Introduction: Read This First — II

work in progress[for a brief explanation of this ongoing series, as well as a full table of contents, go here]

Before concluding this overview and inviting you to plunge into the main part of the book, let me briefly discuss some of the surprisingly few papers written by philosophers over the years that explicitly take up the question of progress in their field, as part of scholarship in so-called “metaphilosophy.” I have chosen three of these papers as representative of the (scant) available literature: Moody (1986), Dietrich (2011) and Chalmers (2015). [2] The first one claims that there is indeed progress in philosophy, though with important qualifications, the second one denies it (also with crucial caveats), and the third one takes an intermediate position.

Moody (1986) distinguishes among three conceptions of progress: what he calls Progress-1 takes place when there is a specifiable goal about which people can agree that it has been achieved, or what counts towards achieving it. If you are on a diet, for instance, and decide to lose ten pounds, you have a measurable specific goal, and you can be said to make progress insofar your weight goes down and approaches the specific target (and, of course, you can also measure your regress, should your weight go further up!). Progress-2 occurs when one cannot so clearly specify a goal to be reached, and yet an individual or an external observer can competently judge that progress (or regress) has occurred when comparing the situation a time t vs the situation at time t+1, even though the criteria by which to make that judgment are subjective. Moody suggests, for example, that a composer guided by an inner sense of when they are “getting it right” would be making this sort of progress while composing. Finally, Progress-3 is a hybrid animal, instantiated by situations where there are intermediate but not overarching goals. Interestingly, Moody says that mathematics makes Progress-3, insofar as there is no overall goal of mathematical scholarship, and yet mathematicians do set intermediate goals for themselves, and the achievement of these goals (like the proof of Fermat’s Last Theorem) are recognized as such by the mathematical community. (Moody says that science too makes Progress-3, although as we have discussed before, science actually does have an ultimate, specifiable goal: understanding and explaining the natural world. So I would rather be inclined to say that science makes Progress-1, within Moody’s scheme.)

Moody’s next step is to provisionally assume that philosophy is a type of inquiry, and then ask whether any of his three categories of progress apply to it. The first obstacle is that philosophy does not appear to have consensus-generating procedures such as those found in the natural sciences or in technological fields like engineering. So far so good for my own account given above, since I distinguish progress in the sciences from progress in other fields, particularly philosophy. Moody claims (1986, 37) that “the only thing that philosophers are likely to agree about with enthusiasm is the abysmal inadequacy of a particular theory.” While I think that is actually a bit too pessimistic (we will see that philosophers agree — as a plurality of opinions — on much more than they are normally given credit for), I do not share Moody’s pessimistic assessment of that observation: negative progress, i.e., the elimination of bad ideas, is progress nonetheless. Interestingly, Moody remarks (again, with pessimism that is not warranted in my mind) that in philosophy people talk about “issues” and of “positions,” not of the scientific equivalent “hypotheses” and “results.” I think that is because philosophy is not sufficiently akin to science for the latter terms to make sense within discussions of philosophical inquiry.

Moody soon concludes that philosophy does not make Progress-1 or Progress-3, because its history has not yielded a trail of solved problems. What about Progress-2? Here the discussion is interesting though somewhat marginal to my own project. Moody takes up the possibility that perhaps philosophy is not a type of inquiry after all, and analyzes in some detail two alternative conceptions: Wittgenstein’s (1965) idea of philosophy as “therapy” and Richard Rorty’s (1980) so-called “conversational model” of philosophy. As Moody (1986, 38) magisterially summarizes it: “Wittgenstein believed that philosophical problems are somehow spurious and that the activity of philosophy … should terminate with the withdrawal, or deconstruction, of philosophical questions.” On this view, then, there is progress, of sorts, in philosophy, but it is the sort of “terminus” brought about by committing seppuku. As Moody rather drily comments, while nobody can seriously claim that Wittgenstein’s ideas have not been taken seriously, it is equally undeniable that philosophy has largely gone forward pretty much as if the therapeutic approach had never been articulated. If a proposed account of the nature of philosophy has so blatantly been ignored by the relevant epistemic community, we can safely file it away for the purposes of this book.

Rorty’s starting point is what he took to be the (disputable, in my opinion) observation that philosophy has failed at its self-appointed task of analysis and criticism. Moody quotes him as saying (1986, 39): “The attempts of both analytic philosophers and phenomenologists to ‘ground’ this and ‘criticize’ that were shrugged off by those whose activities were purportedly being grounded and criticized.” Rorty arrived at this because of his rejection of what he sees as philosophy’s “hangover” from the 17th and 18th centuries, when philosophers were attempting to set their inquiry within a framework that allowed a priori truths to be discovered (think Descartes and Kant), even though David Hume had dealt that framework a fatal blow already in the 18th century.

While Moody finds much of Rorty’s analysis on target, I must confess that I don’t, even though it does have some value. For instance, the fact that other disciplines (like science) marched on while refusing to be grounded or criticized by philosophy is neither entirely true (lots of scientists have paid and still pay a significant amount of attention to philosophy of science, for instance) nor should it necessarily be taken as the ultimate test of the value of philosophy even if true: creationists and climate change denialists, after all, shrug off any criticism of their positions, but that doesn’t make such criticism invalid, or futile for that matter (since others are responding to it). Yet, there is something to be said for thinking of philosophy as a “conversation” more than an inquiry, as Rorty did. The problem is that this and other dichotomies presented to us by Rorty are, as Moody himself comments, false: “we do not have to choose between ‘saying something,’ itself a rather empty notion that manages to say virtually nothing, and inquiring, or between ‘conversing’ and ‘interacting with nonhuman reality.’” Indeed we don’t.

But what account, then, can we turn to in order to make sense of progress in philosophy, according to Moody? I recommend the interested reader check Moody’s discussion of Robert Nozick’s (1981) “explanational model” of philosophy, as well as of John Kekes’ (1980) “perennial problems” approach, but my own treatment here will jump to Nicholas Rescher (1978) and the concept of “aporetic clusters,” which is one path that supports the conclusion — according to Moody — that philosophy does make progress, and it is a type-2 progress. Rescher thinks that it is unrealistic to expect consensus in philosophy, and yet does not see this as a problem, but rather as a natural outcome of the nature of philosophical inquiry (1986, 44): “in philosophy, supportive argumentation is never alternative-precluding. Thus the fact that a good case can be made out for giving one particular answer to a philosophical question is never considered as constituting a valid reason for denying that an equally good case can be produced for some other incompatible answers to this question.”

In fact, Rescher thinks that philosophers come up with “families” of alternative solutions to any given philosophical problem, which he labels aporetic clusters. [3] According to this view, some philosophical accounts are eliminated, while others are retained and refined. The keepers become philosophical classics, like “virtue ethics,” “utilitarianism” or “Kantian deontology” in ethics, or “constructive empiricism” and “structural realism” in philosophy of science. Rescher’s view is not at all incompatible with my idea of philosophy as evoking (to use the terminology introduced earlier), and then exploring and refining, peaks in conceptual landscapes. As Moody (1986, 45) aptly summarizes it: “that there are ‘aporetic clusters’ is evidence of a kind of progress. That the necrology of failed arguments is so long is further evidence.”

A very different take on all of this is what we get from the second paper I have selected to get our feet wet for our exploration of progress in philosophy and allied disciplines, the provocatively titled “There is no progress in philosophy,” by Eric Dietrich. The author does not mince words (to be sure, a professional hazard in philosophy, to which I am not immune myself), even going so far as diagnosing people who disagree with his contention that philosophy does not make progress with a mental disability, which he labels “anosognosia” “[a] condition where the affected person denies there is any problem.” I guess the reader should be warned that, apparently, I do suffer from anosognosia.

Dietrich begins by arguing that philosophy is in a relevant sense like science. Specifically, he draws a parallel between strong disagreements among philosophers on, say, utilitarianism vs deontology in ethics, with similarly strong, and lost lasting, disagreements among scientists about issues like group selection in evolutionary biology, or quantum mechanics during the early part of the 20th century. But, Dietrich then adds, philosophy is also relevantly dissimilar from science: scientific disagreements eventually get resolved and the enterprise lurches forward (every physicist nowadays accepts quantum mechanics, having abandoned Einstein’s famous skepticism about it — though this hasn’t happened yet for group selection, it must be pointed out). Philosophical disagreements, instead, have been more or less the same for 3000 years. Conclusion: philosophy does not make progress, it just “stays current,” meaning that it updates its discussions with the times (e.g., today we debate ethical questions surrounding gay rights, not those concerning slavery, as the latter is irrelevant, at the least in many parts of the world).

Dietrich acknowledges that modern philosophy contains many new notions, and lists a number of them (e.g., supervenience, possible worlds, and modal logic). But immediately dismisses the suggestion that these may represent advances in philosophical discourse as “lame.” His evidence is that there is no widespread agreement about any of these notions, so their introductions cannot possibly be seen as advances. It follows that those philosophers who insist in defending their field in this fashion are affected by the above mentioned mental condition.

The reader will have already seen that Dietrich’s point is actually well countered by the preceding discussion, and particularly the explanation put forth by Rescher for why we see aporetic clusters of positions in philosophy. I will develop my own rejection of Dietrich’s sweeping conclusion in terms of non-teleonomic progress instantiated as exploration and refinement of a series of conceptual spaces throughout much of this book. And I will present (empirical!) evidence that philosophers are more in agreement on a wide range of issues than Dietrich and others acknowledge, though the agreement is about the viability of different positions within a given aporetic cluster, not about a single “winning” theory — which makes sense once we conceptualize philosophy in the manner introduced above and to be developed in the following chapters.

But even simply considering Dietrich’s own examples, it is hard to see where exactly he gets the idea that there is overwhelming disagreement: I don’t know of logicians who differ on the validity of modal logic, though of course they will deploy it differently in pursuit of their own specific goals. Nor do I know of anyone who disagrees on the concepts of supervenience or possible worlds, though people do reasonably disagree on what such concepts entail vis-a-vis a number of specific philosophical questions. Dietrich makes his argument in part by way of a thought experiment in which he brings Aristotle back to life and has him attend a couple of college courses: he imagines the Greek finding himself astonished and bewildered in a class on basic physics, but very much at ease in a class in logic or metaphysics (all three subjects, of course, on which Aristotle had a great deal to write, 23 centuries ago). My own intuition, however, is a bit different (we will come back to the use and misuse of intuitions and thought experiments in philosophy). While I agree that Aristotle wouldn’t know what to make of quantum mechanics and general relativity, he would have a lot of catching up to do in order to understand modern logics (plural, as there is an ample variety of them), and even in metaphysics he would have to take at least a remedial course before jumping in with both feet (not to mention that he wouldn’t know what the name of the discipline refers to, since it was adopted after his death).

Dietrich then moves on to introduce another mental illness, apparently affecting a much smaller number of philosophers: nosognosia, a condition under which the patient knows that there is something wrong, but still has some trouble fully accepting the implications. He discusses two such philosophers: Thomas Nagel (1986) and Colin McGinn (1993). Both Nagel and McGinn conclude that philosophical problems are intractable, and, hence, that there is no such thing as philosophical progress. However, they arrive at this conclusion by different routes. For Nagel this is because of an irreconcilable conflict between first (subjective) and third (objective) person accounts. While science deals with the latter, philosophy has to tackle both, and this creates contradictions that cannot be overcome. Here is Dietrich’s summary of Nagel’s view (2011, 339):

“There are three points of view. From the subjective view, we get one set of answers to philosophy questions, and from the objective view, we get another, usually contradictory, set, and from a third view, from which one can see the answers of both the subjective and objective views, one can see that the subjective and objective answers are equally valid and equally true. Therefore, philosophy problems are intractable. Philosophy cannot progress because it cannot solve them.”

McGinn, instead, says that there are answers to philosophical problems, but these — for some mysterious reason — are beyond human reach. Again, Dietrich’s summary (2011, 339):

“There are two relevant points of view. From one, the human view, philosophy problems are intractable. From the other, the alien view, philosophy problems are tractable (perhaps even trivial). The situation here is exactly like the situation with dogs and [the] English [language]. We easily understand it. Dogs understand only a tiny number of words, and seem to know nothing of combinatorial syntax. Therefore, though it is unlikely we can solve any philosophy problems, they are not inherently intractable.”

Briefly, I think both Nagel and McGinn are seriously mistaken — and I believe most philosophers agree, as testified by the straightforward observation that few seem to have stopped philosophizing as a result of considering these (well known) arguments.

Nagel has made a similar claim about the incompatibility of first and third person descriptions before, specifically in philosophy of mind (indeed, we will shortly discuss his classic paper on what it is like to be a bat). But that alleged incompatibility is more simply seen as two different types of descriptions of certain phenomena, descriptions that do not have to be incompatible, and yet that are not reducible to each other. Briefly, the fact that I feel pain (first person, subjective description) and that a neuroscientist will say that my C-fibers have fired (third person, objective description) are both true statements; they are compatible (indeed, I feel pain because my C-fibers are firing, as demonstrated by the fact that if I chemically inhibit that neurological mechanism I thereby cease to feel pain); and they are best understood, respectively, as an experience vs an explanation. But experiences don’t (have to) contradict explanations, assuming that the latter are at the least approximately true. A fortiori, I would like to see a good example of a philosophical problem that necessarily leads to incompatible treatments when tackled from either perspective. I do not think such a thing exists.

McGinn’s position is, quite simply, empty. While the analogy between the advanced understanding of an alien race vs our own primitive capacities and the similar difference between  how dogs and humans understand English may seem compelling, there is no independent reason to think that philosophical problems are intractable by the human mind. Indeed, they have been tackled over the course of centuries, and we will see that progress has been made (once we understand “progress” in the way sketched above and to be further unpacked throughout the book). Interestingly, McGinn too, like Nagel before him, applies his approach to philosophy of mind, where he claims that the problem of consciousness cannot be resolved because we are just not smart enough. This “mysterian” position, as it is known, may be correct for all I know, but it doesn’t seem to lead us anywhere.

Similarly, where does Dietrich’s contemptuous rejection of the very idea of philosophical progress lead him? Nowhere, as far as I can see. He concludes by quoting Wittgenstein from the Tractatus: “My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) What we cannot speak about we must pass over in silence.” And yet, again, philosophy has persisted in existing as a field (I would be so bold as say, in moving forward!) despite Wittgenstein, and I greatly suspect will do much the same despite Dietrich’s cynicism.

A few comments now on Chalmer’s (2015) contribution to the question of progress, or lack thereof, in philosophy. He stakes a reasonable intermediate position, acknowledging that philosophy clearly has made progress, but asking why it hasn’t achieved more. He arrives at the first conclusion by a number of ways, including noting the incontrovertible fact that, for instance, the works of highly notable philosophers like Plato, Aristotle, Hume, Kant, Frege, Russell, Kripke, and Lewis have clearly been progressive with respect to the thinkers that preceded them, no matter what one’s conception of “progress” happens to be. Chalmers goes on to briefly discuss a number of way in which philosophy has, in fact, made progress: there has been convergence on some of the big questions (e.g., most professional philosophers are atheists and physicalists about mind), as well as some of the smaller ones (e.g., knowledge is not simply justified true belief, conditional probabilities are not probabilities of conditionals).

Still, maintains Chalmers, the progress that philosophy has made is slow and small in comparison to that of the natural (but not, he argues, the social) sciences. He discusses some possible explanations for this difference between philosophy and science, including: “disciplinary speciation,” the fact that new disciplines spin off philosophy precisely when they do begin to make sustained progress, like physics, psychology, economics, linguistics, and so on; “anti-realism,” the idea that certain areas of philosophy do not converge on truth because there is no such truth to be found (e.g., moral philosophy); “verbal disputes,” the Wittgensteinian point that at the least some debates in philosophy are more about using language at cross-purposes than about substantive differences (e.g., free will); “greater distance from the data,” meaning that for some reasons philosophy operates nearer the periphery of Quine’s famous web of beliefs (more on this in the next chapters); “sociological explanations,” where some positions become dominant, or recede in the background, because of the influence of individual philosophers within a given generation (e.g., the unpopularity of the analytic-synthetic distinction during Quine’s active academic career); “psychological explanations,” in the sense that individual philosophers may be more or less prone to endorse certain positions as a result of their character and other psychological traits; and “evolutionary explanations,” the contention that perhaps our naturally evolved minds are smart enough to pose philosophical questions but not to answer them.

Chalmers’ conclusion is that there may be some degree of truth to all seven explanations, but that they do not provide the full picture, in part because some of them apply to other fields as well: it’s not like natural scientists don’t have their own sociological and psychological quirks to deal with, and we may not be smart enough to settle philosophical questions, but we do seem smart enough to develop quantum mechanics and to solve Fermat’s Last Theorem. I think he is mostly on target, but I also think that the missing part of the explanation in his analysis derives from a crucial assumption that he made and that I will reject throughout this book: philosophy is simply not in the same sort of business as the natural sciences, so any talk of direct comparison in terms of progress and truths at the least partially misses the point. Right at the beginning of his paper Chalmers states: “The measure of progress I will use is collective convergence to the truth. The benchmark I will use is comparison to the hard sciences.” This is precisely what I will not do here, though it will take a bit to articulate and defend why.

A final parting note, in the spirit of Introductions as reading keys to one’s book. Friends and reviewers have of course commented on what you are about to read. Some of them found me too critical of, say, the continental approach to philosophy. Others, predictably, found me not critical enough. Some people thought parts of the book are too difficult for a generally educated reader (true), while other people thought some parts would be too obvious to a professional philosopher (also true). This was by design: I am writing with multiple audiences in mind, and I never believed one has to get one hundred percent of the references or arguments in a book in order to enjoy or learn from it (try to read the above quoted Wittgenstein that way and see how far you get, even as a professional philosopher — and there are much more blatant examples available). And of course the complaint has reasonably been raised that I don’t go into the proper degree of depth on a number of important technical issues in philosophy of science, of mathematics, of logic, and of philosophy itself (i.e., in meta-philosophy). Again, true. But what you are about to read is not meant as, nor could it possibly be, either an encyclopedia on philosophical thought or a set of simultaneous original contributions to many of the sub-specialties and specific issues I touch on. Rather, the goal is to pull together, the best I can, what a number of excellent thinkers have said on a variety of issues, connecting them into an overarching narrative that can provide a preliminary, organic stab at the question at the core of the book: does philosophy make progress, and if so, in which sense? I hope that that is justification enough for what you are about to read. And I am confident that better thinkers than I will soon make further progress down this road.

There are, of course, a number of people to whom I am grateful, either for reading drafts of this book (in toto or in part), or for having influenced what I am trying to do here as a result of our discussions. Among these are some of my colleagues at the City University of New York’s Graduate Center, particularly Graham Priest (for discussions about the nature of logic), Jesse Prinz (for discussions about the nature of everything, but particularly science), and Peter Godfrey-Smith (on the nature of science and specifically biology). Leonard Finkleman is one of those who have read the book in its entirety, an effort for which I will be forever grateful. Thanks also to Dan Tippens for specific comments on two chapters (on progress in mathematics & logic, and in philosophy). Elizabeth Branch Dyson, at Chicago Press, has been immensely patient with my revisions of the original manuscript, not to mention as encouraging as an editor could possibly be (and has kindly agreed to finally publish the whole shebang in the form you are reading). I would also like to thank Patricia Churchland and Elliot Sober for the initial support when this project was at the stage of a proposal, as well as two anonymous reviewers for their severe, but obviously well intentioned, criticisms of previous drafts.


[2] Although see also the delightful dialogue by Hansson (2012), featuring a graduate student and two professors of philosophy traveling with him to a conference on teaching philosophy.

[3] Interestingly, from the Greek aporetikos, which means impassable, very difficult, or hard to deal with.


Chalmers, D. (2015) Why Isn’t There More Progress in Philosophy? Philosophy 90:3-31.

Dietrich, E. (2011) There is no progress in philosophy. Essays in Philosophy 12:329-344.

Hansson, S.O. (2012) Editorial: Progress in Philosophy? A Dialogue. Theoria 78:181-185.

Kekes, J. (1980) The Nature of Philosophy. Rowman and Littlefield.

McGinn, C. (1993) Problems in Philosophy: The Limits of Inquiry. Blackwell.

Moody, T.C. (2006) Progress in philosophy. American Philosophical Quarterly 23:35-46.

Nagel, T. (1986) The View From Nowhere. Oxford University Press.

Nozick, R. (1981) Philosophical Explanations. Harvard University Press.

Rescher, N. (1978) Philosophical disagreements: an essay toward orientational pluralism in metaphilosophy. Review of Metaphysics 32:217-251.

Rorty, R. (1980) Philosophy and the Mirror of Nature. Blackwell.

Wittgenstein, L. (1965) The Blue and Brown Books. Harper and Row.


200 thoughts on “Introduction: Read This First — II

  1. Arthur,

    Dualities do offer a very basic, but useful framing device.

    I was just taking exception with Socratic’s statement that they are rigid and deterministic.


  2. I don’t think Socratic was referring to dualities in general, but to Hegel and his predecessors and his acolytes (Marx) going overboard for them and deploying them in a very ridged way (almost like they were logic) rather than just framing.

    They can be useful, but also misleading. The idea of ‘opposite sex’ leads to a lot of BS and even biases.


  3. To simplify so called Hegelian dialectic is more complex than averaging opposites.. It involves opposing views not opposites as such. This blog might be considered such dialectic. All of history probably does not.

    But take that with a large grain of salt. I never read Hegel, tried and failed to read Marx (seemed like gibberish to me) and likely wouldn’t have understood either if had I read ’em.


  4. db,

    “I was more getting at the fact that the field has not progressed in the sense of having a more coherent account of what ethics means, its best approaches, and mechanisms (or if there are any) for normative judgment”

    I honestly don’t know what you mean. There is a significant literature accumulated on meta-ethics, some of which also takes on board empirical results from cognitive science. That certainly looks like the sort of progress you are asking for.

    “do you feel Philosophy would be of value even if it was not capable of progress (regardless of definition)?”

    That’s where Dan is going, but no, not regardless of definition. What is crucial to me, however, is that philosoiphy aids *understanding*, not the search for truth, and certainly not factual truth.

    “How does one assess a “mess” if the only rule is that there are no constraints at all?”

    Have you read the Holmes canon and confronted it with the more recent stuff? It’s pretty clear to me that the latter is a mess…


    “I continue to agree with dbholmes that the distinction between invented and evoked is unsustainable. Many fictions are quite rigid, with respect to what is allowed”

    I doubt I’m going to convince either you or db, but I see the distinction very clearly. While it is reasonable to think of the “rigidity” criterion as a continuous one – which Smolin doesn’t do – the extremes are pretty obviously different in kind: there is almost no rule for what to do with Spock or Holmes, or any other fictional character. By contrast, you can rigorously demonstrate mathematical theorems about chess. If that’s not a quantitative difference with strong qualitative overtones I don’t know what is.

    “I think that the introduction of technical or stipulative vocabulary has very little power to override the common understanding of words”

    So you are throwing away a lot of philosophy, since it is in the business of doing just that. Indeed, pretty much any technical field, including science, does that. I don’t see physicists shying away from using the concept of “mass” just because laypeople are prone to misunderstand it.

    “My suspicion is that within a generation or so, liberal arts and humanities will be largely matters of private pursuit, with the exception of the elite universities and small, private, liberal arts colleges, all of which will be priced far beyond the ability of ordinary people to pursue”

    I love the pessimist in you! I honestly doubt it. I think the humanities crisis is a phase, from which they will bounce back because they are simply too important to be eliminated from public education. But of course that’s an empirical question, not one we can argue from an armchair! Regardless, I would remind you (even though you don’t really know to be reminded) that philosophy has existed and thrived very well for literally millennia without the support of public schools. I suspect it will keep doing so in the future, scientismists notwithstanding.


    “Your reply fails to distinguish between mathematical objects and mathematical *axioms*. It is the axioms that are adopted as real-world models, and out of those one can produce mathematical objects that match real-world behaviour.”

    We have already gone down this road back in the days of Scientia Salon, and people have pointed out to you the existence of plenty of axioms that do not concern the real world. There simply are not parallel lines – in the mathematical sense – anywhere in the universe, for instance. Or geometrical points. Or whatever.

    Moreover, I’m concerned with the whole of mathematics here, not just with the axioms, and I don’t see the point of cherry picking where we should argue.

    “out of those axioms, one can also produce vastly more mathematical objects that do not model or correspond to anything physically instantiated. But the same is true in science!”

    You keep missing the point abut math: it is *not* about the real world. Most mathematicians simply don’t give a fig’s leaf about the real world or the usefulness of what they do to science. It’s a nice side benefit, just like in logic, but not at all the point of the field.

    “This is why your idea of a wider conceptual space fails to produce a neat distinction between philosophy or maths and science”

    It doesn’t have to produce a “neat” distinction, just a distinction sufficiently clear to recover the reality on the ground, which is that, oddly, for all the talk of lack of distinction, I can tell a science paper from a philosophy paper by the first few lines.


    “Now I can ask, mathematical “objects”?”

    Or structures, as it has been pointed out. That’s actually Tegmark’s terminology. It’s vague, but it means the (non physical) objects of study of mathematicians. They include axioms, theorems, geometrical figures, numbers, and so forth.

    Liked by 1 person

  5. “There simply are not parallel lines – in the mathematical sense – anywhere in the universe, for instance. Or geometrical points. Or whatever.”

    Or the dimension of time.


  6. I still say it has nothing to do with Platonism and does not depends on maths being a model for the real world.

    The fact that following such and such rules produces such and such results is as much a fact about the world as any other, even for rules we have just made up on the spot.

    Liked by 1 person

  7. Robin,

    Yet isn’t it important to organize those rules, in order to make sense of them?

    What are foundational, what are emergent, what are evoked, what are invented.

    Ordered, complex, chaotic…


  8. Hi Massimo,
    Since this comment section has re-opened:

    … people have pointed out to you the existence of plenty of axioms that do not concern the real world.

    I deny that there are any widely adopted mathematical axioms that “do not concern the real world”. Even the Axiom of Choice (the usual one pointed to in such discussions) is adopted because it is clearly real-world true about finite sets (it’s only about infinite sets that it may not be real-world true).

    There simply are not parallel lines – in the mathematical sense – anywhere in the universe, for instance. Or geometrical points. Or whatever.

    On parallel lines: Euclidean geometry is adopted because it is a very useful real-world model. Generations of architects and engineers have used Euclidean geometry and still do.

    It does not need to be the case that parallel lines are extant ontological objects for Euclidean geometry to be a real-world model. Indeed, exactly the same can be said about physical theories. There are no “inverse square laws” extant in the universe. You can’t touch or see an “inverse square law”, nor does it have ontological status. And yet the “inverse square law” is adopted as a real-world model (and a very good one).

    The same applies to many physical concepts. Take “pressure”. Again, “pressure” isn’t an extant ontological object, it’s an abstract idea applied to a physical system.

    Moreover, I’m concerned with the whole of mathematics here, not just with the axioms, and I don’t see the point of cherry picking where we should argue.

    But the rest of mathematics is entailed by the axioms, which is why, if the *axioms* have real-world relevance, then so does the rest of maths.

    You keep missing the point abut math: it is *not* about the real world. Most mathematicians simply don’t give a fig’s leaf about the real world or the usefulness of what they do to science.

    I’m not sure that’s true. People who are solely pure mathematicians are rare. Many mathematicians are applied mathematicians, and even more are interested in both pure and applied maths, and historically both have cross-fertilized each other. I think you’d be hard pushed to find mathematicians who simply don’t care about the real-world correspondence of maths.


  9. The same applies to many physical concepts. Take “pressure”. Again, “pressure” isn’t an extant ontological object, it’s an abstract idea applied to a physical system

    I think people knew about pressure before we knew how it works. The explanation is abstract, the phenomena is very ‘kick the rock’ or ‘sit on the chair’ or ‘blow-up the balloon’.


  10. Hi synred,

    The explanation is abstract, the phenomena is very ‘kick the rock’ or ‘sit on the chair’ or ‘blow-up the balloon’.

    True, but your examples illustrate that with “pressure” we’re not dealing with an extant object, rather we are dealing with a way of thinking about the world, in other words a “model”.


  11. What?

    Certainly, people knew about pressure long before we modeled it. It’s a direct experience. Whether ‘experience’ has ontological status or not I leave up to the philosophers. Some, I think, think ‘experience’ is the only thing with ontological status, so the argument could go on forever.



  12. Certainly, people knew about pressure long before we modeled it. It’s a direct experience.

    It’s an *interpreted* experience, and that interpretation is a “model” of how the world works. You’re right that this would have been so long before our modern scientific understanding of pressure (with today’s science being a development and refinement of the earlier concepts).

    The point here, though, is that “pressure” is not an object with ontological status in the way that a “proton” or an “electron” is. Thus the fact that mathematical structures are not ontologically instantiated doesn’t distinguish them from scientific concepts, since many scientific concepts are similarly not ontological objects.


  13. Do I take it that a wave does not have ontological status either?

    Material stuff has ontological status. Patterns of material stuff also have ontological status. Thus a wave that is instantiated in material stuff has ontological status.

    “Pressure”, however, is an abstract concept, a commentary, about stuff (ditto concepts such as temperature, entropy, energy, etc).


  14. So sound (pressure waves) doesn’t have ontological status?

    Pressure seems to me also an a ‘pattern of material’ whether static or moving.

    Do people/animals have ontological status? The stuff we’re made of follows through us kind of like a soliton (perhaps a better analogy than machine), so we’re never the same stuff for long.

    No man ever steps in the same river twice, for it’s not the same river and he’s not the same man.”

    ― Heraclitus

    So does a river have ontological status?

    Just leave it to the philosophers and calculate?

    This would be a good lead into my rant about the absurdly of transubstantiation in the light of QM.

    But that would be even further off topic. It can wait till something comes up when we get back to the normal weekend reads.

    Massimo: If this as any relevance at all, it’s by illustrating that science does need philosophy…


  15. An instantiated wave, being a pattern of material stuff, does indeed have ontological status, as do people and rivers, for the same reason.

    But “pressure” is not a noun, you cannot point at a thing and say “there is a pressure”. That thing might *have* pressure, but the term “pressure” is then a conceptual commentary about the thing.


  16. pres·sure

    noun: pressure

    1. the continuous physical force exerted on or against an object by something in contact with it.
    “the slight extra pressure he applied to her hand”

    the force exerted per unit area.
    plural noun: pressures
    gas can be fed to the turbines at a pressure of around 250 psi”

    synonyms: physical force, load, stress, thrust; More
    compression, weight
    “confined gas exerts a constant pressure”

    2. the use of persuasion, influence, or intimidation to make someone do something.
    “the proposals put pressure on Britain to drop its demand”
    synonyms: coercion, force, compulsion, constraint, duress; More


  17. Massimo great start to this series! However, like you mentioned, a little dense for the general reader on the intro. Looking forward to reading the rest of the series. Yet, I personally don’t give a hoot if philosophy makes progress. Unfortunately for me, I like Continental Philosophy, and I agree with Rorty somewhat about how philosophy can be “conversational” and “therepeutic” somewhat. However, I am looking forward to your work.



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