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I've recently read that Saul Kripke has had a huge impact in philosophy over the last century, especially philosophy of language and "truth". My question is whether reading his works (or studying it through other texts) is something you would recommend to a person with a pure math background and not really used to "philosophical reasoning" (by which I mean that reading through a proof is much much easier than following some deductions in philosophy).

I am very interested in knowing exactly what Kripke has done and why it is important. If you are going to make some recommendations assume I know enough math (Goldblatt's Topoi: The categorial analysis of logic introduces Kripke semantics) and I am at least familiar with some of the history of philosophy of language and logic (Russell, Wittgenstein, ...).

In summary, I want to know if reading his works will be something different than reading a math book on set theory and only leave with the "math" part of it.

Thanks!

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Yes. Reading Kripke's works is very different than reading a math book on set theory, principally because his interests are in "meta" issues, and his works (books), are comprised of his lecture series, in many cases. But if, you do have an understanding of Philosophy of Language and Logic that's derived from your understanding of Frege, Russell, and Wittgenstein, then you will probably find it's easiest to begin with his book "Naming and Necessity," Saul A. Kripke, Harvard University Press, Blackwell, 1980. And of course, I recommend it. It is regarded as one of "the most important works of Philosophy, of the Century!" It's well-worth the effort.

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Saul Kripke died last month, after a very respected and productive philosophic career. An in depth retrospective on his contributions is a very timely request.

Here are three obituaries that summarize what Kripke contributed to philosophy:

A read thru these obituaries will quickly answer the original question posted: YES Kripke's philosophical work is very different from reading a math textbook on set theory.

However, Kripke also wrote and lectured on math subjects as well as philosophical subjects. You will not find the math in his two published books, but scattered among his smaller papers, and the lecture summaries the Saul Kripke center has compiled. If set theory is your primary interest, then WHAT your interest is then matters. A contemporary math textbook would be a more useful reference for what the consensus view is NOW on set theory. The point of reading a particular thinker is to explore the history of that current consensus view, and understand how it was developed. And whether you agree with that consensus or not.

As this is a philosophy forum, I will focus on Kripke's philosophic contributions, and try to elaborate on the summaries of his work in the obituaries. The obituaries mostly pass over Kripke's book on Wittgenstein and private language, noting that his views are controversial among Wittgenstein scholars. This work is not what Kripke's reputation is based upon. It is instead his Naming and Necessity which is considered a critical work in the philosophic canon.

Kripke's N&N continues today to be a vibrant subject of discussion among the philosophic community. Here is a sample of recent work focused on him:

This is a grab bag of published work. Reviewing is reveals several things:

  • The best recent retrospective seems to be that by Hughes, from 2004
  • There is a lot of dispute both about what Kripke argued (two of these papers take opposing sides on whether Kripke used Leibniz's Law of Identity or not in his reasoning), and the validity of his arguments (one of these papers challenges Soames interpretation and rejection of one of Kripke's arguments, where Soames is seen as one of Kripke's best current interpreters and scholars. Several others, including both Hughes and his reviewer also challenge aspects of Kripke's arguments).
  • WHY Kripke was writing, what he was trying to defend, and against what, is only implicitly referenced in most of these papers. I will try to provide that meta narrative, and then give my own take on Kripke's accomplishments.

The problem

Analytic philosophy was the dominant movement within philosophy for the 20th century, and the most clear articulation of it was from Logical Positivism. LP used absolutist definitions to justify its approach to philosophy, which was primarily logic based, and which treated science as a favored stepchild of logic. LP also used these absolutist definitions to try to banish most other approaches to philosophy.

However, non-analytic philosophers pushed aback against the LP attack, and the pragmatic empiricists in particular basically broke the LP movement. Popper showed that science uses refutations, not confirmations, and that all of science is radically contingent. This breaks the "necessity" needed to apply logic to this world. Hume was referenced in that objects in our world are "bundles", not reducible to the same entity over time, hence "we cannot step into the same river twice". So for our world, A=/=A. And Quine argued that as we each have to make guesstimated inferences as to what any language term refers to, all language is a personal inference, and A=/=A between any two language speakers so language also cannot support logic. Quine argued that this broke the analytic/synthetic distinction, and that all knowledge was synthetic -- which most philosophers considered a step too far in his reasoning, but the A=/=A of language does not require accepting Quine's total breakdown of the distinction. And for any logic to apply to our world, there was increasing recognition that "identity" of an object requires it have an "essence", but essentialism is an Idealist concept, and the vast majority of philosophers have adopted physicalism as a worldview.

The consequence of this pragmatic empiricist pushback against LP, is that the applicability of analytic philosophy to our world was is question. Most analytic philosophers tried to adopt a "descriptive" approach to identity, where identity is established by some sufficient fraction of the descriptive elements applying. Kripke appropriately found descriptivism to be far too loose to support analytics -- as The Ship of Theseus and part substitution thought problems readily reveal (he spells out a set of critiques of descriptivist identity in N&N, which these papers basically all agree with). So he set out to challenge the contingency of our world, in order to salvage analyticity. In addition, he also wanted to defend the ability of selves to be causal, in contradiction to the reductive aspects of physicalist Identity Theory. Kripke therefore set out to find a place for "essences" in contemporary philosophy.

Kripke's primary method to do this, was to offer thought problems that appeal to philosophical intuitions of their being necessarily true. He also implicitly inferred essence for selfhood from this. Kripke was writing before the widespread acceptance of non-reductive (emergent) physicalism within philosophy, so he did not explicitly spell out an emergentist justification for his approach. If he were writing today, I believe emergence would figure prominently in his argumentation, as a method to incorporate essences into physicalism.

The linked papers about Kripke mostly argue that he succeeded in this endeavor. However, they are almost exclusively written by philosophers operating in the analytic tradition. It is far from clear that any pragmatic empiricists would accept any of Kripke's arguments. Philosophic intuitions, in particular, carry little to no weight for pragmatic empiricists. So -- one can accept the majority view of analytic philosophers that Kripke was successful, hence this is his value today. Or -- I offer here a summary of the pragmatic empiricist rejection of Kripke's effort to patch analyticity, hence Kripke could be seen as one more unsuccessful effort by analytic philosophy to justify itself.

Empirical Critique of Kripke

Kripke bases his argument on a variety of thought problems of identity, which he claims are necessary:

  • Water is H2O.
  • Heat is molecular motion.
  • Gold is the element with atomic number 79.
  • Hesperus is Phosphorus
  • cats are animals
  • Samuel Clemens is Mark Twain

The first four of these all illustrate aspects of the same problem in Kripke's thinking, and that of most analytic philosophers. Kripke and analytic philosophers focus their study on MATH and LOGIC, not on science. There is a common assumption among analytic philosophers that even if events in our world are contingent, that there are unalterable LAWS OF PHYSICS behind them, and that those laws will fix the relationship between Water and H2O, and Gold and an elemental number. BUT -- "laws" in science are not unalterable. They are not necessary, but are just regularities. They are the result of fundamental symmetries which were discovered in Noether's Theorem https://hackaday.com/2016/06/14/symmetry-for-dummies-noethers-theorem/. So -- "laws" are derivative, not primary. AND -- the symmetry that creates laws, is spontaneously broken, in every case, so our laws all have exceptions https://www.jstor.org/stable/41065.

Note, if neither laws nor symmetries are necessary, then the physical relation between things that Kripke lists cannot be necessary either. The intuitions of analytic philosophers on this question, are wrong.

Addressing his specific examples -- if the values of the constants of the Standard Model of Quantum Mechanics were VERY slightly different, and per physics thinking, they are contingent, and COULD have been different, then H2O would not create the properties of water. Similarly, element 79 need not have produced the properties of Gold.

It would require some more complex change in the nature of physics for heat to not be the result of molecular motion, and it is hard enough for physicists to come up with tweaks to the Standard Model that even allow for any matter to appear at all, so an alternate physics speculation that produces a "heat-like" phenomenon that isn't molecular motion has not to my knowledge been developed, but there is no theoretical obstacle to this.

The details of orbital mechanics in our world would prevent two stable planets around the sun in Venus's orbit, and would not couple them to the Earth's rotation, hence in our world, we have discovered that Hesperus must be Phosphorus. But it would not require absurd tweaks to gravitation and our solar system structure to allow for a two planets to orbit in Venus's orbit and be stable for millennia, and some rotation rates of the earth could then lead to their being different. This identity too, is contingent, not necessary.

That cats are animals -- is subject to the problems of indefinite definition in our world. The margin cases for cats and animals are basically impossible to nail down, hence they are best understood as APPROXIMATE category terms, rather than logic categories. And that cats happen to be animals, was discovered by investigation -- it is possible in principle that mobile entities could be from other kingdoms. True, few plants are mobile, but they could be in principle, and the same with fungi. And these three kingdoms of multi-celled life HAPPEN to encompass the macro-scale life we have encountered, but there could in principle be lots of living things in the universe that do not fit any of our taxonomical categories, and cats could have been the first such discovery. That cats happened to fit into these three categories very well, does not make their fitting NECESSARY!

Kripke uses "modal reasoning" that resorts to "alternate worlds" thinking, but his "alternate worlds" are, in basically every one of these cases, insufficiently imaginative to actually encompass the alternate potential worlds considered by contingent science.

Samuel Clemems necessarily being Mark Twain was argued by Kripke through different means. He admits that Samuel Clemens may have had a different name, and may have been a very different person in "alternate worlds", and that somebody else could have written the Mark Twain stories. What Kripke argues is that the experience of selfhood is different for different people, and in these alternate worlds, that the "self" of our world's Samuel Clemens should be identified with other individuals who might be very different. Here Kripke tends to go reductionist, by coupling these other worlds to our Samuel Clemens by limiting him to the same parents and genetics. This reductionism does not fully capture our human intuition, or biological knowledge, as a few small genetic changes in Samuel Clemens would leave him VERY similar although not identical, such that a non-genetically identical Clemens could very plausibly have written the Mark Twain stories. Most of our intuitions at that point would tend to lump that non-identical Clemens into the "Mark Twain author" identity.

Kripke also basically should have invoked emergence here. He presumes a self-essence, which somehow is associated with the genetics. That would be recognized today as an emergence relation. However, emergence is not considered NECESSARY in contemporary emergent physicalism. What emerges from a substrate, and when emergence happens, are contingent phenomena. I.E. not necessary, and necessity cannot be derived from emergence.

So -- none of these examples are actually necessary, per the current conventions of scientific empiricism.

In additional discussion, Kripke tries to defend against Quine's point that A=/=A between people, by arguing that people can use a Proper Noun properly (I.E. logically validly) without knowing all the details of the meaning of that noun. This argument relies upon their being an essence to the universe, that one can refer to, without being fully cognizant of all aspects of it. The principle is plausible, provided that there is such an essence. How one gets an essence of "The Mississippi River" out of the bundle and variable nature of our world -- is still a problem for Kripke. He tried to put the burden on language, by assertion a "baptism" for such a term, and then learned usage through the community of speakers. BUT -- this still only justifies an approximate and fuzzy usage, not his "rigid designator" claim, and does not actually support valid analytic usage of any such proper name.

The pragmatic alternative

These empirical critiques, if appropriate, rebut Kripke's justifications of analyticity. They leave our world entirely contingent, and analyticity inapplicable by its own standards to anything in our world, and to communication (language) between us.

This does not mean analyticity is useless. The pragmatic alternative is to accept that analyticity is not valid PER ITS OWN STANDARDS, but still can be useful, PER THE STANDARDS OF PRAGMATISM. There is a great deal of insight we can gain from applying analytic methods to our world, even if we cannot always trust its conclusions. We can communicate usefully, even without logical certainty of our shared meaning. Pragmatism does not demand necessity, nor certainty, only utility.

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  • Thanks for this! My orginal bounty expired but I've reopened and will nominate after 24h =)
    – Paul Ross
    Oct 3, 2022 at 21:55
  • @PaulRoss -- I thought I beat the time limit by about 90 minutes ... Glad you appreciate the effort -- I considered your memorial offer to be a nice way to honor a giant of modern philosophy -- despite my not agreeing with his thinking or general philosophic approach. Don't bother to re-open a bounty. Getting myself up to speed on Kripke well enough to post this was worth my time. :-)
    – Dcleve
    Oct 3, 2022 at 22:07
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For an overview of different things that Kripke has done, I would recommend: John Burgess: "Saul Kripke: Puzzles and Mysteries (2013),

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