Tractatus:
Elementary Propositions
The more I read this, the more it seems that it the tractatus is about a hypothetical language: the conditions of possibility of a language with definite sense. That is, language without the possibility of senseless utterances (or thoughts) and so without philosophical problems. Once the system gets off the ground, it seems convincing: at an atomic level, truth is ultimately settled (the atomic sentence either pictures a situation that exists or it does not) and all other utterances are functions of the truth values (of their constituent parts by a logical operator). The question is of course whether the idea of simple propositions and simple objects makes sense, because they are certainly required by the theory. The crux of the argument might be: IF language is to be thus (definitely sensed) then there must be elementary propositions, atomic sentences and atomic facts.
It seems to me that this requirement might be a product of the Fregean mathematical model of language: if truth is a function of assigning truth-value to propositions, then the set of elementary propositions cannot logically impinge on each other, they cannot already begin determining each other's truth by logical implications before the function is metaphorically applied to them; consider the often cited example of a standard atomic fact, This space is red. If this is combined with the logical fact that no space can be two colors at the same time (Wittgenstein's own example) then "This space is red" cannot be elementary because it entails the falsity of "This space is green". We begin to see a what goes wrong: the "possibilities" of redness (or space) contains a logical shape that entails facts outside itself. We are prompted to think this must be true of every thing imaginable. Of course, the fact that the truth-value of negation of any proposition is entailed by the truth-value of the proposition is not problematic, since by definition negation is a truth-function. The next thing to consider is that an atomic sentence refers to a relation between two named objects: true names are after all simple - could the things they describe be simple? Does this entail that each particular (however we conceive those) has a unique name? Imagine each object being numbered, to ensure the simplicity of the name and their sufficient supply. A sentence like "1 is on top of 2" however seems to entail that "1 is below 2" is false. Perhaps the response is that "is below" is not an elementary relation, since it could be understood as containing a hidden negation (is not above). All relations must then be clarified in a way that their negation is reduced out of them: the directions on the compass will only include the infinite gradations from north to asymptotically close to south. Still, something positioned north will entail that it is not positioned northeast; so it seems in any given category of relation, there is one positive, elementary relation (north) and an infinite number of complex relations defineable by being varying degrees of not north. It seems prima facie possible that a similar relation could be used to define distance, and so a totality of nameable particulars could be arranged in a way that none named by elementary propositions implied anything about anything else. The problem seems to be now that there is only one simple object per manifold of relatedness, and an infinite number of objects. The process seems rather baroque, even though it seemed to have intuitive appeal at the outset.
What happens if there are no atomic facts/propositions? Then nothing guarantees that sense is defined. There must in principle be a place where aRb is mirrored in the world by ArB, such that the former simply pictures the latter. If the sentences are complex, then the words and objects are reducible and the question of when reference occurs reverts to that lower level. The existence of atomic facts seems to be a theoretical postulate required by an ideal goal (that language have determinate sense) and by a explanatory device (predicates as truth functions of subjects), though I think the former might be enough to motivate their postulation. Even if I cannot make sense of these postulates, I will press on with the text, hoping that they will be clarified as I proceed 'round the hermeneutic circle.
But why is the Tractatus exciting? I think it's because it's conceit is to expose all philosophical problems as really one problem, as well as the scandalous idea of the self-deception on philosophy's part - not just philosophy but religion and ethics too, but especially philosophy, since it above all strives to proceed forward in full self-transparency. And perhaps it is at heart correct: the root of philosophical problems has something to do with a kind of vagueness or slipperyness of language, that philosophy depends in some way or another on that very vagueness and slippage; the conclusion is not that philosophy lacks sense, but that it is closer to poetic language than it would like to admit. But if I can anticipate my sweeping generalizations of later Wittgenstein, we should be struck by the fact that we do not have, and moreover should not want, some other, idealized, determinate language. Or, maybe more precisely, that we should be highly suspicious of our motives if the reason we desire such a language is largely because it excises philosophical problems from our ongoing conversations. It seems utterly consistent to me that language (ours and the only language we can meaningfully anticipate speaking) when it becomes philosophical that it depends on slippage, that perhaps the greatest self-deception of the philosopher is that there is a slip-proof line in the cosmos between the activity of philosophizing and that of sophistry. The question, I think, then becomes, does philosophy - vagueness and all - make a contribution, defined broadly, to our self-understanding and common destiny, again defined broadly. The weaker claim is that each individual and society as a whole benefits from having gone through the strange conceptual loop from Plato to Wittgenstein: from the cave and back. They possess a caution as well as method for warding off bad metaphysics which if we're being honest characterizes the vast majority of what people believe about the highest and most general state of things. The stronger claim is something I forgot because my rice was done.
The more I read, with Anscombe's help, the more I think I understand what W is up to. The existence of elementary propositions is required by the commitment to the functional semantic model:
If the truth of a complex sentence is a function of its parts, then either those parts are themselves complex, or they are simple. If they are complex then their truth is a function...etc, but if they are simple there must be a distinct function, one prior to the logical functions of conjunction etc, one that maps simple propositions onto what is the case and conversely what is the case onto simple propositions - we could call this the elementary truth function, and claim that it is postulated by the possibility of determinate reference. The question then becomes what kinds of arguments can go into this function? The strange strictures about independence and positivity etc are there to characterize elementary propositions with a view to their appropriateness for being arguments for such a function. So if we imagine a logical truth hidden beneath its logical form - if all A's are B's and some A's are C's then some C's are B's symbolized if 'p & q then r' Here the logical truth of the proposition is due to the interpretation of the sentences, not the (sentential) logical form and as such the truth of this proposition is not captured by truth functionality. As Anscombe puts it, it is "impossible that its tautological truth should consist in its truth for all the combinations [of truth value assignments] unless its components have some mutual independence." If truth functionality is to exhibit the relationship of truth, there cannot be hidden implications lurking with "simple" statements. It would then be possible, as the above example shows, to construct logical truths whose truth is not a function of recursivity. Another way to put this, if A is not independent of B, then whether or not B is true depends on what the elementary function assigns to A, that is, to the truth of a different proposition. This is to contradict the working assumptions that (a) the truth of each simple proposition is a function of whether or not B', and (b) B is logically simple. So not b.
The reason independence is such a tricky requirement is because it seems to be the one that prevents us from coming up with examples of atomic sentences. I suppose we can understand a similar motivation when we think of physics. If we were reductionists, then we would say something like, what this table really is is a concatenation of the things it breaks down into: it is such and such chemical molecules, which in turn are such and such atomic molecules. One we reach the a-tom, the uncuttable, then we have a 'bottoming out' place that anchors what things are. But suppose we never reach such a place? Consider that the atom has long since been decomposed into smaller parts, and those in turn...what if the conclusion to be drawn is that there is no atomic level, that is, what something is cannot be cashed out in terms of what a thing ultimately breaks down to, because it's an unending abyss of new levels and forms, none of which tell us anything ultimate, and all of which tell us that we're barking up the wrong tree. The lesson isn't that logical atomism is wrong - it may not work analogously to physics - rather the lesson is to understand the motivation, indeed the necessity, of positing, in principle, some indivisible level in any reductionist scheme. So to be reductionists about physical things, we need not specify the level at which things bottom out. We merely need to exhibit our commitment to the existence of such a level as a corollary of our overall strategy. To be able to demonstrate such a level would be lovely, however one must stick to the weaker thesis that this is not a result of one's theorizing, but rather an unearthed presupposition of it. Admittedly it seems that Wittgenstein himself was aware that this was the role played by atomic sentences. And I'm sure that the fact that much of the apparatus of the Tractatus was a requirement of working hypotheisis of reductionism rather than a proof for it is a large reason why it was so easy for him to give up the whole picture. If he had somehow envisioned the atomic sentences (as the logical positivists did) it might have been harder for him to let go of them. However since they were offshoots of a bigger scheme, once that scheme was seen as inappropriate the problems involved with logical atomism simply feel away.
I must note that as I read on, (3/31/17) I am less convinced that the teleological cause of dissolving all philosophical problems is the dominant motive and more convinced that instead it is the power seen in Russell's theory of descriptions that provides a clue and a project that has never before been completed; it is more like a discovery of the wall of long lost city and the excitement over the buried possibilities than, say, a desire to fashion a bigger broom to sweep the entire mess clean in a single stroke.
Pictorial Form
Wittgenstein's early view on language is like photo representaitonal painting: language has a grounding resemblance in the objects of the world, It's as though we only had renaissance painters, and left out the rest of the history of painting. Later Wittgenstein broadens his conception of language to include the rest of that history. Except he still leaves out the Metaphyicalists. And probably Magritte too.
I need however to elaborate on this extended metaphor of pictures. It does a lot of work while being highly metaphorical: a proposition is not literally a picture (they however must have some form in common for this to be an apt metaphor) In some ways I think the metaphor of a map is more illustrative. But at any rate, a map is a kind of picture.
Thinking is so difficult. It is like an all but uncontrolled slide down an icy incline; one is furiously trying to get a hold somewhere. And when one grasps something, it almost doesn't matter what, it is from there that one can proceed to climb back up. If indeed the incline is so situated.
I think it is correct to say that the two central elements to Wittgenstein's account are (1) simples and (2) logical form. A proposition just is a (logically) ordered concatenation of simples. Anscombe is helpful in pointing out that spatial form is common to both a shape and the representation of a shaped...this is a clue for grasping logical form: it is just what is common to a proposition and a state of affairs. Indeed one might see logical "space" as the ultimate or ground dimension within which any other particular form is played out...the real point being that logical space is common to all other spaces and that it is not reducible to a foreign regulation.
Elementary Propositions
The more I read this, the more it seems that it the tractatus is about a hypothetical language: the conditions of possibility of a language with definite sense. That is, language without the possibility of senseless utterances (or thoughts) and so without philosophical problems. Once the system gets off the ground, it seems convincing: at an atomic level, truth is ultimately settled (the atomic sentence either pictures a situation that exists or it does not) and all other utterances are functions of the truth values (of their constituent parts by a logical operator). The question is of course whether the idea of simple propositions and simple objects makes sense, because they are certainly required by the theory. The crux of the argument might be: IF language is to be thus (definitely sensed) then there must be elementary propositions, atomic sentences and atomic facts.
It seems to me that this requirement might be a product of the Fregean mathematical model of language: if truth is a function of assigning truth-value to propositions, then the set of elementary propositions cannot logically impinge on each other, they cannot already begin determining each other's truth by logical implications before the function is metaphorically applied to them; consider the often cited example of a standard atomic fact, This space is red. If this is combined with the logical fact that no space can be two colors at the same time (Wittgenstein's own example) then "This space is red" cannot be elementary because it entails the falsity of "This space is green". We begin to see a what goes wrong: the "possibilities" of redness (or space) contains a logical shape that entails facts outside itself. We are prompted to think this must be true of every thing imaginable. Of course, the fact that the truth-value of negation of any proposition is entailed by the truth-value of the proposition is not problematic, since by definition negation is a truth-function. The next thing to consider is that an atomic sentence refers to a relation between two named objects: true names are after all simple - could the things they describe be simple? Does this entail that each particular (however we conceive those) has a unique name? Imagine each object being numbered, to ensure the simplicity of the name and their sufficient supply. A sentence like "1 is on top of 2" however seems to entail that "1 is below 2" is false. Perhaps the response is that "is below" is not an elementary relation, since it could be understood as containing a hidden negation (is not above). All relations must then be clarified in a way that their negation is reduced out of them: the directions on the compass will only include the infinite gradations from north to asymptotically close to south. Still, something positioned north will entail that it is not positioned northeast; so it seems in any given category of relation, there is one positive, elementary relation (north) and an infinite number of complex relations defineable by being varying degrees of not north. It seems prima facie possible that a similar relation could be used to define distance, and so a totality of nameable particulars could be arranged in a way that none named by elementary propositions implied anything about anything else. The problem seems to be now that there is only one simple object per manifold of relatedness, and an infinite number of objects. The process seems rather baroque, even though it seemed to have intuitive appeal at the outset.
What happens if there are no atomic facts/propositions? Then nothing guarantees that sense is defined. There must in principle be a place where aRb is mirrored in the world by ArB, such that the former simply pictures the latter. If the sentences are complex, then the words and objects are reducible and the question of when reference occurs reverts to that lower level. The existence of atomic facts seems to be a theoretical postulate required by an ideal goal (that language have determinate sense) and by a explanatory device (predicates as truth functions of subjects), though I think the former might be enough to motivate their postulation. Even if I cannot make sense of these postulates, I will press on with the text, hoping that they will be clarified as I proceed 'round the hermeneutic circle.
But why is the Tractatus exciting? I think it's because it's conceit is to expose all philosophical problems as really one problem, as well as the scandalous idea of the self-deception on philosophy's part - not just philosophy but religion and ethics too, but especially philosophy, since it above all strives to proceed forward in full self-transparency. And perhaps it is at heart correct: the root of philosophical problems has something to do with a kind of vagueness or slipperyness of language, that philosophy depends in some way or another on that very vagueness and slippage; the conclusion is not that philosophy lacks sense, but that it is closer to poetic language than it would like to admit. But if I can anticipate my sweeping generalizations of later Wittgenstein, we should be struck by the fact that we do not have, and moreover should not want, some other, idealized, determinate language. Or, maybe more precisely, that we should be highly suspicious of our motives if the reason we desire such a language is largely because it excises philosophical problems from our ongoing conversations. It seems utterly consistent to me that language (ours and the only language we can meaningfully anticipate speaking) when it becomes philosophical that it depends on slippage, that perhaps the greatest self-deception of the philosopher is that there is a slip-proof line in the cosmos between the activity of philosophizing and that of sophistry. The question, I think, then becomes, does philosophy - vagueness and all - make a contribution, defined broadly, to our self-understanding and common destiny, again defined broadly. The weaker claim is that each individual and society as a whole benefits from having gone through the strange conceptual loop from Plato to Wittgenstein: from the cave and back. They possess a caution as well as method for warding off bad metaphysics which if we're being honest characterizes the vast majority of what people believe about the highest and most general state of things. The stronger claim is something I forgot because my rice was done.
The more I read, with Anscombe's help, the more I think I understand what W is up to. The existence of elementary propositions is required by the commitment to the functional semantic model:
If the truth of a complex sentence is a function of its parts, then either those parts are themselves complex, or they are simple. If they are complex then their truth is a function...etc, but if they are simple there must be a distinct function, one prior to the logical functions of conjunction etc, one that maps simple propositions onto what is the case and conversely what is the case onto simple propositions - we could call this the elementary truth function, and claim that it is postulated by the possibility of determinate reference. The question then becomes what kinds of arguments can go into this function? The strange strictures about independence and positivity etc are there to characterize elementary propositions with a view to their appropriateness for being arguments for such a function. So if we imagine a logical truth hidden beneath its logical form - if all A's are B's and some A's are C's then some C's are B's symbolized if 'p & q then r' Here the logical truth of the proposition is due to the interpretation of the sentences, not the (sentential) logical form and as such the truth of this proposition is not captured by truth functionality. As Anscombe puts it, it is "impossible that its tautological truth should consist in its truth for all the combinations [of truth value assignments] unless its components have some mutual independence." If truth functionality is to exhibit the relationship of truth, there cannot be hidden implications lurking with "simple" statements. It would then be possible, as the above example shows, to construct logical truths whose truth is not a function of recursivity. Another way to put this, if A is not independent of B, then whether or not B is true depends on what the elementary function assigns to A, that is, to the truth of a different proposition. This is to contradict the working assumptions that (a) the truth of each simple proposition is a function of whether or not B', and (b) B is logically simple. So not b.
The reason independence is such a tricky requirement is because it seems to be the one that prevents us from coming up with examples of atomic sentences. I suppose we can understand a similar motivation when we think of physics. If we were reductionists, then we would say something like, what this table really is is a concatenation of the things it breaks down into: it is such and such chemical molecules, which in turn are such and such atomic molecules. One we reach the a-tom, the uncuttable, then we have a 'bottoming out' place that anchors what things are. But suppose we never reach such a place? Consider that the atom has long since been decomposed into smaller parts, and those in turn...what if the conclusion to be drawn is that there is no atomic level, that is, what something is cannot be cashed out in terms of what a thing ultimately breaks down to, because it's an unending abyss of new levels and forms, none of which tell us anything ultimate, and all of which tell us that we're barking up the wrong tree. The lesson isn't that logical atomism is wrong - it may not work analogously to physics - rather the lesson is to understand the motivation, indeed the necessity, of positing, in principle, some indivisible level in any reductionist scheme. So to be reductionists about physical things, we need not specify the level at which things bottom out. We merely need to exhibit our commitment to the existence of such a level as a corollary of our overall strategy. To be able to demonstrate such a level would be lovely, however one must stick to the weaker thesis that this is not a result of one's theorizing, but rather an unearthed presupposition of it. Admittedly it seems that Wittgenstein himself was aware that this was the role played by atomic sentences. And I'm sure that the fact that much of the apparatus of the Tractatus was a requirement of working hypotheisis of reductionism rather than a proof for it is a large reason why it was so easy for him to give up the whole picture. If he had somehow envisioned the atomic sentences (as the logical positivists did) it might have been harder for him to let go of them. However since they were offshoots of a bigger scheme, once that scheme was seen as inappropriate the problems involved with logical atomism simply feel away.
I must note that as I read on, (3/31/17) I am less convinced that the teleological cause of dissolving all philosophical problems is the dominant motive and more convinced that instead it is the power seen in Russell's theory of descriptions that provides a clue and a project that has never before been completed; it is more like a discovery of the wall of long lost city and the excitement over the buried possibilities than, say, a desire to fashion a bigger broom to sweep the entire mess clean in a single stroke.
Pictorial Form
Wittgenstein's early view on language is like photo representaitonal painting: language has a grounding resemblance in the objects of the world, It's as though we only had renaissance painters, and left out the rest of the history of painting. Later Wittgenstein broadens his conception of language to include the rest of that history. Except he still leaves out the Metaphyicalists. And probably Magritte too.
I need however to elaborate on this extended metaphor of pictures. It does a lot of work while being highly metaphorical: a proposition is not literally a picture (they however must have some form in common for this to be an apt metaphor) In some ways I think the metaphor of a map is more illustrative. But at any rate, a map is a kind of picture.
Thinking is so difficult. It is like an all but uncontrolled slide down an icy incline; one is furiously trying to get a hold somewhere. And when one grasps something, it almost doesn't matter what, it is from there that one can proceed to climb back up. If indeed the incline is so situated.
I think it is correct to say that the two central elements to Wittgenstein's account are (1) simples and (2) logical form. A proposition just is a (logically) ordered concatenation of simples. Anscombe is helpful in pointing out that spatial form is common to both a shape and the representation of a shaped...this is a clue for grasping logical form: it is just what is common to a proposition and a state of affairs. Indeed one might see logical "space" as the ultimate or ground dimension within which any other particular form is played out...the real point being that logical space is common to all other spaces and that it is not reducible to a foreign regulation.
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