Over the last decade and a half — ever since I started the Rationally Speaking blog  which has now evolved into the webzine that is Scientia Salon — I have written about all sorts of core philosophical issues (e.g., ethics, metaphysics), as well as on much other stuff (e.g., the nature of science and pseudoscience) from a philosophical perspective. As I have explicitly put it in a collection of essays entitled Blogging as a Path to Self Knowledge , my reasons for writing have been (and continue to be) twofold: i) because I think that academics are in a privileged position that requires them to engage in discourse with the broader public which, directly or indirectly, grants them such position; ii) because I find the process of writing to be the best way for me to clarify my own thoughts. Often I truly don’t know (or at the very least I’m not sure of) what I think until I sit in front of my laptop and start typing away.
It is particularly in the spirit of (ii), if the reader will indulge me, that I offer the following considerations. They represent my current thoughts concerning a number of philosophical issues about which I have written and have either changed my mind or significantly elaborated my position over the past several years. The list is incomplete, and by necessity what follows are capsules, not fully articulated arguments. They are presented to provide stimulus for further thought and discussion to readers, as well as to allow myself a black-on-white benchmark to which to return in future years, to see how my own thinking might have evolved in the intervening time.
On this I’ve written even very recently , and I am in the process of delivering a manuscript to Chicago Press on the broader topic of the nature of philosophy and philosophical progress, so there is much more to be said. Briefly, however, I think of philosophy as part of the broader field of “scientia,” the Latin word that stands for knowledge sensu latu, and that includes also (at the least) the natural sciences, social sciences, logic and mathematics (I think I need to throw history in there as well).
Philosophy, in my view, is an independent discipline which is however contiguous with the other components of scientia. Anyone who has actually read, side by side, a technical paper in, say, metaphysics and evolutionary biology will never make the mistake of confusing the two. Still, philosophy doesn’t have its own “unique” method, but then again, science doesn’t either. Rather, both have developed tools and practices that have served them well over the centuries. In the case of philosophy, these include conceptual analysis, logically structured formal arguments, thought experiments, and the like.
Just like contemporary science is a significantly different beast from science as it was practiced in the time of Newton (or proto-science when Aristotle was practicing it), philosophy also has evolved over time. This evolution has been marked, in my mind, by three characteristics: a) the retention of a disciplinary core that includes metaphysics, logic, epistemology, ethics, and aesthetics; b) the spinning off of a number of fields once they matured both conceptually and, especially, empirically (physics, biology, psychology, economics); and c) the development — parallel or subsequent to said spinning off — of “meta” disciplines that look at the new areas of inquiry from the outside, the so-called “philosophies of.”
The aim of philosophy is not to make empirical discoveries (though philosophical thinking ought to be informed by the best empirical evidence available), but rather to explore the space of conceptual possibilities. Philosophy is inherently a critical, often prescriptive (as opposed to descriptive) discipline. Unlike Hume or Quine (to mention just two influential philosophers), I don’t think that philosophical inquiry can be turned into (descriptive) social science.
I confess to have often flirted with the idea that metaphysics is an inherently problematic field of philosophical inquiry, and have been attracted both by the logical positivists’ rejection of it as literally meaningless and — better yet — by Hume’s famous “fork”: “If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.”
But I don’t like book burning, so I have tried to take metaphysics on board and to read something that might convince me that my initial judgment was way off base . Looking over my notes, I see that I appreciated metaphysicians’ discussions of topics like time, personal identity, universals vs particulars, and causation, to mention a few . However, I was particularly taken by James Ladyman and Don Ross’ project  of defining metaphysics as that philosophical discipline that aims to see how the different accounts of the world that come from fundamental physics and the “special sciences” (i.e., anything but fundamental physics) “hang together.”
I have since arrived at the (provisional, of course) conclusion that there is value in both Ladyman and Ross’ approach as well as in more traditional conceptions of metaphysics — but I have to confess that I still have no patience for theology, which I consider outside of not only metaphysics in particular, but of philosophy more generally (just like astrology is outside of astronomy, say).
As I mentioned above, and contra Quine, I don’t think epistemology can be reduced to psychology. It is a prescriptive, not descriptive, discipline (with the usual caveat that — like anything else in philosophy — it better be informed by whatever empirical evidence may be relevant). Indeed, I don’t understand how so many seem to derive exactly the wrong conclusion from the recent (very interesting) research about the prevalence of human cognitive biases. Rather than making epistemology and critical thinking irrelevant, such research provides the strongest argument about why we want to study and teach how to think properly. (To use a simple analogy, imagine someone arguing that it is useless to develop and teach probability theory, on the grounds that there is empirical evidence that people are naturally bad at estimating probabilities…)
A particular issue here has caused me an itch which I’ve had to repeatedly scratch for a number of years now: the supposed demise (at Quine’s hand) of the analytic/synthetic distinction . The basic contrast is between sentences that are contingently true (e.g., most bachelors are between the ages of 40 and 60 — I just made that up, so don’t bother checking it on Wikipedia), and those that are true by definition (e.g., bachelors are unmarried men). The first type is synthetic, the second analytic. To a first approximation, science is about synthetic truths, logic about analytic ones, and philosophy somewhere in the middle (with a tendency toward the analytic).
Famously, in the middle of the 20th century, W.V.O. Quine wrote an influential paper  in which he argued against two “dogmas” of the then prevalent form of analytic philosophy, logical positivism: the aforementioned analytic/synthetic distinction and “reductionism” (in the very specific sense that meaning arises from logical constructions of terms that ultimately refer, i.e., “reduce,” to experience).
The issue is very technical, and indeed is one of the best examples of what is both so good and so questionable about 20th century analytic philosophy: very clever, and almost just as irrelevant and maddeningly sophistic. Briefly, though, Quine distinguished two types of analytic sentences:
(1) No unmarried man is married
(2) No bachelor is married
arguing that there is a problem with (2). You see, (2) can be turned into (1) by deploying the concept of synonymity, in particular by observing that “bachelor” is, in fact, synonymous with “unmarried man.” Ah, said Quine, but we lack a good (philosophical) account of synonymity itself, without which we really have no analyticity after all. Being unable to provide such an account, he concluded that the whole distinction between analytic and synthetic statements collapses.
I’m sure you got bored and went off for a coffee in the middle of this explanation. Now that you are back, you may be glad to hear (but please don’t tell my esteemed colleagues!) that I find Quine’s point — again — very clever and “interesting,” but ultimately pretty much irrelevant. Let’s just say that, to a first approximation (and for pretty much any use I can think of), we can assume that (1) and (2) are indeed synonymous, and we know very well that they are true in a substantially different way from the truth of “most bachelors are between the ages of 40 and 60.” So, in my book, the analytic/synthetic distinction is here to stay (with Quineian caveats).
Logic and Math
I must be in a decidedly non-Quineian mood today, since I also reject Quine’s idea that — just like epistemology can be reduced to psychology — so too logic is something that we discover “empirically,” and may therefore need to be modified in the future . Rather, I think that logical principles such as, say, modus ponens, are valid and will remain valid regardless of whatever else we discover about the world. What changes, if anything, is their domain of application. For instance, classical logic has been expanded and refined a number of times, and new types of logic have been invented to account for new phenomena (such as quantum logic ), or to more realistically describe already known problems (e.g., fuzzy logic ).
In this sense, logic is like (without being reducible to) mathematics (and mathematics is like, without being reducible to, logic ). Consider, for instance, Euclidean geometry, and in particular Pythagoras’ theorem. Is it “true”? I’m not even sure what that means, at this point (I used to think the answer was clearly yes, by the way). The Pythagorean theorem is “true” given the axioms of Euclidean geometry, but not “true” if we move to, say, spherical geometry. In terms of its practical applications, the theorem does describe triangular flat spaces on planet earth to a very high degree of approximation, as long as those spaces are not large enough that the curvature of the planet becomes relevant, thus forcing us to move to non-Euclidean geometry.
You may have seen by now where I’m going: despite having had sympathies with the notion of mathematical Platonism , the idea that mathematical objects have an ontological status (“exist”) independent of the human (or any other) mind, and that therefore mathematicians discover (as opposed to invent) them, I’m currently inclined to be more ontologically conservative (how Quineian of me!) and agree that both logic and mathematics are human creations, either tools for thinking about certain kinds of things or interesting objects to explore in and of themselves, for curiosity’s sake.
But, you may object, aren’t there all sorts of things about math (or logic) that turn out to be inescapably true, and that we discover as we go along, for instance Fermat’s Last Theorem? Yes, but the same can be said of, say, the game of chess. I assume we all agree that this is a (very clever, very enjoyable) human creation, in no way “mind independent.” And yet, people have studied the game of chess for centuries, and they have discovered a lot of new properties of it that were not known before. The same, I think, is true for math and logic, except that their space of possibilities is an astounding number of orders of magnitude larger than the one defined by the game of chess.
What about the so-called unreasonable effectiveness of mathematics, often brought forth (for instance by Hilary Putnam and Kurt Gödel) as perhaps the best argument in favor of mathematical Platonism? Ever heard of Borges’ Library?  In his famous short story, the Argentine author imagined a library containing all 410-page long books that can possibly be written by using 25 characters. Although many such books contain nonsensical gibberish or, at best, incorrect information, some will be bound to contain knowledge of the universe as it actually is. The problem, of course, is how to distinguish the gold from the pyrite, a conundrum that leads to depression among the librarians, as well as the flourishing of a variety of religious cults with different takes on the very meaning of the Library.
I’m beginning to be convinced that — to a first approximation, every analogy is incomplete — the math and logic invented by humanity are somewhat like Borges’ Library, which means that they allow us to “describe” not only (uncannily!) the real world, but also a number of interesting “possible worlds” (and, if we had the time and inclination, an even greater number of impossible and/or uninteresting ones). This seems to me, at the moment, to take much of the sting out of the argument from no-miracles in favor of Platonism. It also has a number of nice side effects, as far as I’m concerned, particular in terms of the ultimate nature of the universe (see below) and the nature of consciousness (see part II).
The nature of the universe
As I mentioned above, I’ve been attracted by Ladyman and Ross’ work in metaphysics and philosophy of science, which means that for a while I seriously considered (indeed, even favored) their position of ontic structural realism . Realism is the position in philosophy of science that takes scientific theories to describe (approximately, at best) the world as it really is, as opposed to the rival view of antirealism, according to which scientific theories aim at empirical adequacy, not truth. There are several varieties of both realism and antirealism, and overall I think that while the antirealists do make several interesting points, the balance of things is on the side of realism.
Now, structural realism is a specific type of realism that says that what is maintained when science moves from one theory to another (say, from Newtonian to relativistic mechanics) is the structure of its mathematical description of reality. This may or may not be so, as pretty much the only examples of this type of realism are found in physics (and even there some seem a bit forced). Ontic structural realism is the more specific position that the fundamental ontological description of reality belongs not to particles, sub-particles, strings, superstrings, branes or what have you, but rather to the relationships among different spatiotemporal points. Indeed, ontic structural realists claim that what all current versions of fundamental physics have in common is that they point to the conclusion that at the bottom of reality there are no relata (no “objects”), only relationships (hence Ladyman and Ross’ book title: Every Thing Must Go). This is not the same as, and yet one cannot avoid thinking it is closely related to, Max Tegmark’s idea of the mathematical universe  where he claims that — in a decidedly non metaphorical sense — the universe is “made” of math.
You can see how both ontic structural realism and Tegmark’s mathematical universe would go very well with mathematical Platonism (and so would philosopher Nick Bostrom’s so-called Simulation Hypothesis about the ultimate nature of reality ).
Again, let me reiterate that I considered all these ideas seriously, and have definitely felt their attraction. But in the end I’m far too much of an empiricist to really buy into them. As far as ontic structural realism is concerned, it’s hard to wrap one’s mind around the idea of a set of relations without relata (i.e., without “things” between which the relations actually hold); and all of these ideas seem to me to clearly make the mistake of confusing information (or mathematical descriptions) for physical reality, just as beautifully pointed out by John Wilkins in a recent Scientia Salon essay . (Indeed, I credit John for finally having crystallized my thinking in this regard, helping me to snap out of a type of ontological indulgence that was making me increasingly uncomfortable.)
So, to reiterate: the universe is physical, and our mathematical descriptions of it are just that, descriptions. It would be best not to confuse the two. Next up: morality, free will, self, and consciousness.
Massimo Pigliucci is a biologist and philosopher at the City University of New York. His main interests are in the philosophy of science and pseudoscience. He is the editor-in-chief of Scientia Salon, and his latest book (co-edited with Maarten Boudry) is Philosophy of Pseudoscience: Reconsidering the Demarcation Problem (Chicago Press).
 Rationally Speaking blog.
 Blogging as a Path to Self Knowledge, edited by M. Pigliucci, 2012.
 Neil deGrasse Tyson and the value of philosophy, by M. Pigliucci, Scientia Salon, 12 May 2014.
 As usual, the Stanford Encyclopedia of Philosophy is an invaluable source. Here is their entry on metaphysics.
 See the treatment of those topics in Brian Garrett’s What is this thing called Metaphysics?, Routledge, 2011.
 See especially their Every Thing Must Go: Metaphysics Naturalized, Oxford University Press, 2007.
 As usual, for an in-depth introduction consult the relevant SEP entry.
 Two Dogmas of Empiricism, by W.V.O. Quine, Philosophical Review, January 1951, 60(1):20-43.
 That said, I quite like the exquisite Quineian concept of a “web,” as opposed to an edifice, of knowledge (see The web of belief, by W.V.O. Quine and J.S. Ullian, Random House, 1978.), which gets rid of so many “foundational” problems in philosophy — such as Hume’s famous problem of induction (see The problem of induction, SEP.), shifting to a quasi-coherentist view of truth. I say “quasi” because empirical evidence and sensorial input are themselves part of Quine’s web.
 Quantum logic and probability theory, SEP.
 Fuzzy logic, SEP.
 See The (complicated) relationship between math and logic, by M. Pigliucci, Rationally Speaking, 24 December 2012.
 Platonism in the philosophy of mathematics, SEP.
 The Library of Babel, by J.L. Borges.
 SEP entry on structural realism.
 Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by M. Tegmark, Knopf, 2014. See also my interview with Max on the Rationally Speaking podcast.
 Here is Bostrom’s original article. See also a Rationally Speaking episode on the same topic, with guest David Kyle Johnson, who in turn has recently contributed to Scientia Salon.
 Information is the new Aristotelianism (and Dawkins is a hylomorphist), by J. Wilkins, Scientia Salon, 1 May 2014.
165 thoughts on “My philosophy, so far — part I”
I wouldn’t think of a (conscious) silicobrain (or other technology base) as a simulation of a biobrain. It would be another type of brain.
So your definition of physical reality is rooted at human sense data. Why not chimpanzee sense data? Why not simply your own personal sense data? This latter definition would make sense to me because to me physical existence is subjective. What physically exists for you is not the same as what physically exists for an observer in another universe or multiverse, so the idea of truly objective physical existence is incoherent.
Your definition does not give a truly objective account of physical existence, because it starts by assuming that you personally have a physical existence and that observers in causally disconnected universes do not. I see no reason for making such an assumption. It is however a personally reasonable account of what a concept of subjective physical existence might mean to any particular observer, and one I would endorse myself.
You may well be right about confusion of terms,
I was intending both, namely Realism (“the belief that our reality, or some aspect of it, is ontologically independent of [us]”) and Empiricism (“a theory which states that knowledge comes only or primarily from sensory experience”).
I’d be happy with any of those — given that all of those are linked together by possible causal chains, which is the heart of my definition.
Not if there are no causal links between those domains, no. I’d label those possible other “existences” as “para-existences”. You’re right that an observer in one of those other para-existences would have a different set of what “exists”, but I don’t see any problem with that concept. Among the set of causally disconected para-existences, what “exists” depends on which of the para-existences you are causally connected to. Seems an ok stance to me!
OK, so perhaps we are in agreement then. It is the idea of objective physical existence, where we can say that one universe objectively exists but another does not, that I disagree with.
I identity what you call para-existence with Platonic existence. So I think all possible universes exist in the same sense, and the only reason that our universe seems physically real to us is because we are in it.
That’s fine, but you have to realize that most of the arguments for *anti-Realism* are empiricist ones. Indeed, I would argue that the most natural metaphysics for a strict empiricist is an anti-realist one. You can see this, very clearly, in the differences between Locke, Berkeley, and Hume. Locke is the only committed metaphysical realist of the three, and his empiricism is the most compromised — in many ways, he is much closer to Descartes than to Hume or Berkeley.
Thanks for the reply, which certainly answers very adequately two of my
three numbered questions, but does leave me confused on the
basic question behind them.
That formula (called “wff” often by philosophers, and by mathematicians such as Kleene from 70 or 80 years ago—having expanded “formula” to mean the same as the already perfectly adequate term ‘symbol string’, for some unfathomable reason buried in the mists of time!), the one which you gave, is of course closely related to the rule of inference to which (MP) almost always refers. And that formula is indeed a tautology, as you say.
But at least two questions remain of why you would wish to present your five numbered points and assert them to be a proof that it is indeed a tautology.
Firstly, the usual proof, directly from definition of ‘tautology’, namely checking a 4-line truth table, is exceptionally trivial and well known. Another proof, once soundness of some proof system is known, namely deriving the formula with it while using no premisses, would also be exceptionally easy, though rather unimpressive, since in all likelihood, the rule usually called (MP) is part of the system (IIRC a so-called Hilbert system would have some axioms plus only one rule, (MP) itself.) And, if one had already proved the Deduction Theorem and the rule usually denoted (MP) was there, the formula you gave would immediately be seen to be a tautology. Besides being indecipherable, at least by me, your proof would seem to just complicate things, assuming it does somehow prove what you claim.
Secondly, in what way could those five non-formulas be possibly a proof, or the basis of a proof, that anything is a tautology? I suspect from looking at it, and from some earlier loose rambling here about (MP), that really it is something else you are trying to get at here. And earlier you say ” However it can be shown, using the axioms of identity and non-contradiction and the truth tables for the and and implications operators, that modus ponens is a tautology.” Again this is quite confusing to me at least. Maybe I am missing something, and (MP) is less straightforward than I realize. So please say in some other way if possible what you mean by these proofs, or this proof if they are the same.
As far as the “rambling” above goes, one striking thing here is that, from your answer to me, it is clearly MATERIAL implication that your formal arrow is. And most others here seem to mean that as well, as they should in logic.
On the other hand, in earlier responses from some others there was all sorts of stuff about causation, some of which you and Massimo tried to straighten out, but it seems without total success in convincing the rambler(s). The main misunderstanding seems to proceed by assuming that the A —> B in (MP) should somehow be interpreted to mean that A causes B. Let me reinforce with another tautology, one which might ‘take aback’ a few people here. That formula is the one[(A—>B) or (B—>C)], as may be easily seen to be a tautology with an 8-line truth table. With the mistaken causality interpretation above, one would be forced to believe the ridiculous statement that, for any three ‘physical happenings’, either the first was the cause of the second, or the second was the cause of the third. What this odd tautology is in general, more than anything else, is a dramatic illustration that material implication has a very specific meaning in logic, and is rather different than many think. And please, please, nobody here make the mistake of believing that it tells you the ridiculous falsehood that for any 3 propositions, either the 3rd follows from the 2nd, or the 2nd from the 1st. That misreading is a perfect illustration of mixing up the two languages.
The nature of material implication gives rise to all sorts of bizarre nonsense, not least of which is a useless subject called “Relevance Logic”. To be even meaner, I often think of that as some peculiarly Australasian psychological malady, which happens to inflict only a few philosophy profs and their students. The list of so-called paradoxes of material implication which one finds at the beginning of the texts by these people, purporting to show how material implication is defective, may be easily disposed of by anyone who does logic carefully, like Kleene did almost a century ago. If anyone here has a favourite such paradox which still puzzles them, let me know and I can explain it, making moot any bizarre excursion into some fundamentally inapplicable species of formal logic. (And modal logic, quantum logic, and many-valued logic are not that much better, the Stanford Encyclopedia being rather uneven on various topics, to put it charitably. But I must restrain myself!)
Anyway, to get back to the topic proper, I took the trouble to go through all the submissions here which referred to (MP), just to make sure I was not missing something. And my impression is still that there is some confusion (not by you) about what the arrow refers to in logic. That’s the problem, not (MP) per se. Now there may be something worthwhile that people are trying to get at. The only thing I can conjecture is that they would like to see some kind of proof or verification, surely not a derivation somehow as above, perhaps just an explanation, of the following:
‘If it is known that a physical happening called A did in fact occur, say, at least 5 minutes ago, and if a theory is accepted which tells one that whenever A happens, then B must also happen sometime in the following 5 minutes, then one can rationally conclude that B has in fact happened.’
I find it hard to understand why this needs any proof. Nor would the conclusion: ‘Then if B has not happened, we better drop that theory.’
And maybe they also want to see some physical theory in which those statements fail. The why of that also escapes me completely, as does the meaning of that.
On p. 24 of Tegmark’s paper of the first 51 pages in Ann. Phys. 270 (1998), one can read the following. I’ll leave it to you to dig out the later parts of that paper (from his web site) which flesh this out. As in my reply to Massimo, there may be convincing counterarguments, but none that I have seen yet, so I eagerly await education in this respect. Also, given the 2014 book, I doubt Tegmark himself has been subsequently convinced to no longer assert this:
‘Using Popper’s falsifiability requirement, one might ar- gue that “this TOE does not qualify as a scientific theory, since it cannot be experimentally ruled out”. In fact, a moment of consideration reveals that this argument is false. The TOE we have proposed makes a large number of statistical predictions, and therefore can eventually be ruled out at high confidence levels if it is incorrect, us- ing prediction 1 from the introduction as embodied in equation (6). Prediction 2 from the introduction offers additional ways of ruling it out that other theories lack. Such rejections based on a single observation are analo- gous to those involving statistical predictions of quantum mechanics:’
Presumably the above quote suffices to disabuse anyone here who might have suspected MUH to simply be some academic department coffee room glib toss-off. I know that you don’t.
This may be the only time I have ever convinced anyone of anything. Thanks for the credit.
I got an answer from Tegmark on the question of whether chess can be said to exist Platonically in the same way as a mathematical object. This is the answer I got, which I think, as well as the comments of others on this thread, supports my claim that Platonists would typically hold games such as chess to exist.
I note that he didn’t quite answer the question I was asking, but I think it’s close enough.
Seems to me like he rather skirted the question…
OK, I’ve asked him to clarify, but I think that the answer I want follows trivially from what he said.
Chess can indeed be defined without human baggage, as is clear from the fact that computers can play chess, therefore chess is a mathematical structure just like any other and so has the same ontological status.
Or do you think Platonists believe some mathematical structures to exist and not others?
Setting aside that Tegmark has been criticized for the vagueness of the notion of mathematical structure, if chess counts as one, then Platonism is devoid of specific content. Chess is an entirely arbitrary game (just like all games, really), so to say that it is “devoid of human baggage” is, frankly, nonsense on stilts.
Perhaps you’re right (although obviously I don’t think so). The point is that most Platonists would disagree with you, so you should update your understanding of Platonism accordingly. If that makes Platonism nonsense on stilts in your eyes so be it.
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