Publication: “A Case Study in Formalizing Contingent a priori Claims”

Good news, everyone: an article has been published in Res Philosophica! The abstract is below:

“A Case Study in Formalizing Contingent a priori Claims”

Some philosophers, like Kripke, Williamson, Hawthorne, and Turri, have offered examples of claims that are allegedly contingent and a priori justifiable. If any of these examples is genuine, this would upend the traditional epistemological classification on which (a) all and only a priori justifiable claims are necessary and (b) all and only a posteriori ones are contingent. I argue here that these examples are not genuine. This conclusion is not new, but the strategy pursued here is to formalize these muchdiscussed examples in symbolic logics. Once formalized, a perspicuous representation of their logical form will bring into sharp relief that these examples are not both contingent and a priori. Two takeaways are (1) that the traditional epistemological classification remains plausible and (2) that one’s proposed examples of contingent a priori claims should be supported by a formalization in one’s preferred background symbolic logic.

“Have you ever wanted to type in Peanese? Now you can!” A new LaTeX package for typesetting “Principia Mathematica”

As part of the Principia Rewrite project I am undertaking, I created and published a new LaTeX package for typesetting Principia Mathematica. It is creatively named ‘principia’ and covers all notations through Volume I. Updates to include Volumes II and III are planned.

If you ever wanted to type square dots, now you can! Just input “\pmdot” – or, if you want two dots, “\pmdott”, and so on. What about Principia‘s famous eight-pointed asterisk and slightly-raised dot for theorem numbering? Now you can just type “\pmast” and “\pmcdot” to reproduce them! Here’s a sample picture of the result (here’s the corresponding page of Principia Vol. I):

What about Principia‘s notoriously misaligned existential quantifier? (It was originally typeset by rotating an “E” backwards, causing it to be partly below the text line.) Now you can just type “\pmsome{z}” to get Principia‘s symbol! (You can also type “\pmSome” to get the symbol without an argument.) Here’s a sample (and the corresponding page in the original):

There’s a lot more included in the package: the slightly rounder class intersection and union signs; the analogues for relations with dots in them; the circumflex for class and relation symbols; and of course, the rotated iota for definite descriptions. For more details, check out the package documentation! Comments and suggestions are welcome.

What does Russell mean by a “particular” in the logical atomism lectures?

Today we have another question from StackExchange! A user writes:

I read a bit of logical atomism by Russell but would appreciate if someone explains with examples of what is meant by it. For example it says: “According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or multiple simple particulars standing in a relation”. What is meant with: simple particular exhibiting a quality? Does it refer to things like: water which has quality to be transparent. Or Ball which is round. Or sun which is yellow? If yes, this makes sense and doesn’t seem much novel. So can someone shed more light what is meant by logical atomism (with examples)? And explain it to beginner in philosophy?

Russell’s preferred example of what he means by a “simple particular” is a sense-datum (an object of sensory experience), but it could apply to any object of awareness that is the sort of thing having properties. Importantly, what we often intend to call “particular” are not really particulars: they are in fact more complex. This includes any object that is not in our field of awareness, like objects in the past beyond our memory and objects that we are not (or never are) aware of, including ordinary objects of common sense. As Russell puts it:

The simplest imaginable facts are those which consist in the possession of a quality by some particular thing. Such facts, say, as “This is white.”…What pass for [proper] names [i.e., words for particulars] in language, like “Socrates,” “Plato,” and so forth…are really abbreviations for descriptions; not only that, but what they describe are not particulars but complicated systems of classes or series. A name, in the narrow logical sense of a word whose meaning is particular, can only be applied to a particular with which the speaker is acquainted, because you cannot name anything you are not acquainted with…It is only when you use “this” quite strictly, to stand for an actual object of sense, that it is really a proper name. (The Philosophy of Logical Atomism, Lecture II, pages 522-525)

So ordinary objects like desks are not particulars, that is, they are not logical atoms. They are logical fictions, that is, series of particulars having common properties:

Now the essential point is this: What is the empirical reason that makes you call a number of appearances, appearances of the same desk? What makes you say on successive occasions, I am seeing the same desk?…There is something given in experience which makes you call it the same desk, and having once grasped that fact, you can go on and say, it is that something (whatever it is) that makes you call it the same desk which shall be defined as constituting the same desk…In that way the desk is reduced to being a logical fiction… (The Philosophy of Logical Atomism, Lecture VIII, pages 369-370)

So Russell thinks that many ordinary objects are series of particulars having some common experienced property (like the same color, shape, odor, and so on). The real particulars are the relatively short-lived objects of our immediate experiences.

Publication: Book review, MacBride’s “Genealogy of Universals”

Good news, everyone: a publication came out today in the excellent open-access (!) journal, Journal for the History of Analytical Philosophy. This is a book review of Fraser MacBride‘s On the Genealogy of Universals: the Metaphysical Origins of Analytical Philosophy (Oxford University Press: 2018). Here is a teaser for the review:

Russell has a pessimistic take on the notion of a metaphysical
category: “What, exactly, is meant by the word “category”, whether in Aristotle or in Kant and Hegel, I must confess that I have never been able to understand. I do not myself believe that the term “category” is in any way useful in philosophy, as representing any clear idea.” (Russell, 1945/1967, 222)

In this book, MacBride has shown that Russell had plenty of company. It might even have been universal—and still may be today. Accordingly, and fittingly for a genealogy, in this book MacBride does not explain what a category is. It seems at least this much is true: there are different notions of category—linguistic, logical, and ontological at least—to be distinguished and interrelated according to the philosophical methodology of a past (or present) philosopher. In developing these distinctions and applying them to past figures like the ones MacBride considers, or to ourselves, one should reckon with this particular book.

Happy reading! And thanks to Fraser MacBride for writing an interesting, review-worthy book.

“Why aren’t there any logical atomists around anymore?”

We have another r/AskPhilosophy question today! (Thanks to fellow moderator /u/ADefiniteDescription for the tag that brought it to my attention.) Reddit user RepresentativePop asks:

This is something that struck me recently, but I have no idea why it’s true. If you ask me to name any logical atomists, I would have to start naming people from a hundred years ago (Russell, early Wittgenstein, arguably Moore etc.). But I could name you several German idealists just in my department.

Now that I think about it, one of the first things I remember learning about logical atomists was that there weren’t really any around today (at least, that’s what my professor said).

I may have missed the metaphysical bandwagon here, but was there some devastating critique of logical atomism that blew it to smithereens? Was it because of something in the Investigations? What happened?

Let me first contradict what this professor referred to said: there are logical atomists around today, even in academic philosophy. I am one (I have the Twitter handle to prove it!). So are the following three people, among others:

  • Gülberk Koc Maclean

  • Gregory Landini

  • Peter Simons

That doesn’t mean what this professor said is groundless: there is still a widespread belief that logical atomism was refuted years ago.

That raises a second point: logical atomism is contested ground. None of the people identified as logical atomists above agree precisely on what the view is, and on how it should be best understood. There are shared commitments, to be sure, but we disagree on the details.

Indeed, it is not even clear among past figures who should be counted as a logical atomist. Russell used the phrase. Wittgenstein never did, despite the widespread view that Russell and Wittgenstein are the ‘canonical’ logical atomists: their logical atomisms each get a Stanford Encyclopedia of Philosophy article. (For what it is worth, my view is that taking Wittgenstein as a logical atomist, especially in the Tractatus, is highly misleading. If anything, his logical atomism occurs in the 1913 (Russell) Notes, before the introduction of showing and the view that logic consists of tautologies in the 1914 (Moore) Notes.)

That raises a third point, which is what was really being asked: the story about what happened is complicated. I wrote my thesis on logical atomism (abstract here), and there are still elements of the story that I am piecing together. But here is a narrative that fits the data that I have found so far.

Logical atomism is widely understood as a kind of search for acquaintance-complexes, that is, for complexes composed entirely of constituents with which we have acquaintance. Acquaintance here is understood as just a relation of awareness between a subject and some thing, like an object or a perceptible fact. So-understood, logical atomists aim to make their metaphysical and philosophical language match, mirror, or otherwise show the logical structure of the facts in the world. There is also an implicit reduction program here: one wants to trace all empirical knowledge back to sentences of this ideal language, most of which will be truth-functional combinations of atomic sentences that are made true, when they are true, by atomic facts.

Now that program has been widely discredited by arguments on various fronts against the doctrine of acquaintance. It was also sometimes subsumed under the more easily refuted logical positivist verificationist doctrine of meaning, partly because logical positivists like Carnap were such fans of logical atomism.

The idea of a philosophically ideal language was also partly discredited by arguments on various fronts to the effect that no such language was possible, practicable, or even desirable. One such front is the color exclusion problem that Wittgenstein wrestled with but could not solve (but see the abstract of Sarah Moss’s article on the problem—not everyone thinks it is insuperable). Another front is that some folks, notably Wittgenstein and other philosophers, like Ryle, Stebbing, Wisdom, and others criticized the program of analysis into an ideal language for one reason or another.

So logical atomism, understood in the standard way as the search for acquaintance-complexes, has many issues. But there are other interpretations: many people understand logical atomism as the view that the only facts in the world are atomic facts, and the truth conditions of all other sentences can be given using truth-functional combinations of such facts. Others see logical atomism as a program for doing metaphysics in which logical categories should mirror the metaphysical categories that there are. Still others see logical atomism as a kind of logical research program, with various disagreements over the details.

To add a coda: there are serious problems with the standard interpretation of logical atomism that have been discussed recently in the scholarly literature. I know because (full disclosure) I co-edited this collection of essays in which that interpretation is severely criticized.

So, in answer to the question, “Why aren’t there any logical atomists around anymore?” The answer is, “There are.”