02.15.08
Tractatus Logico-Philosophicus, §6.234 - §6.24: "Mathematics is a method of logic. It is the essential characteristic of mathematical method that it employs equations. For it is because of this method that every proposition of mathematics must go without saying. The method by which mathematics arrives at its equations is the method of substitution. For equations express the substitutability of two expressions and, starting from a number of equations, we advance to new equations by substituting different expressions in accordance with the equations."
On Certainty, §1: "If you do know that here is one hand, we'll grant you all the rest."
In the Tractatus, Wittgenstein is inheriting from Russell the desire to base an entire system of knowledge on a single, indubitable principle - one that is not subject to the same laws of doubt and verification that the rest of our lives seem controlled by. Of course (and please forgive my gross generalizations) this idea doesn't come merely from Russell - it is at the heart of a lot if not all of Western Philosophy. I first encountered a form of this thought in an essay by Richard Rorty that I read a while back. It seems as if what is in the world is not enough, that there must be something outside of the world that anchors everything in the world, that determines it, that gives it meaning. So Plato gives us his Forms, the Idea of the world against which this world is judged/ measured/ evaluated. And Kant makes this move twice - he gives us Categories (pure a priori concepts, not corrupted by the sensible) that give meaningful form to the unintelligent content of our perceptions, and then again he gives us the Ultimate, Unknowable Noumenal that necessarily exists and gives rise to the merely phenomenal. So for Kant, the world requires two structures to prop it up - on the one hand Noumena that are not themselves perceivable but mysteriously generate perceivable phenomena, appearances, and on the other hand the Categories of the Mind, without which the world of appearances is dumb (unarticulated). (I'm picturing here a sheet (I Heart Huckabee's) that is pinned to the wall at two corners but sags in the middle. Or maybe it would be more apt to have two people holding up either side of the sheet between them?) In the Tractatus, this function of determination is played by Logic: §3.42: "The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through the whole of logical space." §4.023: "A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically if it is true." §6.124: "The propositions of logic describe the scaffolding of the world, or rather they represent it. They have no 'subject-matter'. They presuppose that names have meaning and elementary propositions sense; and that is their connexion with the world." (The Ogden translation reads: "The logical propositions describe the scaffolding of the world, or rather they present it. They "treat" of nothing." This is important - the German reads: "Die logischen Sätze beschreiben das Gerüst der Welt, oder vielmehr, sie stellen es dar. Sie >>handeln<< von nichts." This is fucking crazy! - My German isn't perfect, but I do believe that 'stellung' is definitely a presentation, not a representation, which is 'darstellung' or 'vorstellung'. I would translate the passage like: "Logical sentences describe the scaffolding of the world, or rather, they present it. They don't "handle" anything." The theme of presentation versus representation is so important; remind me to get back to it.)
I forgot what I was talking about. Something about Idolatry.
For all of those philosophers of action, Something About the Meaning of the Words 'Explanation' and 'Motivation':
"Mr. Grady said that Mr. Kazmierczak did not leave a note or any other explanation, and police do not understand his motivation. There did not appear to be a connection between the shooter and his victims, police said." - New York Times
The difficulty for the author of the Tractatus is finding that first logical proposition from which all other logical propositions are derived. (I wanted to say "can be derived", but that would not be correct.) And when we formulate the problem in that way, then it becomes apparent that the Tractatus Logico-Philosophicus has a mystical soul. Russell's best answer for the question of what this proposition is is the Law of Identity, that a=a, or "A thing is identical with itself." But Wittgenstein realizes that that proposition - and all propositions of logic - doesn't say anything. (He and Russell fought over this a lot.) To put it in Kantian terms, all propositions of logic are forms without content. They don't say anything.
But the Idol still stands. - And that is because the entire project of Analytic Philosophy (and philosophy as a whole) is misguided. The instinct is to search for that first cause, that a priori concept, that fundamental truth that determines every following truth, etc. But this is putting the cart before the horse. Take the Categories of the Mind, for example. The thought is that every intuition that I have must conform to the forms imposed on it by the Categories. Every thought I have has to filed by the four schema: quality (reality, negation, or limitation), quantity (unity, plurality, or totality), modality (possibility-impossibility, existence-non-existence, or necessity-contingency), and relation (substance and accident, cause and effect, or reciprocity). No intuition can make any sense whatsoever without these pure concepts of understanding. The teleology here says that judgments can't happen without the pure concepts. So it might seem like these Categories exist independently of our experiences, hence the term a priori. And if you follow this thought through, then it becomes obvious that the Categories must be of a fundamentally different nature than the physical world of substance and appearance, including our own bodies and brains - to work the way that they do, they have to be exempt from the laws of the ever-shifting sensible muchness - the Categories have to be solid, immutable. Wittgenstein inherits this dichotomy from Kant, only he applies it to propositions. So instead of having the Pure Concepts of Understanding shape our judgments and make them intelligible, we have the Logical Propositions that shape our empirical propositions and give them meaning. But this is not a necessary step to take. If you look at the whole problem Pragmatically, you can just as easily say, "No. The a priori concepts of cause and effect or necessity and contingency are not Universal Laws that we have been given. They're tools that we - we dumb animals - made in order to help make sense of the world around us, and probably to help us not get eaten by saber-toothed tigers. There is nothing necessary about them. (That word-concept doesn't actually make sense here, anyways.) And the same applies for the rules of Logic." [Wittgenstein v. Turing] And the author of the Tractatus is painfully aware of this possibility, and he struggles with it mightily. He says things like, "in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics." (§6.211) But by the time that he writes On Certainty, the idea that logical-mathematical propositions are anything but tools, anything but servants to our practical needs and uses, has long since been abandoned.
On Certainty, §1: "If you do know that here is one hand, we'll grant you all the rest."
In the Tractatus, Wittgenstein is inheriting from Russell the desire to base an entire system of knowledge on a single, indubitable principle - one that is not subject to the same laws of doubt and verification that the rest of our lives seem controlled by. Of course (and please forgive my gross generalizations) this idea doesn't come merely from Russell - it is at the heart of a lot if not all of Western Philosophy. I first encountered a form of this thought in an essay by Richard Rorty that I read a while back. It seems as if what is in the world is not enough, that there must be something outside of the world that anchors everything in the world, that determines it, that gives it meaning. So Plato gives us his Forms, the Idea of the world against which this world is judged/ measured/ evaluated. And Kant makes this move twice - he gives us Categories (pure a priori concepts, not corrupted by the sensible) that give meaningful form to the unintelligent content of our perceptions, and then again he gives us the Ultimate, Unknowable Noumenal that necessarily exists and gives rise to the merely phenomenal. So for Kant, the world requires two structures to prop it up - on the one hand Noumena that are not themselves perceivable but mysteriously generate perceivable phenomena, appearances, and on the other hand the Categories of the Mind, without which the world of appearances is dumb (unarticulated). (I'm picturing here a sheet (I Heart Huckabee's) that is pinned to the wall at two corners but sags in the middle. Or maybe it would be more apt to have two people holding up either side of the sheet between them?) In the Tractatus, this function of determination is played by Logic: §3.42: "The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through the whole of logical space." §4.023: "A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically if it is true." §6.124: "The propositions of logic describe the scaffolding of the world, or rather they represent it. They have no 'subject-matter'. They presuppose that names have meaning and elementary propositions sense; and that is their connexion with the world." (The Ogden translation reads: "The logical propositions describe the scaffolding of the world, or rather they present it. They "treat" of nothing." This is important - the German reads: "Die logischen Sätze beschreiben das Gerüst der Welt, oder vielmehr, sie stellen es dar. Sie >>handeln<< von nichts." This is fucking crazy! - My German isn't perfect, but I do believe that 'stellung' is definitely a presentation, not a representation, which is 'darstellung' or 'vorstellung'. I would translate the passage like: "Logical sentences describe the scaffolding of the world, or rather, they present it. They don't "handle" anything." The theme of presentation versus representation is so important; remind me to get back to it.)
I forgot what I was talking about. Something about Idolatry.
For all of those philosophers of action, Something About the Meaning of the Words 'Explanation' and 'Motivation':
"Mr. Grady said that Mr. Kazmierczak did not leave a note or any other explanation, and police do not understand his motivation. There did not appear to be a connection between the shooter and his victims, police said." - New York Times
The difficulty for the author of the Tractatus is finding that first logical proposition from which all other logical propositions are derived. (I wanted to say "can be derived", but that would not be correct.) And when we formulate the problem in that way, then it becomes apparent that the Tractatus Logico-Philosophicus has a mystical soul. Russell's best answer for the question of what this proposition is is the Law of Identity, that a=a, or "A thing is identical with itself." But Wittgenstein realizes that that proposition - and all propositions of logic - doesn't say anything. (He and Russell fought over this a lot.) To put it in Kantian terms, all propositions of logic are forms without content. They don't say anything.
But the Idol still stands. - And that is because the entire project of Analytic Philosophy (and philosophy as a whole) is misguided. The instinct is to search for that first cause, that a priori concept, that fundamental truth that determines every following truth, etc. But this is putting the cart before the horse. Take the Categories of the Mind, for example. The thought is that every intuition that I have must conform to the forms imposed on it by the Categories. Every thought I have has to filed by the four schema: quality (reality, negation, or limitation), quantity (unity, plurality, or totality), modality (possibility-impossibility, existence-non-existence, or necessity-contingency), and relation (substance and accident, cause and effect, or reciprocity). No intuition can make any sense whatsoever without these pure concepts of understanding. The teleology here says that judgments can't happen without the pure concepts. So it might seem like these Categories exist independently of our experiences, hence the term a priori. And if you follow this thought through, then it becomes obvious that the Categories must be of a fundamentally different nature than the physical world of substance and appearance, including our own bodies and brains - to work the way that they do, they have to be exempt from the laws of the ever-shifting sensible muchness - the Categories have to be solid, immutable. Wittgenstein inherits this dichotomy from Kant, only he applies it to propositions. So instead of having the Pure Concepts of Understanding shape our judgments and make them intelligible, we have the Logical Propositions that shape our empirical propositions and give them meaning. But this is not a necessary step to take. If you look at the whole problem Pragmatically, you can just as easily say, "No. The a priori concepts of cause and effect or necessity and contingency are not Universal Laws that we have been given. They're tools that we - we dumb animals - made in order to help make sense of the world around us, and probably to help us not get eaten by saber-toothed tigers. There is nothing necessary about them. (That word-concept doesn't actually make sense here, anyways.) And the same applies for the rules of Logic." [Wittgenstein v. Turing] And the author of the Tractatus is painfully aware of this possibility, and he struggles with it mightily. He says things like, "in real life a mathematical proposition is never what we want. Rather, we make use of mathematical propositions only in inferences from propositions that do not belong to mathematics to others that likewise do not belong to mathematics." (§6.211) But by the time that he writes On Certainty, the idea that logical-mathematical propositions are anything but tools, anything but servants to our practical needs and uses, has long since been abandoned.
posted by Joel | 10:32 PM
0 Comments:
Post a Comment
<< Home