Putnam, Kripke, and Logic

So this post is going to cover a number of topics, but it will center around logic and epistemology by focusing on this article in particular.  Here is the plan of attack: I am going to summarize the article as best as I can and then provide some commentary afterwards.  As to whether you read the whole article or just my summary, that choice is yours.

Hilary Putnam is a philosopher of immense talent and wields that talent to argue for positions that are not that common.  The article above sketches the Putnam-Kripke debate on logic, epistemology, and quantum mechanics.  In particular, Putnam argues that quantum mechanics shows us that we need to revise logic as commonly conceived.  The details of the account are not particularly important since Kripke responds with a strong critique.

Kripke argues that if we accept Putnam’s argument, then we must also conclude that 2×2≥5 (see the bottom of page 7 to the top of page 11 for the details)!  Moreover, what Putnam does is assume a number of interpretations of quantum mechanics are simply wrong without arguing for such a conclusion.  Kripke retorts by saying that Putnam does not bear his burden and since his argument is missing on details, it fails as a whole.  Nonetheless, if Kripke’s argument of where Putnam’s argument leads is successful, then that seems to put the nail in the casket on the matter.

However, there is a larger issue at stake here and that is one on whether logic is empirical and one can adopt a logic.  On the one hand, Putnam uses illustrations of how we use to think certain mathematical truths were necessary but now we do not accept them (for instance, straight lines and non-euclidean geometry).  Another example in the paper is whether “all P are Q” implies “some P are Q”.  However, we know that isn’t the correct due to empty terms.  Namely, “all deserters will be shot on sight” does not imply that “some deserters are shot on sight” since the very rule might keep people from deserting.  However, Kripke argues that it doesn’t make much sense for empirical considerations to change our logic nor does it make any sense to adopt a logic.  In particular, there simply is reasoning and while specific systems may or may not capture accurate reasoning, it is not as if one can somehow stand outside of logic and simply adopt one logic amongst many logics.  As a great example, I recommend you read the bottom of page 13 to the bottom of page 14 (apologies as the paper gives weird formatting when I try to copy and paste for quote).

There is then talk about bivalence and the future and how this might tie into whether one can reject bivalence based upon empirical matters.  The author then tries to suggest a mediating position by saying that logic as such might be a priori, but the particular instances of logic and the details might be curtailed by empirical considerations.

On the matter of Putnam’s argument and Kripke’s response, I find Kripke’s counterargument to be solid and without any obvious objectionable point.  He seems to assume Putnam’s system and then reductio it by showing that it leads to a person concluding that 2×2≥5.  However, we certainly don’t want to do that (or, at least, I don’t want to do so), so we should reject Putnam’s argument.  Now, maybe Putnam can try to patch up his account and avoid this objection, but it’s not immediately obvious how he would do so and so we should reject Putnam’s particular argument.

As to whether logic is empirical and one can adopt a logic, I also find myself siding with Kripke on the matter.  As to the straight line example in non-Euclidean geometry, I’m not so sure this is an empirical matter.  If math just is logic, then it follows that Gauss’ discovery of non-Euclidean geometry and the implications for truths that we once thought were necessary is simply a matter of logic, not looking around at the world.  What follows then is that our logic is clarified simply by our reasoning in that our particular system of logic did not match correct reasoning.  As to the principle of subalternation for universal categories (all P are Q implies that some P are Q), this is again a matter of reasoning correctly and thus not a matter of empirical discovery.  While it certainly might be the case that someone discovered this is wrong by the whole deserter example, what seems to be going on there is that reality is reflecting logical rules and so what we are really doing is discovering correct reasoning.  However, that is not empirical matters altering or curtailing or whatever our logic, but simply reflecting the way logic is.

However, on the point of logic being overturned by empirical matters, we also have the infamous case of W.V.O. Quine.  In particular, Quine argued that logic simply is a matter of scientific investigation like every other matter and this entails that logic is open to being changed by empirical discoveries.  But to steal an example from Mike Almeida (see the fifth comment) it seems that we wouldn’t want to reject p–>p even if does solve certain empirical difficulties.  However, I’m not sure that entails that logic is a priori.  While certain empiricists might respond by saying that certain parts of logic (all?) are analytically true, we can sidestep the debate by showing that if empirical considerations can change logic then the law of non-contradiction might be dropped and so the statement could be analytically true and we could reject it in certain instances.  Another objection might be that p–>p is not known a priori but it is so confirmed a posteriori that is has an intrinsic defeater defeater for any empirical matter.  Why should that be thought to be the case though since certainly we don’t want to say that certain scientific theories have intrinsic defeater defeaters merely because they have been confirmed a number of times.  In fact, it only takes one exception to show it is false.  While it is the case that every theory runs across certain anomalies (see Kuhn’s The Structure of Scientific Revolutions), that is a sociological fact and not one that can be used to show that empiricism can be salvaged from this consequence.  If these facts conflict with empiricism, then so much the worse for empiricism.

Lastly, Stairs’ discussion of bivalence and the future does not contain a lot of meat and so I cannot really interact with it much.  He argues that if one combines presentism and indeterminism, then bivalence is not the case about the future.  However, (i) that’s not immediately obvious, (ii) he gives no real argument for the claim, (iii) there are people who hold to all three of those positions and defend them (for instance, William Lane Craig), and (iv) it doesn’t really seem like those matters are really empirical ones and thus it’s not obvious that they would provide a counterexample to Kripke’s position.

All in all, I enjoyed the article and I commend it to anybody who has time.

Feel free to register your thoughts.