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. Robin Herbert

    Hi Massimo,

    However, I like your reference to Wolfram (as controversial as he is), indeed, “the outcome of the rules doesn’t exist platonically, but is an effect of the process of their implementation.”

    That would imply, for example, that a theorem is neither true nor false until it is proved.

    That seems a rather radical position to me.

    I am not sure that this actually represents Wolfram’s position. Would he say, for example, that 110 was not a universal machine until it was proved to be so?

    Liked by 1 person

  2. Robin Herbert

    In any case, I don’t think the idea works. If John has an algorithm that has never run before, at 2:30 pm he claims “There is no fact of the matter about what this algorithm will output”. He runs the algorithm and it finishes at 2:35 pm and outputs a 5.

    He then claims ‘At 2:30 pm today it was not inevitable that this algorithm, would, if run correctly, output a 5’.

    But that is clearly wrong. At 2:35 pm he knows that 5 was the inevitable output of the algorithm, when run correctly. So he knows that at 2:30 pm it was already inevitable that the algorithm, if run correctly, would output a 5.

    So he knows that, at 2:30 pm, before the algorithm had ever been run, that there was already a fact of the matter about the output of the algorithm.


  3. Massimo Post author


    good point, and I’m not sure how Wolfram would react. But the fact is, algorithms — like mathematical objects — are not “out there.” They are human inventions. But they are different in kind from fictional characters a la Sherlock Holmes, because once invented they have rigid properties. The idea, really, is to be parsimonious with one’s metaphysical commitments while still making some sense of the world and retaining useful or undeniable distinctions.


  4. Disagreeable Me (@Disagreeable_I)

    I think that’s right, Robin.

    I feel that a defender of Smolin’s views would argue that it’s not computing the algorithm that matters but defining it. Until you specify the algorithm, (and so evoke it), then there is no fact of the matter about what it will do, because it hasn’t been defined yet and it is meaningless to speculate on what properties an undefined object might have.

    While this doesn’t seem completely indefensible to me, I don’t agree with it, because from where I’m standing the algorithm we are referring to is the same object whether a human being has defined it or not. Even if it has not been defined (a Platonist would say discovered) by a human, there are truths about it, even if human beings cannot discuss those truths until they have discovered/defined it for themselves.

    So, to me, pi has always had the value 3.14159….,. Clearly we can discuss this now that pi has been defined, but what we say applies retrospectively to times before pi was defined and even before there were conscious beings around to think about pi.

    Liked by 1 person

  5. ejwinner

    A game nobody knows or plays has the same ontological status as a political essay nobody ever thought to write. It is precisely meaningless.

    Of course one can invent a game and then claim to have ‘discovered’ it; I can write an essay and claim I discovered it, word for word, hanging out among the aliens or gods; that’s how ‘sacred texts get written, after all – Look at these stone tablets! Ten commandments! Count them, ten!”

    Mathematical Platonism seems awfully like a computerized Kabbalism.

    At any rate this debate is becoming pointless; Assuming the inventiveness of the human mind has great pragmatic value in how we learn from one another and pursue inquiry. Platonism has no means of establishing its claims (hypothetical conjectures, as noted, are no argument), and is only useful as motivating some mathematicians in assuming they are working their way to an ‘ultimate truth;’ otherwise it’s pretty useless.

    But humans hold a lot of useless and unprovable beliefs; faith gives many a sense of purpose and value. As long as I’m not asked to buy such beliefs, why waste time arguing.

    Liked by 3 people

  6. dbholmes

    Hi Massimo, two things…

    1) I suggested “theory” might be changed even for science simply because of the problem it faces in the public sphere these days. You know the whole “evolution is just a theory” garbage. A term like “model” with qualifiers like “proposed”, “supported”, and “verified” (or “accepted”) might work.

    2) More important is this issue with evocation v invention.

    Put simply, with “discoveries” all facts are constrained by existing external realities. You then appear to argue that “evocations” involve a class of facts that are constrained to the same degree as discoveries, simply because (using the game analogy) the “rules” are “set”. This is contrasted with “invention” where there are no set rules, and so few if any constraints, with the analogy to fictional characters who can change based on whoever happens to have their hands on the franchise. But I think the trouble with this can be shown with an example/hypothetical.

    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. Once the author sets definitions about Kirk and Spock and the environment they are living in for that episode, I am not sure how they are any less constrained than their potential moves on the 3D chess set… other than having more degrees of freedom for action, and that “rules” have yet to be laid down for every new bit of space they might explore (or perhaps the history of a character not yet revealed).

    The only assumption which would seem to separate the two groups (characters and game) is that all of the parameters of the game really are “set”, though clearly they can be changed. For example JJ Abrams could add CGI living hologram characters to 3D chess (making it like Star Wars chess), and while purists grumble he can simply say this was a rule and ability not yet seen in the original series (though it was already there!). In short, the game is just as malleable as Kirk and Spock. This is no different for games brought to you by Parker Brothers in real life.

    Evocation and invention seem merely to differentiate between two different states of created objects: a) where one is currently agreeing to stick within defined boundaries (relatively high constraint) and b) where one acknowledges that additional rules have yet to be described and likely will be added (variable constraint). But we really can’t ignore that (a) is an arbitrary, temporary state and that at any time rules can be altered/added.


  7. brodix


    The point I’m making isn’t that the result isn’t certain, but that it models a process, an action. Running the algorithm. If you don’t complete the act, then the result doesn’t exist. You don’t have effect, without cause. If you don’t actually add 1 and 1 together, you don’t have 2. To ignore that is to assume a pure platonism.

    The problem is when it gets to much more complex formulations and the assumption is they are purely deterministic, since it is assumed that actually running the process is irrelevant.

    As the old saying goes, form follows function. Not function follows form.


  8. synred

    The issue is not so much whether in an ideal situation, where all input and rules are known, if identical cause yields identical effect, because if it didn’t there would be no laws of nature, only suggestions

    Quantum Mechanics!

    There can clearly be regularities and laws wo/o strict cause and effect.

    In a board game you role the dice. One could use quantum dice to make it truly random.

    The exact sequence of the game changes, but the rules don’t and the game proceeds.


  9. synred

    pi is only pi in a flat space. Of course, it’s still pi. All depends what you mean (C/D here), (C/D in a abstract Euclidean space of which we have to actual, realized examples.


  10. synred

    I’m reminded of my plan to defraud Pat Robertson. I can tell him that the entire Bible in any language or translation is encoded in pi. If he pays me enough and funds me to buy a really big computer, I’ll find it for him. I’m sure some early results, words, short phrases, could keep on the hook.

    Meanwhile I’ve funded computing pi to ever more digits and provided plenty of work statisticians to debunk claims that ‘God is Love’ or whatever turned up much earlier than would be expected ‘statistically’. And I get rich!


    Liked by 1 person

  11. Seth Leon

    I can see how chess or many other games are teleological as they have a clearly defined goal that one attempts to make progress toward. I don’t see how to apply teleology so clearly however with respect 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).”

    Are there really objective truths that philosophy is after even in the evoked sense ? I am having trouble with this.


  12. Björn Carlsten

    Nice first entry. I really like the idea that philosophy explores “conceptual space” just as science explores “physical space”. I’ve even used your terminology in discussions I’ve had with people, often about ethics; I would’ve cited you, but the conversations were both verbal and informal–alas.

    Regarding Mathematical Platonism,
    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!

    I won’t weigh in on the actual debate that’s raging right now, except to say I largely agree with DM.

    (*hopefully, the journey hasn’t yet ended; who knows the road will ultimately take me)


  13. SocraticGadfly

    Kind of per EJ, and more per my questioning of Smolin’s framework and somewhat getting to the last 1/3 of the piece again (I’m there, Thomas), and Massimo’s look for a more radical jump, or whatever …

    I’m not a scientism evoker, and I think that’s pretty well known, but …

    On the issue of knowledge, and progress in understanding how to define what it is, etc. …

    Why are we not talking about cognitive neuroscience, and behavioral psychology as the branch of psych that’s most scientific, and related issues?

    While not overestimating what they will show us in the future, no more than what genetics and human heritable tendencies will show us in the future, they’ll surely show us more than they will now.

    Heck, in 30 years, we might find more on how the hippocampus, amygdala and other brain parts work, and, how, including at least “a posteriori” knowledge …

    “Reason is, and only ought to be, slave of the passions.”

    Perhaps we’ll find that in a more attenuated way than Hume meant, but still.

    Liked by 2 people

  14. synred

    Platonism what gives?

    4/5/2016 12:30 PM

    So I don’t understand this long thread on Platonism

    I looked back at the allegory of the cave:

    Click to access Allegory_cave.pdf

    It’s not quite how I remember it. See pix to left.

    I’d forgotten the pupets. The ventalions sees inadequate!

    Any was the ‘prisoners’ take the shadows for reality and the true forms that are really real are not directly observed.

    At least in the allegory their reality of ‘forms’ seems quite literal.


    urely this is not what mathematical Platonist of today think? Did even Plato think that?

    Walking behind the prisoners, the puppet-handlers hold up various objects found in the real world. Due to a fire that is burning the mouth of the cave, the prisoners are able to see the objects and each other only as distorted, flickering shadows on the cavern wall in front of them.

    So the puppets are the forms that really exist. The prisoners see only distorted shadows.

    What we call a ‘cat’ is called a cat because it is the shadow of the form of a cat.

    This seems ass-backwards. We get the somewhat fuzzy idea of a cat by abstracting from many, varied examples of cats. The boundaries of what’s a cat and what’s not a cat are fuzzy. They are subject to change and may differ from language to language and from culture to culture.

    And what does it have to do with the existence of possibilities, like possible Axioms or possible rules of games? The ‘existence’ of many different possibilities does not seem to me to require the existence of super reality where they actually exist.

    The idea of possibilities seems straight forward to me.

    And when we decide on a set axioms or rules we are not discovering them, but ‘making them up’! Of course we can only make things up that are possible.

    When we investigate the consequences of a set of axioms (or rules) we are discovering those consequences. The consequences are implicit in the Axioms/rules. Everybody who does it will find the same consequences. It is just logic.


  15. pete1187

    Some interesting discussion so far. As Massimo and others may well know from previous posts, I’m a mathematical realist through and through, even after constantly maintaining an openness to nominalism in all of its forms. I know DM has tackled this topic from the Platonist perspective, but I do think this constant talk of ‘games’ in the comments has gone off the rails a bit. I’m gonna take a different approach, borrowing from comments I’ve left previously here and at Rationally Speaking/Scientia Salon.

    But first, I’ve got a qualm with something Dan Kaufmann claimed:

    “Given that analytic philosophers today are overwhelmingly non-Platonist, it’s not at all surprising that most philosophers don’t think games are abstract objects.”

    Wait. What? I don’t know where you’re getting your information on this but I think it’s horrendously wrong. According to the Philpapers Survey from 2009 (and I’m aware they are not all Analytic Philosophers, only the vast majority of respondents from the data on philosophical background), 39.3% of respondents lean Platonist, 37.7% lean nominalist, and 23% are “other.” If you specify the AOS (Area of Study) to Philosophy of Mathematics the number of Platonists skyrockets to 60%, with only 20% in the nominalist camp.

    I could understand the misinformation coming from an autodidact or even someone with only a B.A. in philosophy (like yours truly), but to see it come from a professional is deeply disturbing. I get it, we all want a lot of agreement to feel like we’re on the right side (even though agreement, at least outside scientific communities with rigorous standards, often has no bearing on the truth of something), but in this case the majority of professionals actually aren’t with you on this issue.

    Now, to get to the heart of the issue of mathematics and it’s place in the world, I’m going to do what I’ve done here before and obliterate the various ‘concreta’ of the natural world that are so often taken for granted by commenters on this forum. And we’re gonna do it with an understanding that comes directly from progress in fundamental physics and the insights we’ve achieved over the last century or so.

    Let’s get started.

    Take a look around you. At the computer screen or phone that you’re viewing this comment on, the walls of the room you find yourself in, hell even your own hands. We know that all of these objects are made of atoms. So far, so good. We’ve got a concrete, material entity to work with. Only we actually don’t. The progress in physics has turned the atom, that bastion of physicality holding back a wave of terrible (ontologically at least) abstracta, in something that’s actually 99.9999999999996% empty space. What’s the non-empty part? Subatomic particles (electrons, quarks, gluons) that currently have no known substructure down to around 10^-20 meters.

    Let that sink in for a moment. Seriously, don’t start formulating your response to my commentary quite yet. Just stare at your hand or the wall again, knowing full well that the “physicality/materiality” of it all is completely illusory. Know that the common sense folk psychological perceptions of “solidity” are directly a result of the Pauli Exclusion Principle and electromagnetism that ensure a certain rigidity and opaqueness to everyday objects. Oh by the way, there’s a nice little section on the wiki for the Paulie Exclusion Principle that sums up the type of abstract mathematical machinery that the principle arises from:

    “According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics. In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin.”

    Have fun trying to reclaim any notions of “concreta” from that. Guys, this is not something you can debate. These are empirical facts of the matter. There is no way around any of this and you can’t simply reply: “Yea but I seriously doubt that’s the full story!!” It is. Full stop.


  16. pete1187

    Now, Massimo objected to all of this (or more accurately the conclusions drawn from all of it) a while back, and I’m going to detail the objections (numbered) and provide a quick reply to each, as I find them terribly wanting and somewhat desperate. I’ve tried to detail the retorts in almost exact detail Massimo, but please feel free to correct me if any of the following is a misconception.

    1) ”I know, but I find that argument wholly unconvincing. First off, there is no such thing as “empty space.” There are fields everywhere. Second, it doesn’t matter how relatively little “physical” stuff there is in the universe, there still is some, and it is responsible for everything we actually call “the universe.”

    Let me be very clear here. There isn’t even a “some” left for a materialist to hold on to for dear life. As Massimo rightfully noted, there is no pure nothingness between the constituents of particles, and anyone with a cursory understanding of physics would know this. But it’s very clear that’s not the issue. The issue is in understanding what things like “quantum fields” and the “fabric of space-time” actually are. If you’re a physicalist/materialist and ask a physicist this, you will not get an answer that you like. In fact, you’ll get a response similar to this:

    “But is a systematic association of certain mathematical terms with all points in space-time really enough to establish a field theory in a proper physical sense? Is it not essential for a physical field theory that some kind of real physical properties are allocated to space-time points? This requirement seems not fulfilled in QFT, however. Teller (1995: ch. 5) argues that the expression quantum field is only justified on a “perverse reading” of the notion of a field, since no definite physical values whatsoever are assigned to space-time points.”

    2) Yeah, I see that as a limitation of modern particle physics, not as a reflection of how the universe is. (NOTE: This is in relation to subatomic particle substructure and the fact that they quite literally behave like zero dimensional mathematical point particles)

    Ahhh the old “limitation of modern physics” line of reasoning. Well I’m sorry, but no future advances in our understanding are going to make things any better for the physicalist. It’s over. If anything things will only get more “abstract” and enigmatic. And for those that might (as an example) look for solace in those somewhat amusing pictures of strings as vibrating strands of energy of different colors, I’ve got more bad news:

    “The cartoon picture you see sometimes, where you zoom into an atom until you eventually see a ‘string’, is unrelated to reality. A string in string theory is not a tiny version of a normal string. It’s not made of any actual material and it doesn’t have any length in the traditional sense. There are no actual strings floating around like you might see in illustrations. It’s an abstract quantum object that is nothing like anything we know from real life. This property is not unique to strings, it’s true for many other quantum things.”

    That’s part of a recent Quora post from Barak Shoshany, a Graduate student at the Perimeter Institute for Theoretical Physics (where Lee Smolin is currently a faculty member). That whole “abstract quantum object” phrase he uses should be a final nail in the coffin for those hoping to hold on to some terra firma at the basis of reality. But the physicalist/materialist isn’t even hanging on to the ledge anymore.

    Gentlemen (and hopefully any ladies that might also read the blog), we do a terrible disservice to ourselves and others when we don’t look at the available evidence, even when it is counter to our strongly held beliefs. It’s a struggle to understand what it might mean for mathematical structures to be at the bottom of it all. I’ve had to shift from calling myself a “physicalist/materialist” to just a good old naturalist as a result. And by the way, that is perfectly compatible with mathematical realism. No supernatural or mystical crackpottery here. Won’t do much good to pray to Lie Algebra’s and multi-variable equations. The only way I wrap my head around it is by thinking that there is some formal structure to reality itself, something that the philosopher Gila Sher has written a bit about. But we can’t delude ourselves and talk about this abstract/concrete distinction with the clarity and nonchalance that many commentators have when modern science seems to have by and large obliterated the difference. I haven’t even brought up the fact that there are many forms of mathematical realism, such as the Aristotelian realism of James Franklin and other philosophers of mathematics that never even posits a Plato’s Heaven type existence apart from reality itself.

    Hopefully this generates some discussion, because getting into diatribes about whether Chess was invented or discovered or what happens when a particular rule changes completely misses the point in several respects. Again, I urge you to think about how goddamn fickle so many of our notions of what constitutes physical objects have become thanks to modern physics. You can’t just sit there and say “Nahhh, it ain’t so” anymore. Or you can, but it’s incredibly disingenuous and smacks of dogmatism.


  17. Daniel Kaufman

    Pete: I wasn’t talking about philosophers of mathematics, but about analytic philosophers generally, and most are naturalists of one stripe or another.

    So, your “deep disturbance” is unwarranted.


  18. Daniel Kaufman

    Nothing about “fundamental physics” implies anything regarding the “reality” of the sandwich I just ate or the table I ate it on. Fundamental physics also does nothing to “obliterate” said sandwich or table.

    Liked by 2 people

  19. brodix


    Yes and as you point out, it only takes dice to introduce significant randomness, but i was only trying to agree with DM and Robin that there is a great deal or regularity in reality. My point is that math models these stable, predicable processes as static formulae, then assumes the process itself is irrelevant and we end up with ideas like block time.


    Possibly we really should give up on the idea of materiality and consider reality as a hologram? Then we wouldn’t call it Physics, but Holographics.


  20. synred

    Time is confusing. I never understood why it would be so different from space just because of the -1 n the metric defining an invariant interval.

    In special relativity you can mix time and space and yet time ‘flows’ and ‘space’ does not.

    It’s beyond me.


  21. pete1187

    > Pete: I wasn’t talking about philosophers of mathematics, but about analytic philosophers generally, and most are naturalists of one stripe or another.

    Dan, I’ve got an immense amount of respect for you considering the contributions you’ve made to Massimo’s endeavors. That being said, I literally just provided you with data that shows a plural majority accepting or leaning towards mathematical realism in a large collection of philosophers (the vast majority of which are in the Analytic school). And you chose to completely ignore it. What are you talking about “generally”? Is there a dataset out there you know about that I haven’t run into? Because I’d be happy to concede the point and go about being in the minority. And why does naturalism have anything to do with this? I already explained, and it’s common knowledge, that you can be a naturalist and a mathematical realist.

    Deep disturbance still plenty warranted.

    > Nothing about “fundamental physics” implies anything regarding the “reality” of the sandwich I just ate or the table I ate it on. Fundamental physics also does nothing to “obliterate” said sandwich or table.

    I don’t even know where to begin quite honestly. I’m not trying to undermine the fact that we can structure the world according to things like sandwiches, tables, economic systems, or anything else. Nor am I implying that all of those higher level concepts are epistemically reducible to mathematical structures. What I’m saying is that the sandwich or table doesn’t have the sort of ontological existence most people would naively assume they do. It looks and “feels” like matter, but again, physics has shown us that the material “components” seem to lack any actual materiality. Of course the sandwich still exists, and of course you can still sit in that chair. But if you’re seriously going to tell me that nothing about fundamental physics implies anything about the ontological nature of a sandwich or a chair, then I’m sorry, but you’re not doing philosophy. You’re ignoring everything I previously stated or neglecting to help me understand where you see materiality/solidity/physicality when I just told you our best empirical methods indicate there’s no “there” there.

    Come on man.


  22. brodix


    Physics treats them both as measurements and as such, they are related. For instance, the distance between two waves would be a measure of space, while the rate they pass a certain point would be time. The reality though, is that with distance, you do measure an aspect of space, but with duration, you measure an aspect of action. Duration is not external to the present, but is the state of the present, as the configuration changes. Time is not so much that vector from past to future that we experience, so much as it is the process by which future becomes past. Potential coalesces into actual and recedes into residual. It’s just that our cognitive function is sequences of distilled information, so we experience it as past to future, such as we see the sun moving from east to west, when it is the earth turning west to east.


    Much of the physics community also thinks the universe began as a point and based on the premise of “spacetime,” expanded out to what we see and the evidence of this is that distant galaxies are redshifted, but the central premise of spacetime is this co-varience between space and time, yet if these galaxies are redshifted because the light is taking longer to reach us, as they move away, that means the light takes longer to cross this space and thus is not CONSTANT to the distance. There seems to be this stable vacuum that light crosses at C, being used as the denominator to this expansion. Which would make it the “Ruler.”

    Sometimes even the smartest of us get a little ahead of ourselves.


  23. Robin Herbert

    Hi Synred,

    “Did even Plato think that?”

    Good question. Plato had support for what we csll Platonism, as well as objections to it. It is not certain what he actually subscribed to, or whether he felt, as the Socrates of his dialogues says, that the thinking should go on after he had gone..

    He famously finishes one dialogue with Socrates dismissing everything they have been talking about as ‘wind eggs’

    Liked by 1 person

  24. Daniel Kaufman


    One cannot be a metaphysical/philosophical/ontological naturalist and a Platonist about anything. One can be a “non-naturalist realist” about mathematics, which typically involves some sort of Neo-Fregean view, but in that case, mathematical truths are truths of logic and are not truths about a set of Platonic entities.

    As for my point re: 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. From naturalizing epistemology to naturalizing morals to deflationary accounts of the concept of truth, the story has been one of pretty steady development in a naturalistic direction.

    You can, of course, go on being deeply disturbed, but I would suggest saving such sentiments for things that are somewhat more important than the ontological status of numbers.

    Liked by 1 person

  25. Daniel Kaufman


    As for the point re: sandwiches and the like, you suggest that I am not doing philosophy, when I say that quantum mechanics doesn’t tell us anything “breaking” — philosophically speaking — about the reality of sandwiches and lunch counters. I would suggest, in return, that you are doing the wrong kind of philosophy. Indeed, precisely the sort of philosophy that we should have stopped doing in the wake not only of the later Wittgenstein, but in the wake of Hume, on the naturalistic reading of him.

    Liked by 1 person

  26. Seth Leon

    If the project here is to define progress, then I’m not sure this why this project hinges on ontological definitions of what ultimately exists ( or what existed apriori ).

    It seems to me that the practical constraints in different fields in regard to determinations of progress have more to do with the value provided by the theories or accounts in question. The value of the account I suppose would need to cover new territory in some way reducing previous uncertainties perhaps uncovering new questions, and could be explanatory, prudential, aesthetic or of some other value. In science this is more straightforward when accounts can be compared with experiment, then with philosophy or with scientific theories that exceed our current capacities for observation & experiment. I certainly see how progress would be difficult to measure in an objective way in philosophy given the subjectivity involved in what counts as value.

    I’m just a layman though curious to see where this is going.


  27. SocraticGadfly

    Michael: Or let your, or should I say “your,” 99.99998 percent empty space stomach, or “stomach,” be fooled into feeling filled, or “filled,” by a sammich, or “sammich,” that is also 99.99998 percent empty space.


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