truth 1, falsity 0 
I just posted version 1.30 of forall x. As usual, the update corrects a number of typos. It also makes some changes. I taught logic this Fall for the first time in several years, and the time away from the book made me realize that some things weren't working as well as they should.

Truth tables


It is standard in philosophy to do truth tables with Ts and Fs, but this makes the shift from sentential logic to quantified logic awkward. The sentential connectives operate in pretty much the same way in a quantified formula as they do in a sentential formula, except that the operators are truth functions in SL and satisfaction functions in QL. I want students to understand the difference between truth and satisfaction, but I also want them to apply what they know about the truth-functional connectives. So I end up saying things like, "Both conjuncts are satisfied, so the conjunction is satisfied. This part's just like in a truth table. Both parts are true, sort of... true-ish... something that works a lot like truth."

In the previous edition of the book, I tried to smooth this over in the chapter on formal semantics by giving the function which defines 'truth in SL' in terms of 1 and 0 rather than in terms of T and F. The definition of 'satisfaction in QL' is also in terms of 1 and 0, and the clauses which define satisfaction for sentential connectives look exactly the same as they do in the definition of truth. So I can say instead, "Both conjuncts are 1, so the conjunction is 1."

The problem is that, by that point, students have acquired habits in terms of T and F from doing truth tables. So I decided to start with 1 and 0 earlier, doing truth tables entirely using 1s and 0s.

This is common in computer science and electronics, even though it's not common in philosophy. My motivation is philosophical, though. Doing truth tables in terms of 1 and 0 underscores the step of abstraction, that these are formal, mathematical values rather than metaphysical truth and falsity. And because they are formal values rather than rich concepts, they can be interpreted differently (as satisfied/not, rather than as true/false).

I think I made this change consistently everywhere, but there are probably still some lingering mention of T and F. New content means new typos.

Proofs in QL


The chapter on proofs is the barest part of the book. It would be the hardest part to learn from directly, if someone were just reading the book rather than taking a course.

In this update, I just made some changes to the presentation of the quantifier rules.

I changed the typographic mark for a substitution instance, and I think it's clearer now. (I won't try to produce it here on the blog.)

I rewrote the Existential Elimination rule so that the proxy constant cannot occur anywhere else in the proof. You have 'Exists x Px' and assume 'Pc' for some entirely new constant c. This is stronger than what's strictly required, but it underscores the conceptual point that c is only functioning as a placeholder name for whatever thing it is that's P. The subproof is the only place where c occurs, because the subproof is the moment in the argument when you say "Something is P. We don't know what, but let's call it c."

I am considering splitting the chapter on proofs into two chapters: One on proofs in SL and another on proofs in QL. This would allow me to add material to both discussions. It would also allow instructors who want to do proofs in SL immediately after doing truth tables to do so more easily. That's not a change I made in this revision, though, and I'm still mulling it over.

Archiving


I archived earlier versions of the book at a SUNY digital repository. Recently, the library here at UAlbany has set up a local digital repository which should offer more features and more visibility. I think that the submission needs to be approved by a librarian, but version 1.30 will appear there soon enough. Until then, it's available directly from my website.

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Ninth blogiversary, belated 
I had meant to annuate the end of my ninth year of blogging here, which fell on October 4. The total contents of the blog at that point were 367 entries comprised of 160,392 words; of those, 48 entries and 17,182 words had been written in the preceding year. So the ninth year was slightly more productive, blogwise, than the eighth.

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Types and tokens of blue 
Yesterday I learned about recent work by jazz combo Mostly Other People Do the Killing. Their album "Blue" is a note-for-note remake of "Kind of Blue". They transcribed all of the solos and performed them with meticulous care so as to produce a recorded album that replicates, as much as they could, the sound of the original.

The exercise has philosophical implications, and they know it. There are echoes of Pierre Menard's Quixote, which they foreground by using the Borges short story as their liner notes. Menard's goal, however, was not to copy but to put himself in a state of mind where he would write words that coincided with Cervantes' original. The parallel exercise would be if the band had tried to live their lives in a way which led them to improvise just the same notes which Miles Davis, Cannonball Adderley, John Coltrane, and the rest improvised back in the 1950s. That exercise would not have produced this album, because that exercise would not have led to something which sounds so precisely like "Kind of Blue".

So it's important that the band transcribed the solos, recorded tracks separately, and acted so carefully so as to preserve information from the original performances. One natural reaction is that such slavish emulation isn't jazz. Moppa Elliott (bassist for the band) discusses this point in an interview about the project. He asks, "Is what we did even jazz? If it isn’t, what does that make it? If it’s not jazz, why not?"

I've now read a bunch of reviews of the album. Perhaps the best is Bruce Lindsay's deadpan paean. It's odd that nobody refers to "Blue" as a cover of "Kind of Blue". Part of this is because 'cover' is a category in rock music, not jazz. Rock and jazz have different versioning practices. But there's a familiar variety of cover where musicians attempt to play a song so that it sounds precisely like a canonical version of that song. In our terms, this is a mimic cover.

The similarity to a mimic cover makes it odd when Marc Meyers in the Wall Street Journal review speculates that, "If 'Blue' is even moderately successful, jazz, rock and soul musicians may be motivated to clone other pivotal works like the Beatles' 'Rubber Soul,'..." Beatles covers and cover bands are already a thing.

In the paper where we introduce the phrase, Christy, Cristyn, and I argue that mimic covers are properly evaluated in terms of their fidelity to the original. I'm not sure whether that's the case with "Blue". Elliott suggests that the point is the opposite, to get people to listen to the original with an attentiveness to precisely those features which couldn't be or at least weren't faithfully reproduced in the cover.

However, because it is a transcription and performance by skilled musicians, "Blue" preserves information about the original (in a technical sense of 'information'). So one gets a kind of access to the original by listening to the new album. Imagine civilization collapses, all copies of the original Miles Davis album are lost, but somehow a copy of "Blue" survives. Certainly the jazz techno-priests in that dystopian future would listen to the album as a way to appreciate the way Davis and his band played, not the way Elliott and his band played. The performances, as repeatable interpretation types, are preserved in this meticulous homage.

In our less counter-factual dystopia, however, we have recordings of "Kind of Blue" to listen to alongside recordings of "Blue". The new album is like one half philosophical thought experiment, one half virtuosic accomplishment, and one half redundancy.

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Some people have a latex allergy 
In the Facebook LaTeXoSoPHeRs group, Kevin Timpe links to a webpage where Josh Parsons claims that philosophers shouldn't use LaTeX. I ended up replying at some length. Rather than just bury my rant over on FB, I'm reposting here.

Parson claims that LaTeX is a proprietary format just like the Word doc format. This is just perplexing. I have Word documents from the 90s that current versions of Word won't read correctly. Even though I have copies of the data, I need to look at hard copies if I want to look back at those papers. But LaTeX source is plaintext, and so the files will be readable until I either lose the data or computers becomes very different.

Plus, here are some advantages of LaTeX he doesn't list.

1. The source/document distinction means that you can include comments which don't show up in the document itself. This has lots of uses. For example, comment out a paragraph that you don't want to forget forever but don't want to include in a submission.

2. The source is plaintext, so you can grep it. This isn't just the cargo cult fascination with bells and whistles, but real timesaving functionality for people who know how to use regular expressions.

3. Although the fact that it specifies typesetting can be a downside (with respect to accessibility) it's an upside with respect to producing typeset pages. I have self published two books using LaTeX. Alternative word processors would not have done the trick.

4. The ability to define commands allows for useful modularity. One of the books I self published is a logic textbook. I defined commands for all of the logical notation. Somebody who uses different symbols than I do can redefine the commands, process the source, and have an edition of the book in whatever notation they prefer.

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<the greatest weight, the greatest weight> 
Imagine an angel comes to you in the night, when you are feverish and in the midst of metaphysical reveries. The angel says that she has been taught metaphysics by God, and so she can answer truthfully any questions you might have. You are slow to react, and this is the first question that you think to ask: Do ordered pairs exist?

The angel boggles and, after an awkward pause, asks you to explain the question.

Well, you say, you encounter individuals like your armchair, your pajamas, your fireplace, and so on. (You pick these because they are close at hand, and you can point at them.) Making sense out of the semantics of relations leads to positing a further thing which is an ordered pair of two objects. For example, the relation "__ is wearing __" holds of a pair of things; e.g. <you, your pajamas>.

The angel laughs. The sound is a bit like a wind chime and a bit like a carnival.

Your mind is too small, says the angel. God considered making a world like that, built out of individuals which stood in pairwise relations to one another. This seemed like it would be a waste of infinite power and infinite intellect. What God did instead was to directly create all of what you think of as ordered pairs. To God, each of these has a separate and true name.

You blurt out, almost interrupting: That's absurd! Surely God thinks of individual things, rather than only of pairs.

In a way, the angel replies. God can think of you by using the name for what you, with your limited intellect, think of as the ordered pair <you, you>.

But... surely individuals are more fundamental than ordered pairs. If two things exist, like the angel and the fireplace, then there are necessarily ordered pairs <angel, angel>, <fireplace, fireplace>, <angel, fireplace>, and <fireplace, angel>. Having enumerated the four possibilities, you consider saying "QED" but instead thump your fist on the arm of your chair.

Of course God made all those, and what God makes must necessarily be so. Yet God, considering only infinite power, might have refrained from making <fireplace, fireplace> while still making <fireplace, angel> and <angel, fireplace> and all the rest. There would not be the thing which you think of as the individual fireplace.

You know, says the angel, you've been very sick and you're taking this lesson very seriously. I think we better stop now.

What would you make of this encounter, after your fever had passed?

[edited for clarity]

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