It is often said that in the "Tractatus" science is opposed to philosophy as senseful propositions to senseless ones. Indeed, Wittgenstein characteries science as the totality of true, senseful propositions, as saying nothing except what can be said (4. 11; 6. 53). Also he says that "most propositions and questions, that have been written about philosophical matters, are not false, but nonsensical" (4. 003). If it isn't clear from these remarks that for Wittgenstein science is an ideal and philosophy is an aberration that hardly has any right to the existence? I think that it isn't clear at all. Trying to show this we should clarify the role of senseful - senseless distinction. This will shed some light on Wittgenstein's understanding both of science and of philosophy.
Let us have a closer look at the thesis (4. 11) of the "Tractatus": "The totality of true propositions is the total natural science (or the totality of the natural sciences)". This thesis looks at first as an overvaluation of the science. It looks as stating that all propositions of natural sciences are true. How outmoded it looks today, after Popper's critics of the verification and justification, after Kuhn's theory of the scientific revolutions, after Feyerabendian critics of science! But let us wait for a moment.
What is this "total natural science"? Is it the sum of all received scientific theories? The answer is "no", I think. Why? Because the total natural science is constituted by the totality of true propositions. According to the conception of the "Tractatus", a proposition is true if it is a picture of some fact. A proposition is true, if "To the configuration of the simple signs in propositional sign corresponds the configuration of the objects in the state of affaires" (3. 21).
Can the theoretical propositions of science be pictures of states of affairs? I think they cannot, for to be pictures they must either be configuration of the simple signs, or be reducible to such configuration by analysis.
Let us begin with the first possibility.
In that case theoretical terms of scientific theories become simple signs representing objects in propositions. For example, sign "gene" represents gene, sign "electron" represents electron and so on. Hence, there must be the theoretical objects such as electrons and genes in the world of the "Tractatus". But their existence is incompatible with what Wittgenstein says. For example, if there were such objects as electrons, some theoretical statements about them (stating what electron is) should become apriori. On the contrary, for Wittgenstein "there is no picture which is a priori true" (2. 225). If there were theoretical objects, some elementary statements about them could depend upon one another (for example, being connected by the causal relation). On the contrary, for Wittgenstein elementary propositions are independent (5. 134 - 5. 136). Hence the theoretical propositions of sciences cannot be configurations of simple signs representing the corresponding theoretical objects.
Now we must think about the second possibility, i.e. the possibility of a reduction of theoretical propositions to the truth-functions of the propositions, which are the configurations of the simple signs representing objects. The members of Vienna Circle tried to accomplism the reduction of this sort without success, as is well known. But Wittgenstein never tried to do this and didn's discuss such possibility in the "Tractatus". He wrote about scientific theories and its statements: "All propositions, such as the law of causation, the law of continuity in nature, the law of least expenditure etc., etc all these are a priori intuitions of possible forms of the propositions of science" (6. 34). What are "a priori intuitions of possible forms of propositions"? Anything but not the pictures of facts. Hence, by definition, they can't be senseful propositions. "Newtonian mechanics, for example, - Wittgenstein continues - brings the description of the universe to a unified form. ...Mechanics determine a form of description..." (6. 341). If so, it cant't be a picture of reality by definition of a picturing relation. So, the propositions of mechanics are senseless, too.
There are some direct evidences in support of the thesis that Wittgenstein sees the theoretical propositions of science as senseless. They can be found, for example, between the notes, taken by Fr. Waismann. So Wittgenstein have said: "Ein Naturgesetzt lasst sich nicht verifizieren und nicht falsifizieren. Vom Naturgesetzt kann man sagen, dass es weder wahr noch falsch, sondern "wahrscheinlish" ist, und "warscheinlish" bedeuted dabei: einfach, bequem. Eine Aussage ist wahr oder falsh, nie wahrscheinlich. Was wahrscheinlich ist, ist keine Aussage" (Waismann Fr. Wittgenstein und der Wiener Kreis. Oxford, 1967. S. 100). "Die Physik konstruiert ein System von Hypothesen, dargestellt als ein System von Gleichungen. Die Gleichungen der Physik konnen weder wahr noch falsch sein" (Ibid. S. 101).
So, the theoretical propositions of science violate the condition of being senseful propositions. They are not the descriptions of facts, hence they have no sense (for the sense is the fact modelled by proposition). Theoretical propositions are conventions more or less useful and simple. Strictly speaking, they are not propositions at all, because they don't satisfy the condition of bipolarity.
Hence, the scientific theories don't belong to the "total natural science", as described in (4. 11). This sound rather paradoxically. Nevertheless this does follow from Wittgenstein's own definition of a true proposition. Wittgensteinian treatment of scientific theories might be understood as his answer to the situation of the scientific revolution which had refuted such respectable scientific views as Newtonian mechanics, atomism, theory of aether in their role of the descriptions of reality. So, Wittgenstein treats scientific theories as conventions. They cannot be neither true nor false. Hence, there are no epistemological problems of their justification. In contrast with the members of Vienna Circle, Wittgenstein doesn't care about verification of scientific theories or elimination of theoretical terms because he doesn't believe that theories need some epistemological foundation or justification of their truth. They need not, becauce they are in reality pseudopropositions.
All that has been said pose a problem regarding Wittgenstein's treatment of philosophical propositions. Most of them are senseless, he says. But so are most of the scientific propositions, as we have seen. And even more: propositions of mathematics violaty the condition of bipolarity too, so they are pseudopropositions. The law of logic, as Wittgenstein says, are without sense (4. 461). (Though he doesn't call them senseless). He states that "tautology and contradiction are not pictures of reality" (4. 462).
We have seen so far that scientific theories, mathematics, logic are situated outside the sphere of senseful propositions. We have discovered therefore that a number of Timportant and respectable intellectual activities generate senseless propositions. No wonder that Wittgenstein writes a treatise on philosophy confessing that its propositions are senseless. Contrary to what is often said, it is not a full-size paradox. Wittgenstein realizes the significance of various propositions violating his conditions of being a senseful proposition.
How can we understand then Wittgenstein's attack upon philosophical propositions and problems that are not false but senseless? Why does he attacks philosophy and doesn't attack physics or mathematics? As we have seen, the senselessness cannot be an explication here, - or, at least, it cannot be a full explication. We need something else to explain this.
Phycical laws and hypothesis are not senseful propositions, but they are devices for generating such propositions. They serve to provide us with them. Hence, they are auxiliary to the sphere of senseful.
About mathematical propositions it is written in the "Tractatus": "In life it is never a mathematical propositions we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to other which equally do not belong to mathematics" (6. 211).
Logical propositions give us the forms of inferences of some senseful propositions from other. They are auxiliary, too, Hence, propositions of scientific theories, of mathematics and logic serve us to move from some senseful propositions to others. They are intermediates.
What about philosophy? Wittgenstein's own propositions in the "Tractatus" "are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speek throw away the ladder after he has climbed up on it). He must surmount these propositions; then he sees the world rightly" (6. 54). So, the propositions of his own "Tractatus" are also intermediate and auxiliary. As such they have a right to the existence. But they are intermediate in the manner different from that of the propositions of scientific theories, of mathematics and logic. For the latters serve to pass from propositions to propositions. The propositions of the "Tractatus" serve to pass from propositions to the insight introducing into the sphere of what can't be said by propositions. Here is a pecularity of philosophy.
So we can say: Wittgenstein doesn't denounce philosophy because of its senselessness. For him the sphere of senseless propositions are acceptable but only as intermediate and auxiliary. The proper place of such propositions is in between.
On the other hand, however, senseless propositions have no right to imitate senseful propositions, to pretend to be "about" their proper objects. Thus, Wittgenstein denies the independent existence of mathematical objects, of logical objects; he doesn't accept the existence of theoretical objects of science. Also, he denies the existence of special objects of philosophy such as "the mental thing", "the I". There is no such thing in the world. Why is Wittgenstein so sure? Because philosophical statements about "the I" are apriori. So they cannot be descriptions of some thing in the world. As Wittgenstein clearly puts it: "Where in the world is a metaphysical subject to be noted? You say that this case is altogether like that of the eye and the field of sight. But you do not really see the eye. ...This is connected with the fact that no part of our experience is also a priori... There is no order of things a priori" (5. 633; 5. 634).
What is apriori, can't be a description of reality, because the description must be falsifying or verifying by reality itself. It is different with the apriori statement. What is apriori is connected with our modes of descriptions of reality, it is the syntax of our descriptions. Logic, mathematics and philosophy are apriori. Theoretical hypothesises of science are not the inferences from factual statements, they are not simply falsified by experience and so they can be treated as apriori too. Wittgenstein always claims the strict demarcation between empirical and syntactical, between descriptions and apriori postulation. This demarcation is for him a necessary condition of clarity and intellectual honesty. This demarcation is more important for the understanding of his thought than the distinction between philosophical propositions and scientifical hypothesises and laws.