2020 update on the Principia Rewrite project

This just in, and just time for the new year:

A Github repository has the source code in Coq and TeX, plus some PDFs for ease of viewing by non-Coq or non-TeX users: https://github.com/LogicalAtomist/principia.

More updates on the Principia Rewrite Project will be posted to the repository once the quantification theory is computer-checked and typeset. Until then, happy New Year!

A critique of George Schedler’s “Are Confederate Monuments Racist?”

In a 2001 piece, George Schedler (SIU) argues that (1) most confederate monuments are not racist and (2) those racist confederate monuments should be contextualized or inscribed differently instead of being torn down. First I will summarize Schedler’s argument, and then I will argue that Schedler’s arguments for conclusion (1) are bad.

Schedler (288) defines monuments as “markers or statues whose purpose is to pay homage to the conduct or character…of some person or group.” Then Schedler (289, paraphrasing) defines racist monuments as monuments whose employed symbols, depicted individuals, or (inclusive) inscription contents are racist, and racist as involving the belief that human beings are divisible into races and that some races are unequal in respect of moral or intellectual qualities.

Schedler (298) then restricts (too narrowly, I will contend) what will be considered in discussing the (potentially racist) meaning of a monument:

In the absence of empirical evidence of the meanings the public attaches to Confederate monuments, I will note prominent features of monuments and the literal meaning of their inscriptions to draw minimal inferences that the untutored public could draw. So, whenever I discuss the view of the masses with regard to a particular monument I am in effect guessing at what meaning the public would attach with respect to race in observing that specific monument.

With that restriction, all the conclusions follow, e.g. Schedler (293) says that the Confederate monuments that “make no reference to African Americans [or to race more generally] are unproblematic, since there is no direct reference to racism in such brief, generalized phrases.” As Schedler (294) puts it, because the Confederate imagery and inscriptions does not “entail a reference to racism” it is cleared as ‘not racist.’ Wherever there is an ambiguity in the monument’s inscription or interpretation, or wherever there is not an entailment of racist doctrines like (1) or (2) above, there is not sufficient evidence to conclude that the monument is racist.

On the other hand, contradicting this earlier restriction what is logical entailed by the contents of an inscription or by the symbolism used in the monument, Schedler gives the best of the doubt to the Confederate monument-makers in arguing that Confederate monuments paying homage to persons of color are not racist. Concerning Confederate monuments, Schedler (303) argues, “By paying tribute to the loyalty, courage, and steadfastness exhibited by African-American friends, they imply a belief in racial equality.” Here is one example Schedler gives: on one panel on a monument to slaves attached to the Harvey Scouts, a Confederate cavalry unit, during the Civil War specifically reads, “A tribute to my faithful servant and friend Willis Howcott… W. H. Howcott.” Schedler (301-302) infers from the use of the word “friendship” that there is an implicit equality asserted between the races.

Schedler’s reasoning could equally be applied to the euphemism “servant” (in place of “slave”). If “friend” (presumably also a euphemism for “slave”) implies an implicit equality, wouldn’t subordinating euphemisms like “servant” implicitly imply an inequality between the races (between “master” and “servant”)? And what about the word that both “servant” and “friend” are euphemisms for? Now Schedler’s argument is that we can only infer what is implied by the literal contents of inscriptions and imagery. But this equally undercuts the argument for the apparently innocuous, even progressive advocacy of racial equality that Schedler is entirely mistaken in identifying in Confederate monuments.

On the other hand, the meaning of statues and monuments is, unlike entailment between contents of statements, a social phenomenon. So is racism. If we confine ourselves merely to the entailment relations among contents, we will find racism almost nowhere, even though it is many more places than that. This constraint thus leaves us blind. For example, if you saw a monument to Adolf Hitler and, upon reading the inscription, found that it was dedicated to his efforts to combat unemployment, you would not conclude that the monument was not racist merely because its inscription was not racist. But that is where Schedler’s constraint puts us.

It is better in such cases as monuments and statues to use something like a principle of reason for practical affairs. If you saw a statue to Robert E. Lee in some highly trafficked public location, and asked what he got a monument for, the reply that he showed exemplary “Southern honor” would not explain why there was a monument to him, and not to someone else. Many people presumably exude the traits of “Southern honor.” One would suppose naturally that Lee was well known locally or regionally for some actions he had done. It does not take a researcher to dig a little deeper than this apparently not-racist explanation and find that the facial “Southern honor” for which Lee gets a monument (many monuments, in disturbing fact) is partly explained, if not wholly or mostly, by his fighting for the pro-slavery side during the Civil War.

This principle helps explains some of the examples that Schedler considers. Why, for example, did the Daughters of the Confederacy fund a monument to Heyward Shepherd, a free person of color killed during John Brown’s failed attempt at a rebellion. If we confine ourselves to the inscription quoted by Schedler (299) and to what is entailed by its contents, it merely celebrates an innocent and free person who died during an armed rebellion and “the character and faithfulness of thousands of Negroes” during the Civil War. But obviously this is insufficient. Why would the monument be to this person and not Brown’s other victims? And why would the character of many other (enslaved) people be mentioned in the inscription if that was the main purpose of the monument?

Although not racist facially, this monument was part of a broader propaganda campaign by the Daughters of the Confederacy: they were eager to portray enslaved persons as happy with their lot, and they did not mind, and even desired, the distortion of this portrayal. Indeed, their inscription contradicts the firsthand account of slaves’ reaction to Brown’s failed rebellion. The monument was not primarily intended to honor an innocent person killed in an armed insurrection, but to use that person of color’s freedom to misleading suggest that enslaved persons of color were happily “faithful” to the institution of slavery and that free persons of color were a casualty of Northern barbarism, thus portraying the slaveholder South in a more favorable but untruthful light.

Thus, Schedler is wrong about Confederate monuments. In the first place, as Dr. Ibram X. Kendi suggests, we should really ask whether they are anti-racist, not merely whether they are racist or not. In the second place, in deciding whether they are racist or not, we should not blind ourselves with Schedler’s constraint of considering only the contents of inscriptions and what they logically entail. This is far too narrow to get an accurate picture. Third, we get a more truthful picture of the racist character of a monument by inquiring into the reasons that it is there: it a dead end to ask not whether the monument, considered in itself as an inanimate object, is “racist.” It is much better to inquire more broadly about the publicly communicated meaning (not merely what is logically entailed), the purposes and aims of its supporters in establishing the monument, and whether the memorialized event, person, or place is well-known for something banal and common like “Southern honor,” or is really well-known for specific actions they took in support of slavery.

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.