Introduction: Read This First — I

[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.”
(Epictetus)

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!

Notes

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

References

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.