Massimo Pigliucci - The Nature of Philosophy: How Philosophy Makes Progress and Why It Matters

W e 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. Wittgensteins 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 doesnt 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:

1. forward or onward movement toward a destination
   

1. or: 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 dont 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 Peter Unger and Lee Smolins 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: