of the definite description in either without violating something like Russell’s "vicious circle principle," that is, as long as we work in Russell’s framework. If we take another approach to the paradoxes, say, Zermelo, then we rule out this possibility another way. Since this rule is derived in some systems and not in others, few would say that in the absence of an axiomatic system that it is self-evident and, therefore, true. It may be self-evident but derived. It doesn’t occur among Hilbert and Ackermann’s axioms, e.g. In their system as I recall from that "dreadful" book their axioms for the sentential calculus they either have no such principle, at all, or, if you insist, it can be derived from logical addition, the principle of excluded middle, and DeMorgan. I’m not sure they do it this way, but it can be done. But this takes us in a direction away from epistemology. If Aune could show that ‘p & ~p’ is ever true. Finally, notice that without accepting the law of excluded middle Aune’s argument can’t really get off the ground. So one might argue that either the law of contradiction or that of excluded middle must be accepted, and accepting it doesn’t require certainty or self-evidence. By self-evident I take it that Bruce means something like ‘known true by intuition’. If you look at the truth tables then there seems to be "no way out," by intuition. Eventually, we will get back to intuitions, most likely.
Suppose we can derive a contradiction from the law of non-contradiction, or in some other way arrive at a contradiction. Aune says that we can rule out these sentences because they are contradictory. (p. 54)But advocates of the self-evidence of logical principles are not ruling out sentences, otherwise there would be no proof by reduction ad absurdum. So what are they ruling out? Answer: taking contradictions as true, that’s all. Further, if we don’t rule out as false apparent counter instances to the law which are derived from certain other propositions, then we could never rule out these propositions by reduction ad absurdum. We would have to rely on self reference. Why are these more important to Aune than any other sentence(s) from which a contradiction is derived?
I think I take a position something like the one Bruce argues against. But my position is not that there is a special class of propositions that intuition justifies, but rather that certain inferences are justified by means of a rational intuition. Now he is sure to wonder what a "rational intuition" is, but that is for another occasion. The point is that, as a rationalist, I’m not affirming a special class of sentences; instead I am defending one way of justifying a connection between sentences.
Aune argues that where ‘P’ has the truth value ‘indeterminate’ the ‘P v P’ can not be either true or false. Two points. First, if you mean by ‘indeterminate’ a truth value, then the claim is trivial. Second, bivalence is not the same as the law of excluded middle. If you accept bivalence and you accept it that both occurrences of ‘p’ mean the same, then the principle will hold, even though you may not know which of the two truth values hold for ‘p’. Again, what Bruce seems to be denying by interjecting ‘IND’ is not the principle of excluded middle but, rather bivalence. If he accepts bivalence, he must accept ‘p or ~p’.
Here is a comment I don’t want the reader to make much of but may be worth mentioning. Aune mentions that some people, e.g. Sorensen (2006) think vague sentences are either true or false. But if a sentence is vague, it is reasonable to suppose that there I no proposition it expresses. If the sentence does not express a proposition, then it might be maintained that it has no truth value. If it has no truth value it cannot provide the sort of counterexample Aune is looking for.
At one point, Aune says that if a proposition has the value IND then the principle of excluded middle fails. But now that he has introduced a new truth value, of course it is going to fail. The relevant "law" would be: ‘p v ~p v INDp’. By keeping bivalence constant and illicitly introducing a new truth value without adjusting bivalence he achieves his end surreptitiously.
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