Introduction: Read This First — I

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

The Nature of Philosophy
How Philosophy Makes Progress and Why It Matters

by Massimo Pigliucci
K.D. Irani Professor of Philosophy
the City College of New York

To Patricia Churchland, without whom this book would have taken a very different path.

Introduction: Read This First — I

“We are responsible for some things,
while there are others for which we cannot be held responsible.”

Readers (including, often, myself) have a bad habit of skipping introductions, as if they were irrelevant afterthoughts to the book they are about to spend a considerable amount of time with. Instead, introductions — at the least when carefully thought out — are crucial reading keys to the text, setting the stage for the proper understanding (according to the author) of what comes next. This introduction is written in that spirit, so I hope you will begin your time with this book by reading it first.

As the quote above from Epictetus reminds us, the ancient Stoics made a big deal of differentiating what is in our power from what is not in our power, believing that our focus in life ought to be on the former, not the latter. Writing this book the way I wrote it, or in a number of other possible ways, is in my power. How people will react to it, is not in my power. Nonetheless, it will be useful to set the stage and acknowledge some potential issues right at the outset, so that any disagreement will be due to actual divergence of opinion, not to misunderstandings.

The central concept of the book is the idea of “progress” and how it plays in different disciplines, specifically science, mathematics, logic and philosophy — which I see as somewhat allied fields, though each with its own crucial distinctive features. Indeed, a major part of this project is to argue that science, the usual paragon for progress among academic disciplines, is actually unusual, and certainly distinct from the other three. And I will argue that philosophy is in an interesting sense situated somewhere between science on the one hand and math and logic on the other hand, at the least when it comes to how these fields make progress.

But I am getting slightly ahead of myself. One would think that progress is easy to define, yet a cursory look at the literature would quickly disabuse you of that hope (as we will appreciate in due course, there is plenty of disagreement over what the word means even when narrowly applied to the seemingly uncontroversial case of science). As it is often advisable in these cases, a reasonable approach is to go Wittgensteinian and argue that “progress” is a family resemblance concept. Wittgenstein’s own famous example of this type of concept was the idea of “game,” which does not admit of a small set of necessary and jointly sufficient conditions in order to be defined, and yet this doesn’t seem to preclude us from distinguishing games from not-games, at least most of the time. In his Philosophical Investigations (1953 / 2009), Wittgenstein begins by saying “consider for example the proceedings that we call ‘games’ … look and see whether there is anything common to all.” (§66) After mentioning a number of such examples, he says: “And we can go through the many, many other groups of games in the same way; we can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities.” Hence: “I can think of no better expression to characterize these similarities than ‘family resemblances’; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way. And I shall say: ‘games’ form a family.” (§67) Concluding: “And this is how we do use the word ‘game.’ For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word ‘game.’)” (§68)

Progress, then, can be thought of to be like pornography (to paraphrase the famous quip by US Supreme Court Justice Potter Stewart): “I know it when I see it.” But perhaps we can descend from the high echelons of contemporary philosophy and jurisprudence and simply do the obvious thing: look it up in a dictionary. For instance, from the Merriam-Webster we get:

i. “forward or onward movement toward a destination”
or ii. “advancement toward a better, more complete, or more modern condition”

with the additional useful information that the term originates from the Latin (via Middle English) progressus, which means “an advance” from the verb progredi: pro for forward and gradi for walking.

How is that going to help? I will defend the proposition that progress in science is a teleonomic (i.e., goal oriented) process along definition (i), where the goal is to increase our knowledge and understanding of the natural world. Even though we shall see that there are a lot more complications and nuances that need to be discussed in order to agree with that general conclusion, I believe this captures what most scientists and philosophers of science mean when they say that science, unquestionably, makes progress.

Definition (ii), however, is more akin to what I think has been going on in mathematics, logic and (with an important qualification to be made in a bit), philosophy. Consider first mathematics (and, by similar arguments, logic): since I do not believe in a Platonic realm where mathematical and logical objects “exist” in any meaningful, mind-independent sense of the word (more on this later), I therefore do not think mathematics and logic can be understood as teleonomic disciplines (fair warning to the reader, however: many mathematicians and a number of philosophers of mathematics do consider themselves Platonists). Which means that I don’t think that mathematics pursues an ultimate target of truth to be discovered, analogous to the mapping on the kind of external reality that science is after. Rather, I think of mathematics (and logic) as advancing “toward a better, more complete” position, “better” in the sense that the process both opens up new lines of internal inquiry (mathematical and logical problems give origin to new — internally generated — problems) and “more complete” in the sense that mathematicians (and logicians) are best thought as engaged in the exploration of what throughout the book I call a space of conceptual (as distinct from empirical) possibilities.

How do we cash out this idea of a space of conceptual possibilities? And is such a space discovered or invented? During the first draft of this book I was only in a position to provide a sketched, intuitive answer to these questions. But then I came across Roberto Unger and Lee Smolin’s The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy (2014), where they provide what for me is a highly satisfactory answer in the context of their own discussion of the nature of mathematics. Let me summarize their arguments, because they are crucial to my project as laid out in this book.

In the second part of their tome (which was written by Smolin, Unger wrote the first part), Chapter 5 begins by acknowledging that some version of mathematical Platonism — the idea that “mathematics is the study of a timeless but real realm of mathematical objects,” is common among mathematicians (and, as I said, philosophers of mathematics), though by no means universal, and certainly not uncontroversial. The standard dichotomy here is between mathematical objects (a term I am using loosely to indicate any sort of mathematical construct, from numbers to theorems, etc.) being discovered (Platonism) vs being invented (nominalism and similar positions: Bueno 2013).

Smolin immediately proceeds to reject the above choice as an example of false dichotomy: it is simply not the case that either mathematical objects exist independently of human minds and are therefore discovered, or that they do not exist prior to our making them up and are therefore invented. Smolin presents instead a table with four possibilities:

existed prior? yes existed prior? no
has rigid properties? yes discovered evoked
has rigid properties? no fictional invented

By “rigid properties” here Smolin means that the objects in question present us with “highly constrained” choices about their properties, once we become aware of such objects. Let’s begin with the obvious entry in the table: when objects exist prior to humans thinking about them, and they have rigid properties. All scientific discoveries fall into this category: planets, say, exist “out there” independently of anyone being able to verify this fact, so when we become capable of verifying their existence and of studying their properties we discover them.

Objects that had no prior existence, and are also characterized by no rigid properties include, for instance, fictional characters (Smolin calls them “invented”). Sherlock Holmes did not exist until the time Arthur Conan Doyle invented (surely the appropriate term!) him, and his characteristics are not rigid, as has been (sometimes painfully) obvious once Holmes got into the public domain and different authors could pretty much do what they wanted with him (and I say this as a fan of both Robert Downey Jr. and Benedict Cumberbatch). Smolin, unfortunately, doesn’t talk about the “fictional” category of his classification, which comprises objects that had prior existence and yet are not characterized by rigid properties. Perhaps some scientific concepts, such as that of biological species, fall into this class: “species,” however one conceives of them, certainly exist in the outside world; but how one conceives of them (i.e., what properties they have) may depend on a given biologist’s interests (this is referred to as pluralism about species concepts in the philosophy of biology: Mishler & Donoghue 1982).

The crucial entry in the table, for our purposes here, is that of “evoked” objects: “Why could something come to exist, which did not exist before, and, nonetheless, once it comes to exist, there is no choice about how its properties come out? Let us call this possibility evoked. Maybe mathematics is evoked” (Unger and Smolin, 2014, 422). Smolin goes on to provide an uncontroversial class of evocation, and just like Wittgenstein, he chooses games: “For example, there are an infinite number of games we might invent. We invent the rules but, once invented, there is a set of possible plays of the game which the rules allow. We can explore the space of possible games by playing them, and we can also in some cases deduce general theorems about the outcomes of games. It feels like we are exploring a pre-existing territory as we often have little or no choice, because there are often surprises and incredibly beautiful insights into the structure of the game we created. But there is no reason to think that game existed before we invented the rules. What could that even mean?” (p. 422)

Interestingly, Smolin includes forms of poetry and music into the evoked category: once someone invented haiku, or the blues, then others were constrained by certain rules if they wanted to produce something that could reasonably be called haiku poetry, or blues music. An obvious example that is very close to mathematics (and logic) itself is provided by board games: “When a game like chess is invented a whole bundle of facts become demonstrable, some of which indeed are theorems that become provable through straightforward mathematical reasoning. As we do not believe in timeless Platonic realities, we do not want to say that chess always existed — in our view of the world, chess came into existence at the moment the rules were codified. This means we have to say that all the facts about it became not only demonstrable, but true, at that moment as well … Once evoked , the facts about chess are objective, in that if any one person can demonstrate one, anyone can. And they are independent of time or particular context: they will be the same facts no matter who considers them or when they are considered” (p. 423).

This struck me as very powerful and widely applicable. Smolin isn’t simply taking sides in the old Platonist / nominalist debate about the nature of mathematics. He is significantly advancing that debate by showing that there are two other cases missing from the pertinent taxonomy, and that moreover one of those cases provides a positive account of mathematical (and similar) objects, rather than just a rejection of Platonism. But in what sense is mathematics analogous to chess? Here is Smolin again: “There is a potential infinity of formal axiomatic systems (FASs). Once one is evoked it can be explored and there are many discoveries to be made about it. But that statement does not imply that it, or all the infinite number of possible formal axiomatic systems, existed before they were evoked. Indeed, it’s hard to think what belief in the prior existence of a FAS would add. Once evoked, a FAS has many properties which can be proved about which there is no choice — that itself is a property that can be established. This implies there are many discoveries to be made about it. In fact, many FASs once evoked imply a countably infinite number of true properties, which can be proved” (p. 425).

Reflecting on the category of evoked objective truths provided me with a reading key to make sense of what I was attempting to articulate: my suggestion here, then, is that Smolin’s account of mathematics applies, mutatis mutandis (as philosophers are wont to say) to logic and, with an important caveat, to philosophy. All these disciplines — but, crucially, not science — are in the business of ascertaining “evoked,” objective truths about their subject matters, even though these truths are neither discovered (in the sense of corresponding to mind independent states of affairs in the outside world) nor invented (in the sense of being (entirely) arbitrary constructs of the human mind).

I have referred twice already to the idea that philosophy is closer to mathematics and logic (and a bit further from science) via a qualification. That qualification is that philosophy is, in fact, concerned directly with the state of the world (unlike mathematics and logic, which while very useful to scientists, could be, and largely are, pursued without any reference whatsoever to how the world actually is). If you are doing ethics, or political philosophy, for instance, you are very much concerned with those aspects of the world that deal with interactions among humans within the context of their societies. If you are doing philosophy of mind you are ultimately concerned with how actual human (and perhaps artificial) brains work and generate consciousness and intelligence. Even if you are a metaphysician — engaging in what is arguably the most abstract field of philosophical inquiry — you are still trying to provide an account of how things hang together, so to speak, in the real cosmos. This means that the basic parameters that philosophers use as their inputs, the starting points of their philosophizing, their equivalent of axioms in mathematics and assumptions in logic (or rules in chess) are empirical data about the world. This data comes from both everyday experience (since the time of the pre-Socratics) and of course increasingly from the world of science itself. Philosophy, I maintain, is in the business of exploring the sort of conceptually evoked spaces that Smolin is talking about, but the evocation is the result of whatever starting assumptions are made by individual philosophers working within a particular field and, crucially, of the constraints that are imposed by our best understanding of how the world actually is.

I hope it is clear from the above analysis that I am not suggesting that every field that can be construed as somehow exploring a conceptual space ipso facto makes progress. If that were the case, we would be forced to say that pretty much everything humans do makes progress. Consider, for instance, fiction writing. Specifically, imagine a science fiction author who writes three books about the same planet existing in three different “time lines.” [1] In each book, the geography of the planet is different, which leads to different evolutionary paths for its inhabitants. However, each description is constrained by the laws of physics (he wants to keep things in accordance with those laws), by some rational principles (the same object can’t be in two places, as that would violate the principle of non-contradiction), and perhaps even by certain aesthetic principles. Each book tells a different story, constrained both empirically (laws of physics), and logically. In a sense, this writer would be exploring different conceptual spaces, by describing different possibilities unfolding on the fictitious planet. However, I do not think that we want to say that he is making progress. He is just exploring various imaginary worlds. The difference with philosophy, then, is twofold: i) our writer is doing what Smolin calls “inventing”: his worlds did not have prior existence to his imagining them, and they have no rigid properties. Even the constraints he imposes from the outset, both empirical and logical, could have been otherwise. He could have easily imagined planets where both the laws of physics and those of logic are different. Philosophy, I maintain, is in the business of doing empirically-informed evoking, not inventing, which means that its objects of study have rigid properties. ii) Philosophy, again, is very much concerned with the world as it is, not with arbitrarily invented ones. Even when philosophers venture into thought experiments, or explore “possible worlds” they do so with an interest to figure things out as far as this world is concerned. So, no, I am not suggesting that every human activity makes progress, nor that philosophy is like literature.

There are two additional issues I want to take up right at the beginning of this book, though they will reappear regularly throughout the volume. They both, I think, contribute to much confusion and perplexity whenever the topic of progress in philosophy comes up for discussion. The first issue is that philosophers too often use the word “theory” to refer to what they are doing, while in fact our discipline is not in the business of producing theories — if by that one means complex and testable explanations of how the world works. The word “theory” immediately leads one to think of science (though, of course, there are mathematical theories too). In light of what I have just argued about the teleonomic nature of scientific progress contrasted with the exploratory / qualificatory nature of philosophical inquiry, one can see how talking about philosophical “theories” may not be productive. Philosophers do have an alternative term, which gets used quite often interchangeably with “theory”: account. I much prefer the latter, and will make an effort to drop the former altogether. “Account” seems a more appropriate term because philosophy — the way I see it — is in the business of clarifying things, or analyzing in order to bring about understanding, not really discovering new facts, but rather evoking rational conclusions arising from certain ways of looking at a given problem or set of facts.

The second issue is a way to concede an important point to critics of philosophy (which include a number of scientists and, surprisingly, philosophers themselves). I am proposing a model of philosophical inquiry conceived as being in the business of providing accounts of evoked truths by exploring and refining our understanding of a series of conceptual landscapes. But it is true that such refinement can at some point begin to yield increasingly diminishing returns, so that certain discussion threads become more and more limited in scope, ever more the result of clever logical hair splitting, and of less and less use or interest to anyone but a vanishingly small group of professionals who, for whatever reason, have become passionate about it. A good example of this, I think, is the field of “gettierology,” which has resulted from discussions on the implications of a landmark (very short) paper published by Edmund Gettier back in 1963, a paper that for the first time questioned the famous concept of knowledge as justified true belief often attributed (with some scholarly disagreement) to Plato. We will examine Gettier’s paper and its aftermath as an example of progress in philosophy later on, but it has to be admitted that more than half a century later pretty much all of the interesting things that could have possibly been said in response to Gettier are likely to have been said, and that ongoing controversies on the topic lack relevance and look increasingly self-involved.

However, I will also immediately point out that this problem isn’t specific to philosophy: pretty much every academic field — from literary criticism to history, from the social sciences to, yes, even the natural sciences — suffer from the same malaise, and examples are not hard to find. I spent a large amount of my academic career as an evolutionary biologist, and I cannot vividly enough convey the sheer boredom at sitting through yet another research seminar when someone was presenting lots of data that simply confirmed once again what everyone already knew, except that the work had been carried out on a species of organisms for which it hadn’t been done before. Since there are (conservatively) close to nine million species on our planet, you can see the potential for endless funding and boundless irrelevancy. At the least philosophical scholarship is very cheap by comparison with even the least expensive research program in the natural sciences!


[1] I am grateful to Dan Tippens for this example.


Bueno, O. (2013) Nominalism in the philosophy of mathematics. Stanford Encyclopedia of Philosophy (accessed on 11 June 2015).

Gettier, E.L. (1963) Is justified true belief knowledge? Analysis 23:121-123.

Mishler, B.D. and Donoghue, M.J. (1982) Species concepts: a case for pluralism. Systematic Zoology 31:491-503.

Unger, R.M. and Smolin, L. (2014) The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy. Cambridge University Press.

Wittgenstein, L. (1953 / 2009) Philosophical Investigations. Wiley-Blackwell.

119 thoughts on “Introduction: Read This First — I

  1. synred

    Depends what you mean by empty space. The inside of an atom is filled with electric field. The Pauli exclusions principle keeps the electrons from being pulled into the nucleolus. The electrons in the table rebel the electrons in your sandwich so yo can pick it up and eat it.

    So it depends what you mean by empty.

    Liked by 1 person

  2. synred

    If in comes up sometime, I’ll post my riff on how QM makes transubstanstion either trivial or silly. The very concepts of substance and same are suspect, never mind empty.


  3. brodix

    I think the problem might be in our reductionist bias creates the conclusion that the smallest components are the basis. So now, after atoms, then quanta and now strings, physics is only sure of the math as real.

    Are they just nodes in the network, as with any other object?

    Conceptually is CERN that much more advanced than banging two rocks together, to see what flakes off?

    Logically the whole would be the network and the node the component. Even the idea of the entire universe as a unit has led to the deduction that there must be a larger network of universes.

    Finite versus infinite.


  4. synred

    “I think the problem might be in our reductionist bias creates the conclusion that the smallest components are the basis. So now, after atoms, then quanta and now strings, physics is only sure of the math as real.”

    You impute to physics views only a tiny number of pretty far out theorist hold. You won’t find many experimental physicist (like me) who are the people doing experiments at places like CERN and SLAC (where I worked) who agree with Tegmark’s Mathematical Universe Hypothesis and only a few like me that pay it the least bit of attention.

    If you like you can look at my reviews of Tegmark here

    If I hadn’t been forced into retirement and suffering from terminal boredom it’s unlikely I would have read his book at all.

    MUH is certainly not an evolving consensus even among string theorist or supergravity advocates like Lee Smolin.


  5. synred

    Conceptually is CERN that much more advanced than banging two rocks together, to see what flakes off?

    Conceptually, yes.

    Experimentally, the technique is similar. The modern version goes back to Rutherford who hit gold with alpha particles, saw they bounce back at him, and realized atoms had a small heavy thing (nucleolus) in them, surrounded by a lot of light things (electrons) orbiting.

    Presumably ‘cavemen’ only learned that rock is made of rock. Their accelerator lacked the energy to figure out they were made of some smaller bits. And indeed atoms where demonstrated by chemistry (Dalton) first and only later was it figured out what the atoms where made of by smashing them.

    Likely found the occasion geo, but didn’t leave any record of what they thought of that. Keeping track of what your experiments do is one of the conceptual break throughs.

    Yes, particle physicist like to smash things together. It’s a tried and true technique. The harder you do it, the smaller distances you can probe … hence LHC.


  6. brodix


    I don’t mean to disappoint you, but MUH(a one to one correspondence between model and physical cause) is essentially foundational to current physics. Consider that the ‘fabric of spacetime’ is the presumed physical explanation for the model of GR. Yet what does it do, other than correlate three spatial dimensions with one time dimension and what are they? Essentially the spatial dimensions are the xyz coordinate system and while they are a handy mapping device, are no more foundational to space than longitude, latitude and altitude are foundational to the surface of this planet. The time dimension is really just the narrative effect, codified as measures of duration, from one event(past) to the next(future). Then they try to dismiss the present being simultaneous by saying that depending on location, events can be perceived in different order, which overlooks the fact that it is the energy that is conserved/present, not its changing configuration. We see stars and the moon at the same time, as the energy strikes our eyes simultaneously, while the information carried was recorded either a moment ago, or years ago. Then the argument is for block time, that all events exist on this spacetime continuum, which completely ignores the conservation of energy, as it is the energy being transferred from one event to the next, that connects them in the first place.

    In its own way, spacetime is equivalent to the clockwork cosmos as an explanation for epicycles; presuming a one to one correspondence between observed patterns and physical explanation.

    Not to mention the entire Big Bang cosmology rests on spacetime being physically real.

    The real problem is as you say, “only a few like me that pay it the least bit of attention.”


  7. brodix


    I certainly agree and I didn’t get into his swamp for any other reason than to educate myself, but it has taken some strange turns and if anyone can light my way out of it with a clearly argued case for the whole bigbanginflationdarkmatterenergymultiverses fiasco, I’d go along with it, but until than I see the emperor as being buck naked.


  8. Daniel Kaufman

    Massimo: While it is front-ending things a bit, could you give some hint or sketch of why you think the question of progress in philosophy matters (the second part of the book’s title)?

    And I mean this beyond pragmatic concerns. So, the problem of getting people to fund a discipline which cannot be shown to “progress” in the expected ways, is not the sort of thing I’m after. I acknowledge this and think that it, too, is part of the problem. And it’s the reason why other humanities programs are in trouble — they can’t show that they “progress” in the manner that people have come to expect. A manner indicated by the sciences, broadly construed.

    You see, I don’t think philosophy really progresses, because I don’t think that’s the *kind* of animal philosophy is. Philosophy’s primary role, as I see it, is critical, and it fulfills this role through the use of a distinctive and powerful tool set: one that includes a number of different logics, linguistic analysis, analogical reasoning, and others. It can progress in the sense that it can develop better tools and better deploy those tools. It can progress in the sense of providing greater clarity with regard to the things we know from other disciplines and from ordinary experience. One can also measure a kind of progress in the corpses it leaves behind — the bad thinking, muddled interpretations, inapt analogies and metaphors…you get the drift.

    But I don’t think that it progresses, in the sense of developing an ever improving picture of anything — not just of the world, but even, as you put it, of “conceptual space.”

    So, beyond practical concerns with philosophy’s place in the university or among the disciplines or in the public conception, is there another reason why you think it matters whether or not philosophy progresses, in some sense other than the largely critical ways that I have enumerated?


  9. Daniel Kaufman

    synred: If Brodix is anything he is an earnest seeker. Could you possibly explain why what he said about MUH’s relationship to physics is mistaken? Or is it the sort of thing that cannot be translated into layperson-speak?

    Liked by 1 person

  10. ejwinner


    When I was in graduate school, I had a professor who believed that if he could only vibrate his molecules, he could walk through walls, although he was never able to explain how he was going to make that happen. Two years later he had a heart-attack (fortunately he survived).

    A hearts may be 99.99(etc.) empty space; but when it infarcts, that’s not good.

    I can see how your information – which by the way is no news, so I don’t have to let anything “sink in,” thank you very much – can be informative in a certain kind of metaphysics; otherwise, I can’t see any use to it, philosophically. We’re still going to debate the ethics of eating free range chicken, and, epistemologically, the qualia of the taste of that chicken, not to mention the ontology of fried, baked, or still running around in the barnyard – possibly with its head chopped off, but still animated, which raises the possibility of a transitional ontology between ‘living’ or not – regardless of whether chickens are empty space (or a mystical illusion, for that matter).

    And your dissertation doesn’t really leave you prepared for a nominalist counter charge that concepts like ‘chicken’ or ‘quark,’ perhaps even ‘time’ and ‘space,’ have no metaphysically necessitated content, but are only linguistic constructs needed to negotiate reality and communicate with others. Whatever ‘that thing there’ is, it will only be knowable through such a concept, so the only question is whether the concept will be necessary, useful, agreed, or arbitrary (in a socially sanctioned way), and in what context.

    What I’m suggesting is, yeah, you’re engaging in a kind of metaphysics, no harm in that; but that’s not the whole of philosophy. You write as though you’ve got the big picture there; I suggest you’re only looking at a corner of the canvass.

    Liked by 4 people

  11. synred

    MUH is not something that anybody I know pays the least bit of attention to — even theorist. Maybe lunch time BS on occasion. Tegmark (has he admits) is considered a bit of a nut.

    I can’t follow what Brodrix is saying, so I can’t explain why it’s wrong. It just makes no sense to me.

    As you may have noticed I like to keep things concrete. Here he kind of gored my cow, so maybe I overacted a bit and didn’t deploy enough ‘weasel’ words.


    I am contemplating an essay on “The Weakness of the Weak Anthropic Principle” the main point of which would be that WAP makes no-sense and spells the end of science if MUH is true or assumed. Some hints of the problems are already in my shorter Tegmark review.


  12. synred

    When I was in graduate school, I had a professor who believed that if he could only vibrate his molecules, he could walk through walls, although he was never able to explain how he was going to make that happen. Two years later he had a heart-attack (fortunately he survived).

    He, of course, couldn’t ‘vibrate is molecules

    He was likely thinking of Quantum Tunneling where a particle can penetrate a potential barrier that has an energy higher than it does (a wall). Something impossible classically, but actually used in devices we build today.

    The probability for a Professor or tunneling through a wall is, to say the least, very small. I can confidently predict it will never happen to anyone anywhere in our universe.

    Tunneling is one of the reasons I dislike Everett’s ‘Many Worlds/ interpretation of QM. In ‘Many Worlds’ there’s an infinite number of splits every time a ‘measurement’ takes place. In some of those ‘worlds’ my finger just penetrated the ‘e’ key on my laptop and I’m writhing in pain with a finger embedded in the plastic. Evidently, not this world though!


  13. SocraticGadfly

    Dan, that is an interesting second point. And, other than Massimo’s (generic?) etymological definition, how do we know what this might be? That’s why I mentioned neuroscience and behavioral science as part of what is normally lumped under cognitive science — for issues of knowledge, how we know etc.

    Is cog sci going to tell us anything new anytime soon about ethics, metaphyics, or other branches of philosophy? No.

    About epistemological issues? Quite possibly, as with volition. If nothing else, if larger chunks of folk philosophy are ruled tout court, that’s progress of some sort.


  14. brodix


    Sorry if I seem presumptuous. I have quite thick skin, so if I’ve offended you, I’ll take your criticisms as best intentioned.

    Would it make sense to say time is an effect occurring due to change in the present and what is measured is essentially frequency? That tomorrow becomes yesterday because the earth turns. The processes occurring create the forms we perceive?

    If this seems illogical, is there some point that stands out as clearly wrong?

    Better be off to bed. Been following the Wisconsin primaries


  15. synred

    Would it make sense to say time is an effect occurring due to change in the present and what is measured is essentially frequency? That tomorrow becomes yesterday because the earth turns. The processes occurring create the forms we perceive

    So I don’t know what you mean by these word. It seems kind circular. ‘change’ presumes ‘time’. Frequency is just regular change at a fixed interval. I a wave goes up and down at fixed intervals (at least approximately). The turning of the earth is an example with a frequency of 1 day per day (by definition of course).

    “The processes occurring create the forms we perceive” makes no sense at all to me. What processes? ‘occurring’ implicitly time as does ‘process’. And what are the ‘forms’ we perceive?

    I don’t pretend to understand time, but I can measure it under the assumption that devices constructed (like a pendulum) don’t change with time (T-invariance) and so oscillate at a constant frequency.

    “The only reason for time is so that everything doesn’t happen at once. ”

    Albert Einstein

    Read more at:

    I suspect this one of those made up Einstein quotes. I thought it was Woody Allen.


  16. synred [a]

    So you don’t need a human to prove theorems.

    I can imagine even an automated axiom generator at least in a narrow regime of possible systems. Though programmers would have to code something about what sort of axioms in what kind of math could possibly be generated.

    I don’t think this is particularly Platonic. The concept of ‘possibilities’ seems adequate.

    [a] I was a post-doc at Argonne where this work is being done — not in math, of course.

    Liked by 1 person

  17. Robin Herbert

    Hi synred,

    “So you don’t need a human to prove theorems.”

    We just need ’em to write automated proof checkers, prepare the proofs and understand the results.

    When i was in uni there was much talk of building machines that could conceive of stuff that humans can’t, like n dimensional spaces so as yo advance the maths on these, but I think we’ve a way to go yet.

    “I don’t think this is particularly Platonic. The concept of ‘possibilities’ seems adequate.”

    I agree, but when i suggested this last time we were discussing Smolin and evocation, I got shot down big time. I think they thought I was smuggling Platonism in by a back door.

    Liked by 1 person

  18. Massimo Post author

    Technical communication (before my next round of replies):

    I think it will be a good idea, for the purposes of this series, for me to close comments on a given post once the next is published, in order to move the conversation along.

    However, I will then gradually re-open old discussion threads, in case people really have an irresistible urge to continue (within limits, I will still exercise my discretion about individual comments or commenters), and for new readers who will stumble on the site in future weeks or months.

    Liked by 1 person

  19. Massimo Post author


    “Your argument suggests that Kirk and Spock are somehow “invented”, while the 3D chess game sitting between them was “evoked”. This is despite the fact they may have all come from the same author and arguably the same intellectual process”

    The author may be the same, but not the intellectual process (well, depending on what you mean by that term). Right, the distinction is clear: once invented by someone, Kirk and Spock can be made to “do” all sorts of things, with few constraints. But once the rules of 3D chess are laid down one can describe its rigid characteristics in very precise and objective terms. (I know, I’ve played 3D chess…)


    “It might be amusing for you to learn that it was reading your former blog posts on Rationally Speaking that first interested me in Mathematical Platonism. Previously, I believed that mathematics was purely a mental construct. But you started me a journey of discovery that resulted* in my conversion; you helped me become a Mathematical Platonist! Imagine how torn I am between amusement and distress when I read you opine on the subject today!”

    Very funny indeed! Well, at the least this shows we can both change our minds about things, even though in this case we went in different directions!


    I do think you are correct about your dispute with Dan about the frequency of Platonists among philosophers (though it is still a minority position, albeit a strong one). But I really can’t take seriously any talk along the lines of “the universe is made of math,” and your points about the Pauli principle etc., while correct (I think, I’m not a physicist!) seems to me irrelevant. To say that the universe is *made of* math appears to me to be a category mistake, and Tegmark himself had a really hard time defending his (confused) ontological claims in front of an audience of philosophers when he came to CUNY’s Graduate Center. I was in the audience, and it was painful (and, mischievously, a little pleasurable) to watch.


    “One cannot be a metaphysical/philosophical/ontological naturalist and a Platonist about anything”

    I don’t think that’s right. Ladyman and Ross (Every Thing Must Go), for instance, declare themselves to be naturalist Platonists. I think your objection may confuse naturalism with physicalism. One cannot be a Platonist and a physicalist, but naturalism is broader than physicalism, and it can (albeit awkwardly) accommodate Platonism.

    “most analytic philosophers, today, being naturalists, it is based on my thirty years or so in the profession; the dominant litearture and the arc that this literature has taken since Quine”

    I think that flies in the face of the numerical survey that pete mentioned, and which I have also read (I make a big deal of it in the last chapter of this book). This tells us, I think, something interesting: when asked anonymously, more philosophers turn out to be Platonists than it emerges from a deep acquaintance with the published literature. It appears that Platonism is a belief that is more widespread than one would think, but it tends to lurk underground because people are not comfortable publishing about it.

    “While it is front-ending things a bit, could you give some hint or sketch of why you think the question of progress in philosophy matters (the second part of the book’s title)? … I don’t think philosophy really progresses, because I don’t think that’s the *kind* of animal philosophy is. … It can progress in the sense of providing greater clarity with regard to the things we know from other disciplines and from ordinary experience. One can also measure a kind of progress in the corpses it leaves behind. But I don’t think that it progresses, in the sense of developing an ever improving picture of anything”

    In response to your question, I think it is intellectually interesting (beyond the pragmatics) to ask what sort of beast philosophy is, and whether or in what sense it makes “progress.” As a practitioner of the discipline, this seems to me something I like to be clear about.

    Notice that the title of the current book is “The Nature of Philosophy,” while originally it was “Does Philosophy Make Progress?” — which reflects my broader interest about what kind of intellectual discipline philosophy turns out to be, regardless of whether it makes progress.

    As for your other observations, I think it will become clearer near the end of the book that we are much closer to agreement than you may think now.


    “as with Bishop Berkeley’s idealism, I believe Samuel Jonson already had a swift kick of refutation for such things”

    As is well known, Jonson completely and spectacularly missed Berkeley’s point with his alleged refutation.


  20. Disagreeable Me (@Disagreeable_I)


    I have to agree with Peter that naturalism is perfectly compatible with Platonism. You seem to mean by naturalism some form of physicalism or materialism, but to me naturalism is about rejecting the supernatural (Gods, psychic powers, ghosts, superstition, magic and so on) where the supernatural consists of entities or forces that contravene or suspend the laws of physics. Numbers, games and other mathematical objects are not supernatural in this sense, so there is no contradiction between Platonism and naturalism. I myself am both a Platonist and a naturalist.

    @Brodix, @Synred, @Dan,

    Even as an ardent MUH-supporter myself, I think what Brodix has said is wildly overblown. I agree that most physicists pay it no attention and consider Tegmark a bit strange for pursuing it. In my view, the MUH has little to do with physics and much more to do with philosophy.


    I don’t know what Plato believed, but I don’t think the allegory of the cave has much to do with modern mathematical Platonism.

    > I don’t think this is particularly Platonic. The concept of ‘possibilities’ seems adequate.

    I would say that Platonism is just taking the concept of possibilities seriously. There’s nothing particularly mystical or supernatural about Platonism in my view, although this is a common misunderstanding. Platonism, to me, is just adopting the attitude that when we say things like “I believe there *is* a solution to this problem” or “there *is* a set of interesting possibilities in this space we should explore”, the verb “is” should be understood as connoting a kind of abstract existence. I’m not saying that mathematical objects are floating around in a Platonic realm, I’m just saying that the concept of existence is a mental and linguistic toolkit which is useful and appropriate to apply in the case of mathematical objects.

    That’s not to say that this doesn’t have some interesting consequences (particularly for me in philosophy of mind and the MUH), but the basic idea of Platonism is initially pretty modest. I don’t really think there is a fact of the matter on whether mathematical objects *really* exist (because I think the idea of *real* existence — unqualified with respect to a particular context or linguistic convention — is meaningless). I just think it is most appropriate and useful to adopt the attitude or convention that they do.

    Liked by 1 person

  21. brodix

    Arthur, DM, Dan,

    To google some references and ask a few questions about what seems broadly assumed, does anyone here think past and future are as physically real as the present state, aka “block time”

    Here is the wikipedia link on it, for reference;

    My own view would be a form of presentism;

    With the caveat that what we overlook is that it is not this point of the present going past to future, but change within it turning future to past, i.e., tomorrow becomes yesterday because the earth turns.


  22. brodix

    All of which ties into my previous point that because processes can be modeled as static equations, it becomes assumed the actual process is irrelevant, i.e.. 1+1 always equal 2, so actually adding them is unnecessary to prove this.

    Then then ties back into what math assumes to be, a reductionistic and ontological description of reality and the practical complications created.


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