Tuesday, July 28, 2009

The illusion of plausibility

Suppose I asserted that the difference of the positions of B and G# in the A major scale was identical with, supervened upon, or was in some other way explicable in terms of, the greater than relation that the number 23 bears to the number 18. You would no doubt wonder what the hell I was talking about. Just as notes in a scale are one thing and numbers are another, so too are positions in the scale and positions in the sequence of numbers different things, and that’s that. Relations of identity, supervenience, explanation, etc. simply don’t hold between the two. (Of course, there are mathematical relationships between notes in a scale; the point is that the relationships between notes are clearly not reducible to or entirely explicable in terms of mathematical relationships.)

Note that this has nothing to do with the lack of a law-like correlation between the two – whatever that could mean in this context, since we’re talking about abstractions rather than concrete objects or events. And even if we reverted to speaking of concrete objects and events, we don’t think that the reason talk of identity, supervenience, etc. makes no sense in this context is that we find no regular correlation in nature between (for example) the playing of B on a musical instrument and there being 23 of something in the vicinity. Correlation or lack thereof just has nothing to do with it. Even if we found that some such bizarre correlation held, we wouldn’t think “Aha! B in the A major scale must be identical to or supervenient upon the number 23!” Such a claim would be just as unintelligible in the presence of the correlation as in the absence of it.

I propose that the same thing is true of claims like this: “Having a thought with the content that P is identical to, supervenient upon, or otherwise explicable in terms of having a sentence with the meaning that P encoded in the brain”; “The semantic-cum-logical relations between thoughts are identical to, supervenient upon, or otherwise explicable in terms of the causal relations between brain events”; and other claims of this sort. Such claims are simply nonsensical. Logical relations are one thing, causal relations are another, and that’s that. If you don’t see this, either you don’t understand what a logical relation is or you don’t understand what a causal relation is – or, more likely, you are in the grip of some ideology that leads you to speak nonsense. Similarly with the claim that having a thought involves having a sentence in the head. Having the thought that 2 + 2 + 4 – that is to say, grasping the proposition that 2 + 2 = 4 – is one thing, and having some sentence instantiated somewhere (whether on a chalkboard, in a notebook, in a computer, in a brain, or wherever) is another, and that’s that. If you don’t see this, then, again, either you don’t understand what a proposition is, or you don’t understand what a sentence is, or you are in the grip of some ideology.

The ideology in question is, of course, materialism (or physicalism or naturalism, if you prefer). If you start with the assumption that thinking simply must be identical to, supervenient upon, or otherwise explicable in terms of brain activity, then it will seem to you at least plausible that logical relations might be reducible to causal relations, thoughts identifiable with the having of brain sentences, etc. But no one would think these things plausible even for a moment if they were not already seeing the world through materialist glasses – indeed, they would take the evident absurdity of such proposals as prima facie evidence of the falsity of materialism. (And that is, I propose, part of the reason why most philosophers historically have not been materialists.)

“But what about the correlations holding between certain mental events and certain brain events?” Well, what about them? Again, no one would think for a moment that a correlation between (say) the playing of B on a musical instrument and there being 23 of something in the vicinity is even prima facie evidence for the plausibility of the claim that the difference of the positions of B and G# in the A major scale was identical with, supervened upon, or was in some other way explicable in terms of, the greater than relation that the number 23 bears to the number 18. Or if he did think so, it could only be because he is already in the grip of some bizarre ideology (Pythagoreanism?) which independently insists already on there being some deep metaphysical connection between musical relationships and mathematical ones – and which has deadened thereby his ability to spot clear category mistakes.

From an Aristotelian point of view, such correlations are in any event not the least bit surprising despite the falsity of materialism. Since soul and body are related as form and matter, mental and physiological correlations are no more surprising than the “correlation” that exists between the form of some particular tree and the matter than composes it. But in neither case is there any question of identity, supervenience, etc., since form and matter in general are simply irreducible.

Peter Geach said it well: “When we hear of some new attempt to explain reasoning or language or choice naturalistically, we ought to react as if we were told that someone had squared the circle or proved the square root of 2 to be rational. Only the mildest curiosity is in order – how well has the fallacy been concealed?” (The Virtues, p. 52) Like Pythagoreanism, materialism is philosophically interesting, often defended by thinkers of genius – and ultimately simply and clearly wrong.

88 comments:

The Cogitator said...

"Having the thought that 2 + 2 + 4 – that is to say, grasping the proposition that 2 + 2 = 4 – is one thing, and having some sentence instantiated somewhere (whether on a chalkboard, in a notebook, in a computer, in a brain, or wherever) is another…."

Indeed. I am fond of this sort of illustration, since it is so elementary. http://veniaminov.blogspot.com/2009/04/why-naturalism-naturally.html

The addition relation was and will be true long before and long after an individual's neural emulation of it in, say, math class no February 7, 1985. This alone should suffice to demonstrate that the two entities–– one an abstract, formal reality, the other a concrete, material instance–– are intrinsically irreducible.

Presumably the materialist could retort, "But the addition relation in question only became 'the addition relation of 2 + 2 = 4' for me when it obtained as a neural event in my head." The point, however, is that a myriad of neural events, all specifically distinct and transient, emulate the same exact addition relation. If the addition relation is wholly reducible to a particular brain event, then each of us would need to have the same exact brain event in order to experience the same abstraction that allegedly supervenes on it. But since our neural emulations are all intrinsically unique, idiosyncratic, then either we must suppose the abstraction magically generates the exact same brain event in all heads at any time, or that none of us ever actually experience and employ the same abstractions as anyone else.

Cue James Ross and "Immaterial Aspects of Thought"!

Edward Feser said...

In addition to Ross, Plantinga has a very good discussion of this in chapter 6 of Warrant and Proper Function.

Rodak said...

the point is that the relationships between notes are clearly not reducible to or entirely explicable in terms of mathematical relationships.)

That's not "clear" to me. If you will read this, you will find the relationships between notes explicated in the most minute detail, and all of it done with numbers.
What is there left unexplicated?

Crude said...

Rodak,

Just to be clear, are you asserting that "the relationships between notes are reducible to or entirely explicable in terms of mathematical relationships"? I'd be interested in hearing that before anyone really continues here.

Rodak said...

Yes. An "interval" is something that can be measured. There is a mathematical correspondence between one note and the next.
That said, I guess we can quibble over what's meant by "entirely."

One Brow said...

http://en.wikipedia.org/wiki/Piano_tuning

http://en.wikipedia.org/wiki/Piano_key_frequencies

http://en.wikipedia.org/wiki/Equal_temperament

There are very precise physics and mathematical relationships involved.

Crude said...

But Ed didn't deny there was a "mathematical correspondence". He certainly didn't deny mathematical correlations (he explicitly says there are mathematical relationships). He's talking about total reducibility, and complete explanation.

Anyway, thank you for answering. I'm an amateur at best here, but now that that's been aired (even with the caveat) I'll be happy. All in the service of good further discussion here.

Rodak said...

Crude--
What, to your way of thinking, is the remainder of the relationship between notes, once the "precise physics and mathematical relationships" are discounted?

Edward Feser said...

One Brow and Rodak,

Are you saying that the series of natural numbers has musical properties? For example, is there something the number 23 sounds like? Is it different from what 18 sounds like? Do numbers in general differ in pitch? Do they sometimes form chords? Are they sometimes dissonant?

These are, of course, obviously absurd questions -- numbers no more "sound" like anything than they taste or smell like anything. That there are mathematical relationships between notes -- something I explicitly acknowledged -- changes this not at all. There are also mathematical relationships between the objects here in my study, but it doesn't follow that these relationships exhaust all there is to the objects. "X can be mathematically described" does not entail "X can be _exhaustively_ mathematically described."

Rodak said...

"X can be mathematically described" does not entail "X can be _exhaustively_ mathematically described."

Fine. So please describe the relationship between two musical notes without reference to the physics/math involved so that I may understand what you mean.

Edward Feser said...

If you know what words like pitch, chord, dissonance, etc. mean, then you already know what I mean. Indeed, if you've ever heard music (or heard anything at all for that matter) then you know what I mean. What's the problem?

Rodak said...

All of those things can be described mathematically. Moreover, they can all be described more precisely in terms of number than they can in language.
Sound cannot be abstracted from the material that carries it. If a tree falls in the woods and there is nobody there to hear it, then, No, it does not make a "sound" although it does create a vibration.
If the tree falls in a vacuum, it does not make a sound.
It would seem that a materialist explanation of sound is the only one that is an accurate description of what sound is.
As for music, our response to it is largely a matter of nuture, not of nature. Louis Armstrong, a musical genius in his own right, famously said (disparagingly) of bebop "It's Chinese music." He thus displayed his inability to appreciate the beauty of musical sounds produced in modes and scales that he had not been trained to recognize as beautiful; both whatever Armstrong thought of as "Chinese" music and bebop were beyond his range.
Armstrong also famously said of jazz "If you have to ask what it is, you'll never understand." But I've always considered that ever-so-clever statement to be a cop-out.

The Cogitator said...

I'm going to have to side with Dr. Feser's end-of-the-line retort. As with so many things in natural philosophy, if you don't get it (or don't want to get it), you just will not get it.

First, people for centuries have used and understood music WITHOUT exact mathematical reduction-theory. Should we say "music" REALLY meant nothing to them, in their benighted lack of our superior mathematical insight? If we deny there is anything intrinsically meaningful to the existence of musical form per se, as opposed to its numerical correspondences, then there is no common term we are disputing. If "musical form" doesn't MEAN ANYTHING apart from its mathematical emulations, then how are we employing it meaningfully in this (so far mostly numberless) dispute?

Second, just because music is (as it turns out) never expressed without also displaying mathematical properties, this does not mean music just is mathematical form. I cannot see without my eyes but this does not mean I see with my eyes. Analogously, I cannot play music without mobilizing precise mathematical relations, but this does not mean I "play math" when I play music. A triangle does not exist without its three angles, but is it really reducible to any of its angles? Is a line or an angle triangular? No and no. I can posit three noncoplanar angles which also sum to 180˚, but this does NOT mean I have a triangle. Sadly, I see most reductionism as inadequate even to pass the simple "test of reversibility," a principle for testing axioms which is, one would hope, imbibed in first year geometry.

Consider:

All music displays exact mathematical relations/structures.

All physical entities in science display exact (quantifiable) relations/structures.

Therefore, all physical entities are music.

Hmm… let's review our logic, shall we?

All roads under rainy skies are wet.

My road is wet.

Therefore, my road lies under rainy skies.

This may be true, but it is patently invalid; maybe a streetsweeper or a water-balloon fight just went by my house. My street is wet but not under rainy skies.

If music JUST IS its mathematical substructure, then how can similar mathematical structures appear in nature but not also BE music? Identity is a VERY costly and unwieldy principle to ground one's anthropology on. But radical reductionists don't seem to notice or care.

Best,

Jack. said...

Rodak is always fun to read, makes one glad to be a Catholic.

The Cogitator said...

Now let us watch Rodak play the Socinian in Protestant clothes, heheh. ;)

(One need not have read any Marx, Darwin, or Freud to be a Marxist, Darwinist, or Freudian by convention; nor need one have read any Ricoeur [a loss in its own right] to be a Ricoeurian. To be into hermeneutics and theology just is to be some kind of Ricoeurian.)

Rodak said...

Huh?

The Cogitator said...

"Huh?"

As with so many things in natural philosophy, if you don't get it (or don't want to get it), you just will not get it.

Rodak said...

Corrective transposition supplied:

All music displays exact mathematical relations/structures.

All physical entities in science display exact (quantifiable) relations/structures.

Therefore, all music is a physical entity.

One Brow said...

Are you saying that the series of natural numbers has musical properties?

Why would I respond to a post that starts out by saying you can't mathematically describe the relationship between notes with a comment that numbers had musical properties? It's a disjoint topic whose resolution has no bearing on the original point. Only someone seeking to distract, rather than discuss, would bother to bring it up.

There are also mathematical relationships between the objects here in my study, but it doesn't follow that these relationships exhaust all there is to the objects. "X can be mathematically described" does not entail "X can be _exhaustively_ mathematically described."

However, in this case, the the topic X (="the relationship of one musical note to another") is exhausitively described by the mathematical terms like "ratio", "geometric series".

I should probably clarify that this does not mean musical notes are just ratios. While I am sure you would not pretend that is what I said, you might think that I think this is what I said, given you previous comment.

Crude said...

Rodak, you asked me what's left out - I'm responding late, but Ed has already given a better reply than I would have.

You keep mentioning how descriptions of sound can be given in mathematical terms. But you're missing that that's not controversial here - Ed admitted this right in his post, and I admit to it as well. Indeed, the Aristotilean account -requires- correlations. The question is one of identity, and of exhaustive accounting. Again: I can happily agree with you about, say, mathematical description capturing a lot of relevant details about sound. I'll simply point out, easily and self-evidently, that it's not a complete account.

Now, you're making reference to cop-outs and "ever-so-clever" responses, but so far I haven't seen a response from you to these questions Ed had:

"Are you saying that the series of natural numbers has musical properties? For example, is there something the number 23 sounds like? Is it different from what 18 sounds like? Do numbers in general differ in pitch? Do they sometimes form chords? Are they sometimes dissonant?"

Any response? I'd love to know what 4 sounds like. It's a favorite number of mine.

(By the way - for someone who professes commitment to a totally fideistic belief in God, dismissing "If you have to ask what it is, you'll never understand" as a cop-out is pretty amusing.)

One Brow said...

All music displays exact mathematical relations/structures.

All physical entities in science display exact (quantifiable) relations/structures.

Therefore, all music is a physical entity.


That's still an invalid syllogism.

Jack. said...

Rodak: If I get the Russian Phillimonnic Orchestra to play a concert in a room full of deaf people is no music being produced?

Simerly do a group of blind people need to see the numbers on the wall in order to do math?

One Brow said...

If you know what words like pitch, chord, dissonance, etc. mean, then you already know what I mean.

Sorry, but you haven't provided anything to support your argument. Pitch is the property of a single note, not a relationship between two notes. Dissonance and chords can be exactly described mathematically.

Indeed, if you've ever heard music (or heard anything at all for that matter) then you know what I mean. What's the problem?

If this were not you, it would sound to me like you are trying to fall back on the idea of qualia, how people experiecne music. However, I'm sure you are above such cheap tricks. So, I really don't know what you mean.

One Brow said...

First, people for centuries have used and understood music WITHOUT exact mathematical reduction-theory. Should we say "music" REALLY meant nothing to them, in their benighted lack of our superior mathematical insight?

1) People who are versed in the mathemtical nuances of pitch, dissonance, chords, etc. understand music better than people without such knowledge.

2) The relationship between two different notes on a musical scale is unchanged whether or not a listener hears teh music of understands it. The listener adds nothing to the discussion.

The Cogitator said...

Rodak:

"All music [A] displays exact mathematical relations/structures [B].

All physical entities [C] in science display exact (quantifiable) relations/structures [B].

Therefore, all music [A] is a physical entity [C]."


All bread [A] is brown [B].

All shit [C] is brown [B].

Therefore, all bread [A] is shit [C].

"Huh?"

As a conventional Riceourian, you probably think all reason and logic are just disparate language games. I think this is why you don't the logic involved here seriously enough to admit either you are wrong or my syllogism is right.

Best,

Rodak said...

Neither of two musical notes may be described as "4." Any two musical notes, however, do relate to "sound" and that relationship, in terms of the relationship of the two notes to each other, can be described in numbers.
Please keep in mind that I was replying to (and calling into question) this statement:
the relationships between notes are clearly not reducible to or entirely explicable in terms of mathematical relationships
My answer was "Yes, they are" and I provided links to explain why I said yes. Then I explained why I said yes in my own words.
All of that said, if you won't listen to me, listen to One Brow, who is quite obviously more the expert, where numbers are concerned, than am I. (He points out that the syllogism is still invalid--but it now at least expresses my position.)
And nobody has yet, btw, been able to say what is left to say about the relationship between two notes, once the math has been set aside. That's because, my friend, you can't.

Rodak said...

Therefore, all bread [A] is shit [C].

Aye, my lad, so 'tis. But you have to EAT it first!

The Cogitator said...

One Brow:

Can everything you have so far said and everything you will ultimately say in this thread be wholly reduced to pure mathematical structure? (Recall that reduction does NOT mean emulation.)

If so, can your having typed it, or going on to type anything more "add to" the integrity of the mathematical structure that you are, so to speak, catching up to?

If not, spare us all any more of your comments.

Best,

Crude said...

One Brow,

Just out of curiosity, why would bringing up qualia be a "cheap trick"? Is asking for an explanation of the experience of sound, or suggesting that the experience is part of the explanation, somehow dirty pool? To me, it seems that insisting that sound has been "exhaustively explained" with the silent qualification of "well, so long as we avoid questions of experience and subjectivity" to be a cheap trick. Maybe you can explain why I'd be wrong here.

Mind you, I suspect Ed has something different in mind, but I'd like to see this anyway.

The Cogitator said...

Rodak:

I'm not hungry, thanks.

The invalidity of the syllogism I provided, and which you then modified, only underscores the invalidity of hardcore reductionism.

Best,

Rodak said...

Assuming that the musicians are not also deaf, yes.
Explain to me how there is a "sound" if there is no ear.
There are vibrations, but until they enter an ear there is no sound. There may still be music, however, because instruments might be able to measure the vibrations and make notations that another musician could play at a later time for a hearing audience.
Beethoven continued to compose after he went deaf.

One Brow said...

Can everything you have so far said and everything you will ultimately say in this thread be wholly reduced to pure mathematical structure? (Recall that reduction does NOT mean emulation.)

If so, can your having typed it, or going on to type anything more "add to" the integrity of the mathematical structure that you are, so to speak, catching up to?


I'll be happy to discuss that, if you first explain the relevance of "everything you have so far said and everything you will ultimately say in this thread" to the concept of the relationship between two musical notes, and why the discussion of the first will bear fruit to the discussion of the second. Otherwise, I'm not sure what the point would be, besides changing the topic.

If not, spare us all any more of your comments.

I would never post somewhere I was unwelcome. If you were Edward Feser, I would certainly stop.

Edward Feser said...

Well, what can I say. This is just surreal. Are you guys just arguing for arguments' sake, or what?

One Brow begins: "Why would I respond to a post that starts out by saying you can't mathematically describe the relationship between notes with a comment that numbers had musical properties?"

My post did not start out the way One Brow says it did; in fact, it started out by _acknowledging_ that the relationships between notes can be (partially) described mathematically (see the end of the first paragraph), but insisted that these relationships nevertheless could not be _exhaustively_ described mathematically.

Re: One Brow's later comment, whether we focus on the qualia associated with music or on the physics of sound doesn't affect my point at all. A purely mathematical description doesn't _exhaust_ either perceived differences in pitch (to take one example) or the physical differences between two sounds considered as vibrations. To think otherwise is to assume that the musical facts and facts about physics can be read off _entirely_ from mathematics. But this is obviously false. The physical world _has_ a mathematical structure but it is _more than_ a mathematical structure; music _has_ a mathematical structure but it is _more than_ a mathematical structure.

Anyway, at least One Brow recognizes the obvious invalidity of Rodak's syllogism.

One Brow said...

Just out of curiosity, why would bringing up qualia be a "cheap trick"?

The original post was discussing the "the positions of B and G# in the A major scale", etc. These positions are unchanged regardless of the experience of the listener. Not once did I see a reference to the experience of music in the original post.

Is asking for an explanation of the experience of sound, or suggesting that the experience is part of the explanation, somehow dirty pool?

If the topic of discussion is the general nature of experience, certainly not. When the topic of discussion is the actual relationship between the notes themselves, adding in a listener only confuses the issue.

To me, it seems that insisting that sound has been "exhaustively explained" ... Maybe you can explain why I'd be wrong here.

Rodak has actually been saying that the sound of the note is different from the note, and I believe I have heretofore not mentioned the sound at all, nor did Feser in the original post.

Rodak said...

Anyway, at least One Brow recognizes the obvious invalidity of Rodak's syllogism.

Uh, let's not blame the syllogism on me; all I did was play around with a syllogism that was (snarkily) hurled my way.

A purely mathematical description doesn't _exhaust_ either perceived differences in pitch (to take one example) or the physical differences between two sounds considered as vibrations.

It does exhaust the way to most precisely describe those differences in their essence. The sounds in question might be "heard" quite differently by different people (the significance of my Louis Armstrong citation)--but the numbers don't change.

One Brow said...

My post did not start out the way One Brow says it did; in fact, it started out by _acknowledging_ that the relationships between notes can be (partially) described mathematically (see the end of the first paragraph), but insisted that these relationships nevertheless could not be _exhaustively_ described mathematically.

with which I disagree. The *relationships* can indeed be exhaustively described mathematically.

Re: One Brow's later comment, whether we focus on the qualia associated with music or on the physics of sound doesn't affect my point at all. A purely mathematical description doesn't _exhaust_ either perceived differences in pitch (to take one example) or the physical differences between two sounds considered as vibrations. To think otherwise is to assume that the musical facts and facts about physics can be read off _entirely_ from mathematics.

Actually, it is only assuming the "perceived differences in pitch" and "the physical differences between two sounds considered as vibrations" can be described mathematically, and the physical aspects are inherent to the notes themselves. The comparison require no new physical entities, just mathematical manipulation of the entities present.

Anyway, at least One Brow recognizes the obvious invalidity of Rodak's syllogism.

I even recognize goalpost shifting from time to time.

The Cogitator said...

Unibrow: (heheh, that is a cool moniker)

"1) People who are versed in the mathemtical [sic] nuances of pitch, dissonance, chords, etc. understand music better than people without such knowledge."

I'm sorry, man, but do you have any idea how tinny and asinine this sounds to an actual musician or music-lover? (I am not a musician but just imagine.) Did Beethoven collapse his work into raving Pythagoreanism? Or was there maybe something more to this genius than all the mathematical savvy available to him could have given?

Further, I am hardly asking you to go or shut up. But your methodology renders your efforts superfluous, so I am dramatizing the inconsistency of your position. If, in fact, all that exists is WHOLLY REDUCIBLE to pure mathematical structure, then all we have ever said or will say is "already there," Platonically latent, waiting for us as it were, and what we DO say "adds nothing" to the mathematics underlying it. This was your whole point about a performer or listener adding NOTHING to the nature of music since, by your lights, there is NOTHING more to music than its base mathematical structure. If so, then all music is already being played in the Pythagorean heavens and our compositions are superfluous at best. It is thus not too surprising that Pythagoreanism terminated in suicide and silence.

+ + +

Rodak:

You keep on not getting it. (Careful, that kind of amusement can become a habitus.) I presented the syllogism I did PRECISELY in order to refute your reductionist take on music and mathematics. Your tweaking of it just added a new example of the SAME logical error.

+ + +

I think all of us in this thread agree the potential for music is inherent in all subsistent mathematical reality, a reality that exists, and has existed, without, and before, it is expressed concretely in the recital hall. But that right there should give us a decisive pause. If the mathematical structure always exists wholly and maximally on its, but if the musical realities which, in analytical hindsight, correspond to it do not exist in the same way, then OBVIOUSLY the two modes of being are not identical to one another.

Best,

Rodak said...

The persons "not getting it" is the group that cannot see that the only question being adddressed concerns the relationship between two musical notes and how that relationship can best be described.
The answer to that query is: mathematetically. Any other type of description is vague at best and unavoidably thoroughly subjective. The essence of that relationship can be succinctly described using numbers, and by no other means.
Get just as airy-fairy about it as you like: Beethoven really doesn't enter into it.

Rodak said...

"mathematetically"

That is not, however, how the word can best be spelled.

The Cogitator said...

Rodak:

Sigh. Proto-habitus.

Rodak:

Being able to DESCRIBE something in one language does NOT mean the first language is WHOLLY reducible to the latter language. I am stunned to see a hermeneutical fellow like yourself being so obstinate and wooden here. Different things ARE different.

Reductionist challenge for the week:

REDUCE 危機 to English and "cool" to Swahili.

Best,

(P.S. I welcome readers here to have a look at my latest hylomorphic reflections: http://veniaminov.blogspot.com/2009/07/zen-and-art-of-hylomorphism.html )

The Cogitator said...

WARNING SIGN TO ALL THE REST:

As soon as Beethoven is denied relevance to a discussion on music, you know the discussion has jumped the shark. ;)

One Brow said...

Did Beethoven collapse his work into raving Pythagoreanism?

The more relevant question would be whether Beethoven, with a deeper understanding of the mathematics and physics of muscial theory, could have perhaps produced even more interesting music than he did? Surely, you would not claim it would be less so simply because he possessed such knowledge.

Or was there maybe something more to this genius than all the mathematical savvy available to him could have given?

Of course there was.

... If, in fact, all that exists is WHOLLY REDUCIBLE to pure mathematical structure, ...

I don't recall making this claim for anything more epansive that the relationship between a pair of musical notes.

then all we have ever said or will say is "already there," Platonically latent, waiting for us as it were, and what we DO say "adds nothing" to the mathematics underlying it. This was your whole point about a performer or listener adding NOTHING to the nature of music since, by your lights, there is NOTHING more to music than its base mathematical structure.

I don't recall making this claim for anything more epansive that the relationship between a pair of musical notes. I did not even address the issue of sound.

One Brow said...

BTW, The Cogitator, I like your handle too.

Rodak said...

Fine. I'm still waiting for somebody--anybody--to describe the relationship in a language other than that of math.

Rodak said...

Rodak:
"The persons "not getting it" is the group that cannot see that the only question being adddressed concerns the relationship between two musical notes and how that relationship can best be described."

One Brow:

"I don't recall making this claim for anything more epansive that the relationship between a pair of musical notes."

Tommy, can you hear me?

The Cogitator said...

Unibrow:

Like all good things in my life, it [The Cogitator] was given to me by another (none other, in fact, than Dave Armstrong).

Best,

Edward Feser said...

One Brow,

“I even recognize goalpost shifting from time to time.” Cute, but there is no goalpost shifting going on. You are correct that we need to distinguish between the entities themselves and the relationships between the entities, but that does not affect the point. Take some parallel examples: If Bob is six feet tall and Jim is four feet tall, there is a difference of two feet between them. Still, the “taller than” relation is not exhausted by the “greater than” relationship holding between the numbers 6 and 4; there is a geometrical element that goes beyond the merely arithmetic element. Similarly, if event B occurs two minutes after event A, the fact that there is a two minute divide separating them does not entail that the “later than” relationship is exhausted by the “greater than” relationship. Spatial relationships and temporal relationships can be described mathematically, but they are not exhausted by any mathematical description.

All of this should be obvious, but if it isn’t, consider also that 6 would still be greater than 4 even if there were no time and space, and thus no such things as one thing being taller than another or one event being later than another.

If you deny all of this then you have to say that neither spatial descriptions nor temporal descriptions add anything to arithmetic descriptions. Into the bargain, you’d have to say that spatial descriptions and temporal descriptions, since they are both just arithmetic descriptions, do not differ from each other. Both of these claims are obviously false. (Since I just know someone is going to bring relativity theory in at this point, keep in mind that to say that time and space are intertwined does not entail that temporal descriptions and spatial descriptions are just the same thing.)

Similarly, “being higher in pitch than” is not reducible to the “greater than” relationship between numbers.

Or maybe you’d say that the relations “being higher in pitch than,” “being taller than,” “being later than,” etc. are all entirely reducible to “being great than,” and thus identical with each other – adding absurdity to absurdity? Please say no…

One Brow said...

Similarly, “being higher in pitch than” is not reducible to the “greater than” relationship between numbers

Dr. Feser,

I agree with your whole comment, including the quoted part thereof. I acknowledge that the difference between being 4 and 6 feet tall is not reducible to mathematics.

However, there are mathematical descriptions available to us that are different from "greater than". I believe I have already referred to the notions of ratio (and subsequent relation of geometric series), they would would be the building blocks for the mathematical relationship between two different pitches on the musical scale. No doubt a complete mathematical analysis would involve a variety of differential equations to explain the interference effects (at least, from what I remember of my physics classes way back when) and possibly other tools as well. However, this relationship (again, I am only making a claim for the relationship between musical notes) is describable with only mathematics.

One Brow said...

The Cogitator,

My handle as well. I've been "One Brow" for some 25 years years to a few old college friends.

At least I wasn't "malenke wee" (I'm not bothering to put the Russian phrase in the Cyrillic alphabet, nor will I translate, or D. Feser may well ask me to leave).

Edward Feser said...

One Brow,

While I don't think the relationships between notes are exhausted even by the more complex sort of mathematics you're referring to, the fact that they are not exhausted by the "greater than" relation -- a claim you agree with -- is enough for the point I'm making in the main post. So, it seems we needn't continue to dispute the rest.

Re: the translation you mention to Cogitator, not only am I not inclined to ask you to leave, but I'm awfully curious about what it might be. But maybe I'd regret it if you provided it. I guess you could always use asterisks... ;-)

One Brow said...

Dr. feser,

Fair enough.

"malenke" is the approximate transliteration of the Russian word for small. "wee" is a part fo the body men, in particular, do not like to think of as being small. Needless to say, the former "malenke oui" was never fond of this nickname.

Mike Flynn said...

To settle the dispute, go here:

http://www.youtube.com/watch?v=xr3aB4v8hXI

Note that Kam is playing the basset clarinet, which is tuned in A rather than B-flat. Thus, in the score:

http://www.scribd.com/doc/249571/Mozart-Clarinet-Concerto-In-A-K-622

you will find the clarinet part scored in the key of C. To find the ratio of B to G#, you will need to search the clarinet part for instances of B follows closely on D (or vice versa). But I truly doubt that the emotional imapact of the trilled D.

Ganz natuerlich, here is it played again, also on the basset. All the same notes are played.

http://www.youtube.com/watch?v=DVXFONkLPok&feature=related

Forsooth. Reductionism, it seems, is the enemy of humanism.

Anonymous said...

Mike:

I don't know if you are interested, but after the extended discussion you had with UnBeguiled over the difference between "simultaneity" and "instantaneity" he asked you for a simple definition and some examples.

I kind of usurped the request, and offered a response. Furthermore, it did seem as though UnBe understood the distinction finally. I hope I didn't misrepresent Dr. Feser's argument, but it was encouraging that UnBe did eventually recognize Dr. Feser's reasoning.

Anyways. Thanks for the link to youtube. Beautiful.

Interstellar Bill said...

Let's not forget that what a musical note is: a sound that is a) brief, b) characterized by a pitch, and c) part of a rhythm that defines a melody. Neither rhythm nor melody can be reduced to numbers, however mathematically they allow themselves to be perceived. If that were so then computers would write all our hit songs.

The discussion here has only been about a mere element of music, consonance, which is hardly its essence (which is rhythm, since melody can't exist without it). Remember that consonance as a result of string-length ratios is in actuality investigated by prolonging a 'pitched' sound far beyond any possibility of its being a musical note, showing that musicality is not the issue. (It is the long notes that string tuners use in real life, since those evince the best discrimination thresholds.)

In music, however, a note can be so brief that alone it would have no pitch, but in a symphony its consonance (or unfortunate dissonance) is perceived directly, showing that consonance is a two-sound qualium separable from that of pitch, as binaural consonance so vividly shows.

The putative reduction of music to math that was discussed above actually missed its target. Consonance is not a property of musical notes qua notes, but of the pitched sounds comprising them. Making consonance identical to numbers would leave music untouched anyway, since consonance is but one of its many resources.

Reductionism doesn't just shoot blanks, in its crass eagerness it aims at the wrong target to boot!

P.S. Can we just spend some wonderment on the intricacies of auditory neural processing that enable pitch and consonance to be so perceptible? That's where the math actually lives, and it encompasses far more than string lengths being integer ratios or not. Sounds have to be perceptually segregated in either space or quality to have a relationship of consonance in the first place, but that very segregation involves neural sophistication still far beyond the reach of computers. Reductionism hasn't made a dent in the cocktail-party effect, so it's hardly fair that it try a sucker-punch (however weak and lame) on consonance, the indispensible perceptual foundations of which it all the while assiduously ignores.

Rodak said...

Can we just spend some wonderment on the intricacies of auditory neural processing that enable pitch and consonance to be so perceptible?

Neural processing, eh? That's what I'm talking about! And that said, we would have no problem stipulating the truth of:

“The semantic-cum-logical relations between thoughts are identical to, supervenient upon, or otherwise explicable in terms of the causal relations between brain events”;

Rodak said...

Neither rhythm nor melody can be reduced to numbers, however mathematically they allow themselves to be perceived.

Both, however, can be reduced to written notation; and such notation can theoretically be done after the event, even for music that is composed extemporaneously "by ear."

that very segregation involves neural sophistication still far beyond the reach of computers.

Perhaps, so; but (as you point out) it remains a physical event, in the material world. Music is probably the highest form of beauty that man is capable of manifesting in the world. But, that said, music cannot be shown to be targeted at anything other than its own beauty (and man's enjoyment of same) although we may well believe that it points to the joys of Eternity.

Rodak said...

To come back around to the original issue, then: it's not that the relationship of one musical note to another can't be reduced to numbers--it can; it is, rather, that when it comes to so reducing that note, like Bartleby, we prefer not to: it's an aesthetic choice, or a consignment of value.

Josh said...

Very well, Rodak, reduce that above mentioned Mozart score to numbers and ratios and some such, and we'll see what enlightening thing you have to tell me about it.

My own suspicion is that your findings after doing that will have exhausted nothing but some trivial point.

It seems to me that music is mystical, mysterious, deeply conversant with the soul; all very scary things to naturalists. How bored you must have been watching Amadeus when Salieri confesses to have been hearing the voice of God, where if you "displace one note, there would be diminishment."

I can't pretend to be a philosopher, a lot of what you guys say is over my head, but I'll be damned if someone can tell me that numbers are what's important in the study of music. And if music's mysterious hold over us is merely a consignment of value that people agree upon more or less, I might venture to say that you still haven't explained anything to me. People like music because they like it?

Interstellar Bill said...

Rodak

The magic wand of supervenience utter fails to explain how reason and beauty are actually nothing but causal relations, an absurd notion anyway. I believe something because it's true, not because of putative electrochemical neural causality. Musical notes aren't reduced to numbers merely because we don't want to, but because it's impossible in principle to do so. But then mind-reductionism is self-admittedly an abandonment of all principle anyway, being indistinguishable from epiphenomanalism, which is well known to be biologically and empirically bankrupt.

'Neural processing' does not imply your beloved computationalist reductionism, but is rather a general reference to the unconscious but still mental activities of auditory neurons. (No getting away with merrily assuming a neuron is nothing but a computer, to secretly posit what you overtly seek to prove.)

In order to seem coherent, mental reductionism must smuggle mentality back in somehow, usually with such sly synonyms as 'modelling' or 'representation', which are magically declared to be physical when they're obviously not.

My major beef with reductionist physicalism is the immense waste of time it inflicts on its believers as they look in all the wrong places for a theory of mind, like a drunk searching under a streetlight for keys dropped in darkness somewhere else.

Aaron said...

"...like a drunk searching under a streetlight for keys dropped in darkness somewhere else."

Just curious, did you by chance get that line from a Plantinga essay? I feel like I've read something similar to that analogy before.

Rodak said...

I have said nothing that would warrant that little exercise in sarcasm. But, knock yourself out.

Rodak said...

My point was that a neuron is a physical body, not metaphysical thing. Music heard is a physical entity, not an idea.

Most of you are responding to each others' takes on what you claim that I've said, rather than what I've actually said. I actually said, for instance: "Music is probably the highest form of beauty that man is capable of manifesting in the world." And in response I get that ridiculous spiel about reducing Mozart to numbers. I really don't know if this lack of reading comprehension, anti-Protestant bigotry, or plain stupidity. But I am somewhat surprised that a man of Feser's reputation allows it to continue on his blog without comment.

Rodak said...

One final thought: I'm wondering just what all-y'all think a digital recording of a Mozart symphony is... Magic, perhaps?

Anonymous said...

If you think an explanation of Mozart's symphony can be exhausted by a physical description of said disc... or that the only thing that can be left out after that physical description is "magic"... *lol*

Rodak said...

Now that was a profound--nay, a transcendently brilliant!--analysis of the implications of what I wrote. You've outdone yourself and your entire college of peers. My most heartfelt congratulations, sir. I am humbled.

Anonymous said...

Says the man who cries and sniffles when someone is sarcastic in his direction. *lol*

The error in your reasoning has been put on display here throughout, and by multiple contributors. That you'll stamp your feet and insist you're still right should concern anyone why? You're a fideist, you're going say you're right no matter WHAT anyone says. *lol*

Rodak said...

This reminds me again how much I miss Zippy. He and I disagreed on just this kind of topic, but he was always fair, and always honest.

Anonymous said...

Mathematical proof of fairness and honesty please. Also of Zippy. tyvm

Josh said...

Well, I, for one, would apologize if you've said "Music is probably the highest form of beauty that man is capable of manifesting in the world." That's all well and good, because it seems you might admit then that a mathematical description of the notes in a symphony wouldn't begin to touch on what makes it the highest beauty. Is that not what he said originally, that the mathematical description would not be exhaustive?

I'm not trying to make enemies on this, I just don't understand the whole attempt on naturalists' part to use a tool like mathematics to explain an aesthetic, transcendental thing like music.

Rodak said...

Can you explain how stating that the relationship between two notes CAN be reduced to mathematical relationships is to state that a Mozart symphony can be "explained" in terms of numbers? A squeaky wheel can produce two notes, and it can be shown in terms of mathematical relationships why they are distinguishable from each other by the ear. There is nothing metaphysical to be considered in the relationship between two notes. Nor is there any correspondence to be made between a symphony and two notes produced by a squeaky wheel--or a grand piano.

Josh said...

If there is nothing metaphysical about two notes, then where does this highest beauty come in?

Rodak said...

In the confluence of hundreds and thousands of notes, organized and orchestrated for the pleasure of both performer and listener.

Anonymous said...

In other words, he doesn't really mean beauty. Notes and music are nothing but math, which is beautiful, and beauty is nothing but math. Music is the highest beauty the way a dog turd is the highest beauty. Millions upon millions of atoms and molecules arranged into a latticework of rich brown glory.

Never trust a naturalist given to poetic description. It is for them what an ink cloud is for a squid.

Rodak said...

Ah, Feser's scatologist-in-residence is awake and moving again. I have to say that the quality of Feser's acolytes does not quite measure up to the eloquence of his rhetoric. Strange.

Anonymous said...

Now that was a profound--nay, a transcendently brilliant!--analysis of the implications of what I wrote. You've outdone yourself and your entire college of peers. My most heartfelt congratulations, sir. I am humbled.

*lol*

Interstellar Bill said...

Please now, Rodak, stop mangling words:
'reduced to written notation'
is hardly the same as the reductionism peddled by physicalists. Music notation can by no stretch be called a reduction by you, only by unphilosophical musicians.

'A neuron is a physical body, not metaphysical thing.'
I never used the word 'metaphysical', let alone apply it to neurons. I merely tried to say that being biological (not merely physical), neurons have a nanointentionality that cannot be described in any physical way.

'Music heard is a physical entity, not an idea.' Wrong again. Music is a perceptual entity, not merely a physical one (different recitals of the same music look totally diferent on an oscilloscope). It's not enough to make a stereo digital recording of a music production in a studio, at high S/N, to declare it reduced to the physical (you didn't record the music itself, merely the sound waves carrying it).

Rather, you have to take two microphone recordings made near a street band recital that was surrounded by a loud outdoor crowd during a fireworks show high overhead, and have your fabulous HAL-9000 'AI' computer isolate the band's soundtrack (and write down a score) as well as a musician could who was listening (without straining) to the band with his ears in the same place as HAL's mikes (which can even have their own pinnae). Then you can crow about how music is nothing but the physical.

Rodak said...

you didn't record the music itself, merely the sound waves carrying it

And how do you show that "the music itself" even exists apart from those sound waves?

Rodak said...

Or to put it another way: The atmosphere, or something even more solid, is definitely carrying the sound waves; but how do you say that the sound waves are "carrying the music?"--i.e. that the music is distinct from the sound waves? Where would the music "be" in a vacuum?

The Cogitator said...

Rodak:

Music, like all formal realities, is "in" matter like meaning is "in" words, not like dirt is in a carpet. I don't hear the air when I hear music; I hear the formal reality of the music as it informs the air and then informs my auditory cells and neurons. The SAME music thus informs multiple "patches" of matter (the composer's brain, the composition sheets, the instruments, the air, my brain, a compact disc, etc.). You can't reduce the music to any one of them since not any one of them sounds like music without the music itself in its formal integrity.

Best,

Rodak said...

Music, like all formal realities, is "in" matter like meaning is "in" words, not like dirt is in a carpet.

That's a proposition; something you've learned by rote. And the rest of what you say, the same. Now I ask for a proof of those propositions.
I predict, in advance, that any response you make will take you no further than the far walls of Spinozaville.
What I have been saying all along is that these things cannot be proven by reason. Reason will take you only to the edge of ultimate Reality. If you want to go beyond that point, you must grasp the hand of Kierkegaard and make the leap of faith. Beauty may point us in the direction of God, but reason cannot make that beauty a proof of God's existence.
I believe in God because at the point where reason fails me, I choose to believe in God.

Mike Flynn said...

Rodak asks:
"Where would the music "be" in a vacuum?"

Ans:
Ask Beethoven.

Alt. Ans:
http://www.scribd.com/doc/249571/Mozart-Clarinet-Concerto-In-A-K-622

On the lack of beauty in two solitary notes:
Sticking with the A-major scale, the two notes B and G# exist in a certain relationship to the tonic. In another key, the G# would not be heard as a leading tone even though the mathematical description of the two notes and their interval would be exactly the same. The G# would not want to resolve to A. Were the notes sounded simultaneously, it would matter which was the first: if G#, it would be the first and third of a seventh chord (in A-major); but if B, then the G# would be a fourth note in a tetrad.

Rodak said...

Ask Beethoven.

That is a complete non sequitur.

As for your quote, that does not discuss two notes in isolation. Two notes without a further musical context are the sound of a doorbell: ding-dong; of a European ambulance alarm; or of a braying ass: hee-haw.

You continue to avoid the central issue with irrelevant comments on peripherals.

Mike Flynn said...

Rodak asks:
"Where would the music "be" in a vacuum?"

Ans:
Ask Beethoven.

Alt. Ans:
http://www.scribd.com/doc/249571/Mozart-Clarinet-Concerto-In-A-K-622

Rodak responds:
That is a complete non sequitur.

You asked how "music" (not doorbells or braying asses) could exist "in a vacuum," by which you clearly meant "in the absence of air waves." I gave two examples. Beethoven was deaf: compression waves in the air meant nothing to him; yet, he had music. In the second example, the music exists
"on paper" [metaphorically speaking] and not in sound waves. It is the same music on the score as was realized by Sharon Kam in the YouTube link provided earlier. One comprised sound waves, the other did not.

Rodak said...

Look, I've already stipulated that music is transcendent. But, in so stipulating, I have said that reason can take us no further than understanding that we find music to be beautiful.
To the extent that music exists (prior to its composition, notation, performance, etc.) only in the mind of Beethoven, does it also somehow have an existence extrinsic to the mind of Beethoven? Or, is music in the mind of Beethoven intrinsic to Beethoven, as Spinoza claims God and Nature to be intrinsic to each other? Can we get to that music which exists without the mind of Beethoven in any other way than by making a leap of faith--by choosing to believe that it exists "out there?"

Mike Flynn said...

To the extent that music exists only in the mind of Beethoven, does it also somehow have an existence extrinsic to the mind of Beethoven?

Of course. It exists here:
http://www.youtube.com/watch?v=xwCujH0SQIw

and here:
http://www.youtube.com/watch?v=Vrh3GlBKgww
in an entirely different piano;
not to mention here:
http://imslp.org/wiki/Piano_Sonata_No.21,_Op.53_(Beethoven,_Ludwig_van)

Rodak said...

Mike--
You quote me, having excised from what I wrote the entire clause "prior to its composition, notation, performance, etc." which completely changes the sense of my question, and then you proceed to respond to something I never asked.
What's your point? What do you imagine that you've accomplished by that kind dishonesty?
I'm wasting my time here.
Talk amongst yourselves.

For the record, this is what I actually asked:

"To the extent that music exists (prior to its composition, notation, performance, etc.) only in the mind of Beethoven, does it also somehow have an existence extrinsic to the mind of Beethoven?"

If anybody wants to respond to this seriously, please do so via email. Thanks.

Rodak said...
This comment has been removed by the author.
Dianelos Georgoudis said...

If music were entirely reducible to math then it would be possible for a mathematician who was born deaf to experience music.

Now it's obviously impossible for this deaf mathematician to experience the *sounds* of a piece of music. But I wonder whether it may not be possible for this deaf mathematician to experience the "essence" or "form" of a piece of music, and hence to experience its beauty. Perhaps Pythagoras is right after all.