My philosophy, so far — part I

babel3by Massimo Pigliucci

Over the last decade and a half — ever since I started the Rationally Speaking blog [1] 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 [2], 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.

Philosophy Itself

On this I’ve written even very recently [3], 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 [4]. 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 [5]. However, I was particularly taken by James Ladyman and Don Ross’ project [6] 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 [7]. 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 [8] 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 [9]. 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 [10]), or to more realistically describe already known problems (e.g., fuzzy logic [11]).

In this sense, logic is like (without being reducible to) mathematics (and mathematics is like, without being reducible to, logic [12]). 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 [13], 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? [14] 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 [15]. 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 [16] 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 [17]).

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 [18]. (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).

[1] Rationally Speaking blog.

[2] Blogging as a Path to Self Knowledge, edited by M. Pigliucci, 2012.

[3] Neil deGrasse Tyson and the value of philosophy, by M. Pigliucci, Scientia Salon, 12 May 2014.

[4] As usual, the Stanford Encyclopedia of Philosophy is an invaluable source. Here is their entry on metaphysics.

[5] See the treatment of those topics in Brian Garrett’s What is this thing called Metaphysics?, Routledge, 2011.

[6] See especially their Every Thing Must Go: Metaphysics Naturalized, Oxford University Press, 2007.

[7] As usual, for an in-depth introduction consult the relevant SEP entry.

[8] Two Dogmas of Empiricism, by W.V.O. Quine, Philosophical Review, January 1951, 60(1):20-43.

[9] 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.

[10] Quantum logic and probability theory, SEP.

[11] Fuzzy logic, SEP.

[12] See The (complicated) relationship between math and logic, by M. Pigliucci, Rationally Speaking, 24 December 2012.

[13] Platonism in the philosophy of mathematics, SEP.

[14] The Library of Babel, by J.L. Borges.

[15] SEP entry on structural realism.

[16] 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.

[17] 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.

[18] 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

  1. Both money and marriage are invented constructs and have unknown objective properties. That does not make them any less mind-dependent. They happen to be independent of individual minds, but that’s not really the same thing at all.

    I don’t know what my future thoughts are, therefore they are not mind-dependent? Unkown is not the same thing as mind-independent. The real point is “cannot possibly be false.” If you discover a function you cannot differentiate but you can devise a functional to give a mathematical equivalent, what does it mean to say that it cannot possibly be false that this given function can’t be differentiated? If you make up Zermelo-Frankel axioms for set theory, what does it mean to say the axiom of choice or the continuum hypothesis “cannot possibly be false?”

    Looking at it with a more positive slant, I would suggest that applied mathematics is real mathematics. But there’s no confusion about the empirical origins there. I would also suggest that maybe axiomatized mathematics is not more real than applied mathematics.


  2. I’m with you on this Massimo.

    Also, I don’t know what it means for the universe to be physical. I think ‘physical’ is a concept which is meaningless when applied in an objective sense, especially to the whole universe, because it can only be defined circularly. A physical object is an object that can affect other physical objects. So how do you ground the whole thing? If computationalism is false, maybe we can, because maybe consciousness is a property of certain physical objects only.


  3. Hi Coel,

    1) Agreed.

    2) Some are empirically true in this sense, and some are not.

    3) OK, but some axioms can be adopted that may not be empirically true, for example various non-Euclidean geometries, or mathematics involving complex numbers or quaternions which, although they have practical applications, are hard to make empirical sense of in terms of how they relate to numbers of things.

    Would you regard that proof as empirical or axiomatic?

    It’s not necessarily either/or. The more you interpret it intuitively/visually, the more it is grounded in our empirical understanding of reality. But you could carry out the same proof with a formal logical argument, in which case it would be axiomatic.


  4. Hi DM,

    It’s not necessarily either/or.

    An excellent answer, and my point in asking the question!

    I think we’re not far apart. I agree with you on adding non-empirical axioms to the mix — see my “Jane Austen” comment above.

    I do think that the whole process is very similar to that which physicists adopt concerning “laws of physics”, with both mathematicians and physicists exploring “what if?” scenarios by playing with axioms/laws.

    I also think that because of this maths and theoretical physics can pretty much merge (e.g. string theory).

    Are there any axioms that mathematicians use that are direct contradictions of what happens empirically (as oppose to ones that add to those empirically verified, or where the empirical status is unclear)?

    By the way, things like non-Euclidean geometries and complex numbers are exactly the sort of thing that I regard as matching empirical reality, and are part of why I regard the two as fundamentally linked in a way that can only be explained by maths being rooted in empirical reality.


  5. DM,

    Regarding your argument that a simulation is the same thing as the real thing:

    Adopting an example Massimo has used in a debate with one of the Singularity proponents (and Massimo correct me if I botch your example), suppose you simulated the process of photosynthesis. Would you then argue that you’ve created sugar?


  6. Hi Coel,

    We may be close in some respects but you should bear in mind how weird my overall worldview is to you (I assume). I believe the universe literally is a mathematical object, and that the concept of objective physicality is incoherent. I assume you’re nowhere near coming over to my side on these issues.

    It’s very hard to invent any complex system of axioms that can’t be used for something. If you try to invent a set of axioms that contradicts one physical system you’ll possibly find that it models another physical system very well.

    But I would say that there are all kinds of mathematical “games” that mathematicians study just to see what they can prove about them. These are basically axiomatic systems that really don’t mean anything, but can prove interesting and challenging to think about. Conway’s Game of Life is not a bad example.


  7. Not buying this for a second. If it doesn’t produce chemicals – it has no means of influencing bodies.


  8. Not buying this for a second. If it doesn’t produce chemicals – it has no means of influencing bodies.

    100% true and 100% beside the point.

    You could in principle replace a brain with an computer. You could wire up all the nerve endings to the inputs and outputs. Such a computer could control the body. Would this be simulated control or actual control?

    If you think this thought experiment is too fantastic you don’t have to imagine it is a human brain. Assume it’s the brain of some simpler creature if you like. The point remains the same. You can replace a brain with a simulation of a brain because simulated control is control. You can’t replace an organ that produces a chemical product with a simulated organ because a simulated chemical is not a chemical.


  9. Hi DM,

    Read your post. I think you’re going too far with the brain-computer analogy. Analogies are great, but that doesn’t make the two the same thing. Similar to the analogy between DNA and computer coding, it doesn’t mean DNA is the same thing as coding. DNA is just chemicals, so why couldn’t consciousness be the same? When you take certain hallucinogens you alter your consciousness. If the brain really can be replaced by pure computation, then I don’t see how there can be a coherent computationalist account for drugs altering someone’s state of consciousness.


  10. No, you couldn’t, since a brain doesn’t work just by way of electrical signals, but chemical interactions, which you ain’t gonna have inside a computer…


  11. No, you couldn’t, since a brain doesn’t work just by way of electrical signals, but chemical interactions, which you ain’t gonna have inside a computer…

    Yes you can because the influence of the chemical interactions can also be simulated. If the chemicals are secreted into the bloodstream then of course we have a problem, but that could be solved by attaching physical glands of some kind to the computer or simply simulating the whole organism.


  12. I believe the universe literally is a mathematical object, and that the concept of objective physicality is incoherent. I assume you’re nowhere near coming over to my side on these issues.

    Well let’s see. I hold that the universe is a collection of “objects” (= fundamental particles), and that the nature/behaviour of these particles is logical/mathematical, and that there is nothing about these particles except their logical/mathematical behaviour.

    As for any Platonic existence of mathematics, well I’m not sure what that even means and can’t conceive it, unless what you mean by a “mathematical object” is what I would call a “particle described by maths”, in which case I agree. As ever, the semantics of this is tricky.


  13. Hi Andrew,

    Thanks for reading. Of course I could be taking the analogy too far, but I don’t think I am. The power of computers is that any informational process at all can be implemented by any computer at all (within certain constraints of feasibility).

    The analogy that is sometimes taken too far is to compare the brain to a familiar physical desktop computer with discrete RAM, hard disk, USB ports, graphics card etc. But I see no reason not to see the brain as an actual computing device carrying out a computational process.

    To your specific points:

    DNA is just chemicals, so why couldn’t consciousness be the same?

    DNA is a physical substance. You can have a test tube filled with DNA. Do you imagine that you can have a test tube filled with consciousness?

    If you refer to the role of DNA as a means of transferring genetic information, it does not have to be chemical at all. DNA can be sequenced and the genetic information transferred over the internet as electrical impulses. If you want, it is even possible to reassemble it remotely, producing a new organism with the same genome.

    When you take certain hallucinogens you alter your consciousness. If the brain really can be replaced by pure computation, then I don’t see how there can be a coherent computationalist account for drugs altering someone’s state of consciousness.

    This isn’t really a problem at all. Drugs affect brain chemistry which affects the way signals propagate around your brain. This changes the computation in ways which could be part of the simulation.


  14. Haven’t we been here before?

    We have been here before but we are talking past each other. I would love to have a beer with you or something to thrash it out, but you’re busy and I’m thousands of miles away anyway.

    The chemical properties of sugars can also be simulated, but produce no calories.

    True. So what? Simulated sugar is not of any use to an organism, but simulated control is actual control. The analogy to sugar is false because the product of the brain (and the process by which it is produced) is fundamentally informational.


  15. I’ll buy you a beer next time you are in New York. But it is wrong (and question begging) to say that the product of the brain is information. The brain produces electrical stimuli and chemicals, and sugar is very much a chemical, last time I checked, so the analogy holds.


  16. Hi Coel,

    and that there is nothing about these particles except their logical/mathematical behaviour.

    Oh really? Not even the property of being real? What then distinguishes them from a mathematical model of such particles or from an imaginary universe where the laws of physics are different?

    If you are really committed to the idea that particles have no non-mathematical properties, then the universe is a mathematical object and all other possible universes exist in the same way as this one does. I suspect this is not (yet) your view.

    You are right not to be sure what Platonic existence means. The idea that existence has a clear meaning is an illusion, in my view. I see Platonism as an attitude. We can either talk about these things as if they exist or talk about them as if they do not. Either way, it seems clear to me that they have at least a “fictional” existence we assume for the sake of convenience.

    With this somewhat clarified, my belief is that the universe exists in precisely the same way as this. To deny that mathematical objects really exist is in my worldview also to deny that the universe really exists, which is fine by me as I think existence is a problematic concept when applied to universes or multiverses.

    The whole worldview is explained in detail here:


  17. Or I’ll buy you one next time you’re in Aberdeen 😉

    The brain produces electrical stimuli and chemicals

    Sure. So does that mean that if we replace the brain with a computer which is wired up to apparatus which will produce the right electrical and chemical signals under the direction of the computer that consciousness is possible?


  18. I did, and I don’t think that’s a problem, because from the “point of view” of the computer it doesn’t “know” if its signals are getting turned into real chemicals or not. If we imagine that the computer is conscious when it is producing chemicals, what do you think happens when the chemical dispensing apparatus is removed and all the sensory input to the brain replaced with a simulation?

    Another way of looking at it is that the brain is not really a device for producing elecricity or chemicals. You can’t just replace it with a gland. It’s job is to process information in very specific ways and send very specific output. Photosynthesis is not like this. There is no specific pattern in which sugar is distributed by a chloroplast. Any device which produced sugar in appropriate quantities would do as a replacement.


  19. Massimo,
    Thanks for your replies. Something more substantial in a couple of cases below would have been great, but I realize you have only so much time, and many other important things to do.
    PH: “To me, the abstract system of natural numbers … is no more nor less existent independently of the human mind than is some abstract system…chess.”
    MP: Well, you can say that, but why?
    Because, apparently different from you, it would seem to me highly surprising if it were not the case that either all abstract systems exist, or none of them do. The only caveat here would relate to computability, which is one aspect where Tegmark has changed from his main (1996?) technical publication on this. But the examples of chess versus numbers here would not be a problem re computability.
    What one means by “exist” is not so easy to articulate I think, although we all believe we ‘know’ what it means ‘deep-down’. But surely, to the extent one can assert anything general here, it is either true of all systems or of none. And (hoping to not belabour a point of which most here are presumably aware) though pure mathematics foundations seems far more ‘settled’ than fundamental physics, following important work, in logic mostly, during the 1st half of the 1900’s, it is also not clear that the notion of abstract, or mathematical, system is in any way final. (More awareness as just above might help clarify other matters in the correspondence here, where the various meanings of “implies”, especially material implication in formal logic, as opposed to causation etc., would make the discussion more relevant to the nature of MP. I would be so bold as to suggest learning logic in a math department as opposed to a phil department, if possible. The “M” in “MP” just above is of course ‘modus’, as opposed to a male name, originally Italian I think !)
    PH: “no more convincing than those who argue against Tegmark by baldly asserting that material existence and abstract existence cannot possibly be the same thing”
    MP: So you are you going to eat a simulated steak for dinner tonight?

    This was one of the more disappointing ones, but I take it as a joke! Actually I was pushing Tegmark’s MUH idea a bit on Jerry Coyne’s blog several years ago, in slight irritation there at a couple of militant (if I may again misuse that adjective) anti-platonists who had a rather arrogant self-assuredness about their attitude in this respect. One of the replies was a similar joke, though I think it was not presented as such. Here he suggested we both go up 10 floors to Jerry’s apartment; then he’d descend on the lift, and me through the window. The comparison of us two was then supposed to convince whatever was left of my consciousness of my error in not dismissing outright the assertion that abstract and material existence are one and the same. AFAIK no philosopher or anyone else has even begun to give a convincing general argument here—just tedious lists of examples everyone accepts as being in one or the other category of possible existence.
    PH: “Tegmark, who at least asserts his position is capable of observational falsification”
    MP: Yes, he asserts so, but a number of his critics have argued pretty convincingly that it can’t, really.
    I would be extremely grateful for at least one or two references here. The ones I have seen so far seem equally shallow and unconvincing as just above in 2. Note that there is a lot more on this falsifiability of MUH in Tegmark’s main early paper in the Annals of Physics than he has in the recent book—quite a different audience justifies that.
    PH: “my request above for some convincing argument as to why ‘abstract chess’ should be obviously mind-dependent.”
    MP: Because it is an arbitrary creation of the human mind, or do you think there is a Platonic realm that includes the rules of chess?
    See my replies above. And if Tegmark is correct, that realm includes everything else as well, including our friend Jerry’s apartment. But also, one should think carefully (in view of Godel) about the difference between a collection of so-called rules, even axioms if you wish, and the set of all propositions which happen to be true about a system (in many cases). As an amusing aside, where may one find these rules about chess, presented abstractly or formally?—and would a version of Godel’s incompleteness apply, or is everything here too finite?
    Finally, I must say the argument about being ontologically ‘economical’ carries little weight with me. Why should not having one category of existence, rather than two (abstract and material), not be considered more economical; or else, rather than one plus a very lengthy and unconvincing dismissal of the existence of the abstract?


  20. Hi Massimo,

    Actually I’d like to take a different tack in answering this point.

    Maybe, but you really don't see that you just snack in non-simulated chemical reality that way?

    OK. Bear with me. Are you actually willing to entertain the idea that a computer might be conscious if situated in a body as long as it has apparatus to squirt out chemicals and electrical signals under its control?

    If so, is it still possible that it might be conscious if we move it to a robotic body?


  21. Hi DM,

    “DNA is a physical substance. You can have a test tube filled with DNA. Do you imagine that you can have a test tube filled with consciousness?”

    The DNA is still chemicals though, which was my point. The analogy between DNA and computer coding is useful for a more intuitive understanding of the process, but that’s all it is. That is where I think you’ve gone too far with your brain-computer analogy.

    I don’t imagine a test tube filled with consciousness, but I do imagine consciousness as a certain byproduct of biochemical reactions and electrical stimuli.

    “Drugs affect brain chemistry…”

    It sounds like you’re conceding the point that the brain can’t be simply replaced by pure computation.


  22. “Are you actually willing to entertain the idea that a computer might be conscious if situated in a body as long as it has apparatus to squirt out chemicals and electrical signals under its control?”

    How would a computer produce chemical reactions?


  23. As far as I know no one has suggested that the axiom of choice or the continuum hypothesis “cannot possibly be false” and so you are simply attacking a straw man. It pretty much flies in the face of the definition of words such as “axiom” or “hypothesis” to say that they cannot possibly be false.

    Also, I am not sure as to the distinction you are making between real mathematics and non-real mathematics or how you propose to do applied mathematics without axioms.

    If you discover a function you cannot differentiate but you can devise a functional to give a mathematical equivalent, what does it mean to say that it cannot possibly be false that this given function can’t be differentiated?

    I am not sure how a functional can be mathematically equivalent to the differentation of a non-differentiable function given that functionals and functions have different kinds of domains, but if they can then who is it that you say claims that it cannot possibly be false that the underlying function cannot possibly be differentiated?

    If there was a procedure that really was mathematically equivalent to the differentiation of a function then it would follow that the function in question was differentiable.


  24. Hi Andrew,

    OK, I take your point that DNA is described by analogy as something like computer code but it should not be confused for a software algorithm. Very true.

    But not all analogies are false. The heart can be described analogously as a pump, yet I would say it actually is a pump all the same, if a pump is a device for moving fluid through a vessel. Similarly, if a computer is a device for processing information, I think the brain is a computer. Perhaps I’m wrong, but I have yet to see a convincing explanation of why this is.

    Your argument from drugs for example. Whatever chemicals can do can be simulated. We don’t have to imagine that a mind is a simple static algorithm, in fact it is certain that it is not. We can imagine our conscious computer to be simulating all the chemistry within a brain if we wish. The question is whether this simulated chemistry would achieve the same function as real chemistry, and if the product of the brain is control then I don’t see why not.

    Also, I would note that if you can have a test tube full of sugar but not a test tube full of consciousness then sugar is simply not a good analogy for consciousness.


  25. How would a computer produce chemical reactions?

    The same way a computer produces sound or video, by having a peripheral. So you can imagine that the computer has a little component inside it with a store of chemicals, and that this peripheral releases the chemicals under the control of the computer. Massimo’s point was that a brain produces chemicals, so here we are only concerned with the output of the system and not the specifics of how the output is produced.


  26. 100% true and 100% beside the point.

    Of course it matters – if it doesn’t produce something physical to interact with the body, then nothing happens – doesn’t matter if the body is robotic or not.


  27. Massimo, are you talking about chemicals used internally in the brain or chemicals secreted into the bloodstream by glands such as the pituitary? If we’re talking about the functionality the brain evolved to deliver, then chemicals used internally are only important insofar as they enable the brain to do this job.

    So if you’re talking about internal chemicals, then these are not the products of the brain. It doesn’t matter whether it produces these or not as long as it processes information correctly internally. This could be done by simulating the effects of the chemicals.

    If you’re talking about external secretions, this can be achieved by attaching secretion devices to the computer and it doesn’t matter how the chemicals are produced as long as they are produced in the right quantities.


  28. Whatever ideas or experiences might have led us to come up with Modus Ponens (even if we could know what these were) does not determine the nature or basis of Modus Ponens. To state otherwise is to make the genetic fallacy.

    Modus Ponens is simply a consequent of a few ground rules of reasoning:

    1. There are true statements
    2. There are statements whose truth is consequent upon the truth of other statements
    3. If a statement is true then it is true
    4. If a statement is true then it is not false
    5. The statement which asserts the truth of two other statements is true if and only if both of those statements is true.

    Given those then it follows that Modus Ponens is a tautology.

    If anyone disagrees with (1), (3) and (4) then they have pretty much dealt themselves out of the conversation since they cannot assert the truth of their own statements.

    For the rest it is a matter of being on the same page in order to do reasoning. Obviously there is much language to which these statements do not apply, for example meaningless utterances, statements whose truth depends on unstated indexicals like time, location etc, ambiguous statements. We can, and do, derives systems of logic which encompass more than just two truth values or systems of logic which use continuous rather than discrete truth values.

    But there seems to be some confusion about what is asserted when we say that some statement of mathematics is true.

    When we say that the Pythagorean Theorem is true, what is meant is that it is true that there will never be a counter-example to that statement in the context of those axioms (whether this is provable or not).

    If this seems a trivial sort of truth to some people then so be it, but that kind of truth is the basis of any sort of reliable knowledge we have about the world and so I would struggle to find an example of a less trivial kind of truth.


  29. Of course it matters – if it doesn’t produce something physical to interact with the body, then nothing happens

    You don’t think computers can produce physical signals? If you think chemicals need to be produced for consciousness then as I said we can just attach a device to dispense chemicals to the computer the same way your monitor or your speakers dispense light and sound.


  30. Yes it does, it’s just that you call those facts “axioms”.
    A confusion of observer and object language. Suppose we take a proof of the PT in classical logic and translate it into another logic (call it HB) which is identical except that “True” and “False” are replaced by “Heckle” and “Jeckyll”. which have no meaning except those they are assigned in the rules of the logic.

    The proof would establish that the Pythagorean Theorem is “Heckle” rather than “Jeckyll”..

    So the statement in the observer language “The Pythagorean Theorem is Heckle in HB” does not depend upon any facts since it would be true even if the axioms of HB were false. Moreover it is necessarily true since there can be no circumstances in which it is false.

    So the statement “Theorem T is true in H” for any given axiomatic system H is always true and does not depend on any facts (unless you are denying the possibility of truth itself).


  31. “What reason is there to think that our reasoning is correct if determinism is false?”
    Sometimes it is, sometimes it isn’t. Likewise if determinism is true. But if determinism is true, then when our reasoning is correct, we’re just lucky to have been (pre)determined to correct reasoning in that instance. If determinism is false (which isn’t to deny that much more of our thoughts and behavior are (pre)determined than we ever suspected not long ago; it only denies that ALL of them are (pre)determined by antecedent conditions.) Why then can we be pretty sure that, if determinism is false, sometimes our reasoning is correct? Because of just what you say: we take ability to reason as a given. But if det is true then we have no way to tell whether we do that because it’s true, or because we’re (pre)determined so to believe even though we’re wrong. Besides the Popper quote, my position was much influenced by Jmes N. Jordan, “Determinism’s Dilemma,” Sept 1969 Review of Metaphysics; and Raymond Tallis, Aping Mankind (2011), especially his last chapter.


  32. And I should correct the last paragraph “So the statement “Theorem T is true in H” for any given axiomatic system H ,if true,, is always true and does not depend on any facts (unless you are denying the possibility of truth itself).


  33. Would all parties at least concede that a sufficiently accurate and fine-grained simulation of a human body (obviously including its brain) and a suitable environment could reproduce all the externally observable behaviours of a human?


  34. Robin,

    To ‘get to 1st base’ with this, one needs clear definitions of all sorts of words you use in the first few paragraphs; e.g.

    1. “modus ponens”: Does this refer to deducibility only, or to the assertion that that rule of inference is sound (i.e. truth preserving)?

    2. “consequent” as in 3. Are truth and deducibility being carefully distinguished? Indeed, is some kind of sanitary distinction between the formal language, and the language used to speak about that formal language, being observed?

    3. “tautology” This has a very precise meaning to most mathematicians. A few others, and it seems also philosophers who at least take modern logic seriously, would include a logically valid formula in 1st order logic which is not a tautology in the former sense (i.e. the sense using truth tables) also as a tautology. Or do you mean something other than one of those?

    “Given those, then it follows that Modus Ponens is a tautology”:
    This has no meaning whatsoever to me without at least some answers to 1, 2 and 3, and also without an explanation of how either a rule of inference or else an assertion concerning truth, an assertion which is not in the formal language, (depending on how you answer 1.) could even be an object of the kind one calls a tautology (in pretty much any treatment of logic since about 1930).


  35. Thanks for the response Massimo.

    There’ve been a lot of posts in the meantime but I did want to get back to the response you had. I completely agree with you that it is strange to talk of relations without any strong reference to “relata.” This is weird even for someone like me who subscribes to mathematical realism and the existence of abstract objects. I also agree that this position obviously needs to be further refined down the road so that we can get a theory or unified framework of how the physicality we experience comes from a deeper mathematical structure (if it is indeed the case). Ladyman and Ross have moved in that direction, and hopefully others will follow suit.

    In relation to the comments about the electron substructure, I want to be clear that I don’t mean to suggest they aren’t objectively real at all, and I apologize for any confusion. Of course electrons are real, its just the nature of that “reality” that’s under debate here (I am and always will be a firm believer in scientific realism; instrumentalism is garbage in my humble opinion). Now if the electron has no substructure, a physicalist would have a difficult time sounding coherent when he or she states that its indeed “physical.” Even if they are at base vibrating strings of energy that are many orders of magnitude smaller (think Planck scale), that already starts to radically alter what “physical” actually entails. I’m reminded of the funny visuals of these oscillating bluish masses that represented strings in the PBS special “The Elegant Universe” that aired years ago. What exactly is that bluish “energy” that makes the string itself? Tough to ponder (and again feel free to substitute other theories of everything), but physics often points us to the counterintuitive nature of the world.

    As far as mathematics being a human creation, well the symbols and the activity of doing mathematics certainly are, but this borders on a trivial statement. One thing that I really can’t understand is, if our mathematics describes structures or relations that are inherent in the universe, doesn’t that mean those relations actually exist? And isn’t the meat of mathematics those relationships themselves, rather than the conventions and syntax we happened to develop? When nominalists claim that it “a human creation” and “we developed it,” I just start to think about Matthew McConaughey’s character Rust Cohle in True Detective. In one episode he berates the need for humans to constantly see things in relation to themselves and think its all about them. It’s almost that need to be the center of the universe again, contrary to what Galileo, Copernicus, and others have discovered at the ages drag on. We’re not that special. Mathematics might be done by humans and other sentient and non sentient beings, but the truths it exposes are not ours. They’re inherent in the universe. Some might question which parts can be mapped to it, but there is no question that vast swaths certainly do. In addition, the whole euclidean/non-euclidean debate is something of a sleight of hand. Every single one of these structures is amenable to the deeper foundations of set theory (or category theory, topos theory, etc). Whether a universal mathematical edifice is in the works or a plethora of equally consistent mathematical structures exist is an active question that I will not touch on at the time (though many who work on the foundations of math think a universal structure is very much in the cards).

    It’s unfortunate I’ve lost a comrade in arms on the mathematical realism debate, but I know philosophy of mathematics is one area where you and many others are constantly wrestling with both sides. Thats perfectly understandable, and it is testament to how hard these questions are and how far removed they are from some sort of empirical grounding. I know you’ve moved away from the realist side at this point, but as ever you’re better than most at constantly questioning a position and trying to get to the ultimate truth of it all. Keep your options open, as everyone should.


  36. Oops, brain fart, I meant integral (and yes, I was thinking of a Delta function.) Your picture of the loving analysis discovering new things which, lo, turn out to be useful, It seems to me that doing the math first, then figuring out the axioms and the rigorous proofs have usually come afterward. And your picture seems derived from philosophical prejudices about how the axioms (stand ins for Platonic Forms I would guess,) are the eternal, unchanging perfection. And yes, it does seem to me that you rate pure mathematical truth more highly, so highly that applied mathematics does not even exist.

    The alleged straw man came from this: “And yet in doing so we discover things that we did not know before and which cannot possibly be false.” I believe the contrary, the history of science shows that the greatest skepticism should be exercised upon someone who dares claim they have a mathematical or logical proof that shows how things must be. Yes, much mathematics is highly abstract, so abstract it doesn’t have any visible connection to ordinary experience. That’s one reason mathematics frequently does not give us knowledge, despite being “true”: We don’t know what it means! I don’t even share the apparent belief that mathematics is sort of an algorithm cranking out models of the universe. Nobody really is writing the library of Babel. I think mathematics is as just as much a creative exercise as composing music or devising an experiment. “Explaining” how mathematics depicts the world is much like explaining how music depicts emotions.

    To my eyes, you appear to be insisting that the axioms and their consequences are prior to experience, but give nevertheless give true knowledge about the world. When I blink in astonishment and inquire how this can be if axioms are simply terms of the art (so to speak,)
    and not in some sense true (corresponding to reality,) you not only reject any suggestion that they can be discovered: You insist that it makes no difference that axioms can be optional, or even arguably wrong!

    My point about applied mathematics is that it is much harder to drivel about independence from reality. I read the protests about not believing in a Platonic realm. Unfortunately it doesn’t make these views more plausible by claiming mathematical existence is…nowhere. I could say the same about Heaven. I hope this isn’t getting too testy, but, yes, I do think there is a real issue in the entire notion of mathematical truth. No, saying that it only applies nowhere doesn’t seem like understanding the questions, much less the answer.


  37. “I am taking the usual scientific stance that there is a “real” world and that we obtain information about it empirically. ”
    This is Realism–a metaphysical thesis–not Empiricism–an epistemological thesis.

    Just a matter of how the terms are used in the discipline. It may be part of the reason why philosophers and scientists seem to be talking past each other, in discussions like this. They are using key terms with different senses.


  38. HI phoffman56,

    1. Modus Ponens here refers to the tautology “((a->b)&a)->b” and nothing else. I don’t think that by itself it can be called sound.

    2. The distinction you are talking about is what Kleene calls the “observer language” and the “object language”, and I have mentioned this distinction a few times. But logic is not something completely isolated from everyday language. It is a formalisation of the assumptions that I have set out. If it were not then it would not be good for anything except as an academic exercise.

    3. I obviously mean a tautology in the logical sense.

    For your final paragraph I refer you again to Kleene and in particular his book “Mathematical Logic” in which he makes the observer language/object language distinction and also discusses how logic can apply to everyday situations expressed first in every day language.

    He says that any atom in the object language can stand for a statement in the observer language that is capable of being true or false.

    Once that assignation has been made then the observer language can be forgotten about while the argument is treated formally in the object language.

    So, going by one of the giants of logic, something can be a tautology in the formal sense and also stand for an argument about statements made in the observer language.

    There is no dichotomy as you suggest and if there was then, as I said earlier, logic would be more or less useless.


  39. We have to take our reason as a given either way. If determinism is true, we are not simply lucky when we are right. We have evolved a brain with the capacity to reason and a brain which can reason correctly is more useful than a brain which reasons incorrectly. Thus we can be very confident about our most basic ability to reason.

    (Yes, this argument is justified with reason, but we have to take reason as a given to get anywhere so that is unavoidable)

    Of course this all goes out the window when we talk about very abstract topics. We get people talking past each other, missing the point, failing to connect the dots, etc. People often disagree, so it’s obvious that humans are not perfect reasoning machines. However people do generally agree on the most simple cases, such as the basic rules of logic.

    If determinism is sometimes true and sometimes false, I would have much more confident in the deterministic reasoning because I can give a broad strokes account of how and why it works. Where indeterminism comes into it, I see no reason to think that reliability is improved. Seems more like a case of luck to me.


  40. Well said on this. I believe in the MUH but I am far from convinced it is a falsifiable scientific hypothesis. What would a falsification look like? Finding some non-mathematical property of reality? Such as? What would that look like? How could we be sure it didn’t have a mathematical underpinning?


  41. In the same way, I can declare my premises about distances and fuel consumption to be “axioms” of my system, and by conclusion to be true within that system. Thus they are “axioms”, not empirical “facts”, in the same way that you are asserting that the axioms leading to Pythagoras are “axioms” and not empirical “facts”.


  42. Hi DM,

    Oh really? Not even the property of being real? What then distinguishes them from a mathematical model of such particles or from an imaginary universe where the laws of physics are different?

    Well I said that “there is nothing about these particles except their logical/mathematical behaviour”. The word “behaviour” there is important, and includes the ability to affect something else, to bump into another particle — with those interactions between particles being described mathematically.

    The idea that existence has a clear meaning is an illusion, in my view.

    I regard “existence” as the property of being able to bump into something that can bump into something that can … leading to a long chain of causality that can, in principle, eventually impinge on human sense data. (My definition is expounded here.)


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