4.12 The proposition can present the whole of reality, but it cannot present that which it must have in common with reality in order to present it—logical form.

In order to present logical form, we would have to be able to put ourselves, along with propositions, outside logic, that is to say outside the world.

Is “logical form” then unthinkable? It is unpresentable, unrepresentable. What might we take it to be? Obviously an unknown something that propositions have to share with reality in order to represent it. But this x the unknown has now become an unthinkable unknown. From a logical point of view there cannot be any foundations or prerequisites for logic. Outside a logical point of view we cannot think about logic qua logic. So hypotheses about the evolution of the brain cannot tell us anything [relevant] about the law of excluded middle, for instance. If it is a biological contingency that we recognize logical necessity this does not make it less necessary. So ideas about the foundations of logic are either extra-logical or themselves logical. The theory of logic, or the philosophy of logic, the metaphysics of logic, is either something irrelevant such as biology or psychology, or else it is merely logic itself. Or else it is a hopeless muddle.

McManus pp. 94-95: “When we imagine ourselves identifying a logical form that a proposition must possess in order to represent a particular possible fact, we can only latch on to something that might impose a superficially intelligible (pseudo-) requirement by staying ‘within logic’: that is, by using a proposition that picks out the thus-and-so of the imagined logical form—an object’s being in a particular spatial location, say. But such an identification takes for granted that we understand how this state of affairs must be represented, that its logical form is such that it must be represented using a proposition that captures an object’s being spatially located. But now the ‘requirement’ exposed is that possible facts that are characterized like this must be … characterized like this. Our quest for a genuine requirement must drive us, it seems, ‘outside logic’, and with it, outside any presupposed frame of reference with which to characterize the world. Our ‘indication’ of the logical form now becomes an inarticulate pointing at a bare that, about which we now find that we cannot ask the sort of question of con-formity which we set out to ask.”

There is, McManus argues, no similarity as such, nor sharing of the same form as such. Things are only ever like or unlike in some or other particular respect. What is like what then depends on how we look at things, on how we choose to categorize or characterize things.

4.116 Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.

This seems to be aimed at Frege, who thought he had to hint at some important points and count on his readers to grasp what he was trying to get at. Schopenhauer might also be a target, perhaps surprisingly. Frege and Schopenhauer attack obscurity and praise clarity and precision, yet Frege's reliance on hints is well known, and Schopenhauer endorses mysticism. On p. 610 of volume II of The World as Will and Representation he writes that "all religions at their highest point end in mysticism and mysteries, that is to say, in darkness and veiled obscurity." On the next page he writes about what mystics find but then adds that "nothing of this is communicable except the assertions that we have to accept on his [i.e. the mystic's] word." In some ways Wittgenstein seems to be agreeing with Schopenhauer here, but he also appears to imply that mystics can have no incommunicable thoughts.

Wittgenstein here also makes a point about meaning. Where there is meaning, there is clear (i.e. precise, determinate) meaning. So can what the mystic finds have any meaning at all?

4.115 It will refer to the unsayable by presenting clearly the sayable.

I translate bedeuten as "refer to" and follow the other translations in translating indem as "by," although the result sounds a little odd to me. Indem can also mean "while" or "because." Is the idea really that there is an unsayable that can be meant, signified, or referred to? Or is there some irony at work here?

4.114 It should delimit the thinkable and therewith the unthinkable.

It should limit the unthinkable from inside, by way of the thinkable.

There is no other way, surely. By thinking only what can be thought we see what cannot be thought. Or: by thinking clearly (or self-consciously?) we see what thinking is and, thus, what it isn’t or cannot be.

Echoes here of Kant’s talk of limiting reason in, e.g., § 59 of Prolegomena. At B xxx of the Critique of Pure Reason he says that he has had to suspend knowledge in order to make room for faith (Ich musste also das Wissen aufheben, um zu Glauben Platz zu bekommen) and the references in Prolegomena to the limits of reason relate to this idea. We might wonder, therefore, whether Wittgenstein is implying that he limits the thinkable in order to make room for some faith in the ineffable.

4.113 Philosophy limits the disputable territory of natural science.

Black’s paraphrase (p. 187): “By clarifying thoughts, philosophy demarcates the boundary of the realm where disputes are possible, i.e. the realm of states of affairs.” How can it do this? By clarifying only, not by discovering the limits of science. But if the border is disputed, how can we agree on the limit set by philosophy? Why should we accept it? How can what it offers be mere clarification and nothing more?

4.1122 Darwinian theory has no more to do with philosophy than has any other hypothesis of natural science.

Because evolution is only a theory? No, because philosophy is not about why we think as we do in an historical or causal sense. Nor is it about how we think in any biological sense. In this sense it isn’t about thinking at all. It is about thoughts only in the logical sense.

Schopenhauer offers an alternative to Darwinian theory in The World as Will and Representation. Presumably Wittgenstein did not subscribe to this alternative, but he might have thought that philosophy should not decide between competing scientific hypotheses. Science should do that.

4.1121 Psychology is no more closely related to philosophy than is any other natural science.

Theory of knowledge is the philosophy of psychology.

Does not my study of sign-language correspond to the study of thought-processes, which philosophers held so essential to the philosophy of logic? Only they got entangled mostly in inessential psychological investigations and there is an analogous danger for my method.

So the work of philosophy is not psychological? Not in the sense of a scientific psychology anyway. But if theory of knowledge, which has dominated philosophy from Descartes through Kant at least, is the philosophy of psychology, then why isn’t psychology closer to philosophy than other sciences? Do other major branches of philosophy correspond to other natural sciences? Surely not. Presumably then the philosophy of psychology is not taken here to be closely related to psychology. Because, despite the obvious relation, it is a wholly different kind of activity. Philosophy is not the science of the mind, or any discipline aimed at producing true propositions about the mind (whatever it might take itself to be aimed at). The inessential and psychological is contrasted here with something else, which I call logical and could be called clarificatory or elucidatory. Old philosophers are also contrasted with Wittgenstein, who presents himself as doing something new. But what is his [new] method? Has he told us? And what is the danger that it faces? Mistakenly mixing metaphysics with logic? Or is that the old danger? Mistaking nonsense for sense? Definitions for facts? Clarifications for discoveries or theories? Perhaps.

Mounce (p. 32): “Psychology is irrelevant to philosophy or logic because it is not a psychological process that gives sense to logical form; on the contrary, it is only logical form that can give sense to a psychological process, that can make it, for example, a genuine thought as opposed to a random succession of images. Thus the psychological activity involved in correlating a mark with an object is in itself entirely meaningless. What gives it a meaning, what makes it a genuine correlation, is the logical structure into which the mark enters.”

Anscombe (pp. 82-86) identifies “Carnap and his school” (p. 86) as people who seem to have fallen into the danger identified here by Wittgenstein.

4.112 The end of philosophy is the logical clarification of thoughts.

Philosophy is not a subject but an activity.

A philosophical work consists essentially of elucidations.

The result of philosophy is not “philosophical propositions” but the clarification of propositions.

Philosophy should make clear and distinct thoughts that, without it, are, as it were, unclear and indistinct.

I am echoing Descartes here at the end, for no very good reason, but the translation seems as good as any. The clear and sharply distinguished are to be produced from the cloudy and blurred together. But can a thought need logical clarification? Mustn’t it already have a (perfectly good) sense? The work of philosophy starts to sound either chimerical or else psychological/therapeutic.

Schopenhauer Fourfold Root p. 4: “In general the real philosopher will always look for clearness and distinctness; he will invariably try to resemble not a turbid, impetuous torrent, but rather a Swiss lake which by its calm combines great depth with great clearness, the depth revealing itself precisely through the clearness.”

4.111 Philosophy is not one of the natural sciences.

(The word “philosophy” must refer to something either over or under, but not standing alongside the natural sciences.)

So philosophy does not contain or consist of true propositions. No metaphysics then. But this need not be taken as a negative judgment on philosophy. It could be above the sciences.

4.11 The totality of true propositions is the whole of natural science (or the totality of the natural sciences).

Black (pp. 185-186) criticizes this remark for being incompatible with the more sophisticated 6.341.

4.1 A proposition presents the existence and nonexistence of states of affairs.

So, e.g., “The monkey is in the tree” presents the existence of the relevant state of affairs and the nonexistence of the state of affairs presented by “The monkey is not in the tree.” Or is it only the former that it presents?

4.0641 One could say: The negation is related already to the logical place that the negated proposition determines/defines.

The negating proposition determines another logical place than does the proposition negated.

The negating proposition determines a logical place with help from the logical place of the negated proposition, in that it describes it as lying outside this place.

That one can again negate the negated proposition shows already that what is negated is already a proposition and not merely the preliminary to a proposition.

This seems fairly straightforward and correct. If I say “The monkey is in the tree” then I determine a logical place, a specific possibility from the world of all possibilities. To negate this, and say “The monkey is not in the tree,” is then to refer to quite another possibility. Whatever is denied must already have sense or meaning for there to be a meaningful denial [of it].

4.064 Every proposition must already have a sense; assertion cannot give it one, because the sense is the very thing asserted. And the same goes for negation, etc.

Can we say that meaning is not something one does to a sentence then? It already has a meaning if we can do any such thing as assert it, deny it, and so on.

Anscombe (pp. 58-59) says that this is an attack on Frege, but a potentially confusing one, since Frege would agree with it. The problem for him is that he thinks that when one makes a judgment, one “advance[s] from a thought to a truth-value” (Anscombe gives the reference as “Sense and Reference” p. 65 in Philosophical Writings of Gottlob Frege.) Wittgenstein, she says, is attacking this idea. Having a sense means being true or false, so there cannot be propositions that have a sense but are neither true nor false. Frege and Strawson, Anscombe says (and she argues that Wittgenstein agrees), are wrong. They make it seem as though it is merely contingent if we construct a sensical proposition and find that it has a truth-value.

4.063 A picture to explain the concept of truth: a black spot on white paper; one can describe the form of the spot in that one can answer for each point on the sheet whether it is white or black. To the fact that a point is black corresponds a positive fact, to the fact that a point is white (not black), a negative one. If I indicate a point on the sheet (a Fregean truth-value) then this corresponds to the assumption that is proposed for judgment, etc. etc.

In order though to be able to say whether a point be black or white, I must first know when one calls a point black and when one calls it white; in order to be able to say “p” is true (or false), I must have determined under which conditions I call “p” true, and thus I determine the sense of the proposition.

The point at which the simile breaks down now is this: we can indicate a point on the paper without knowing what white and black are; to a proposition without sense however nothing whatsoever corresponds, because it signifies no thing (truth-value) whose properties are called false or true; the verb of a proposition is not “is true” or “is false”—as Frege believed—but rather that which “is true” must already contain the verb.

Anscombe (note 1 on pp. 105-106) says that Wittgenstein’s reference to “the Fregean Annahme” (assumption) is really a reference to what Russell says about Frege in Principles of Mathematics Appendix A, §477. She argues that Russell and Wittgenstein get Frege (in “Function and Concept”) wrong, and mistakenly attribute to him a technical meaning of ‘assumption.’ Assumption in this sense means something like the assertion of a proposition as either true or false, so that the truth-value of the proposition can be thought of as a verb, meaning the checking of an imaginary box next to “is true” or “is false.” Anscombe notes that Frege did say that the verb of the proposition is “is true” in the Begriffsschrift, but he never said this of “is false” and he rejected this earlier view of his in “Sense and Reference.”

Anscombe pp. 152-153 notes that Wittgenstein’s talk of determining the conditions under which I call a proposition true sounds like verificationism to some people, but it is just a reference to truth-conditions. The emphasis is on logic, not epistemology.

Ostrow (p. 84): “What is important in the notion of the assumption for Wittgenstein is that it brings out how the possibility of saying something determinate about the world depends logically on a prior inner connection between language and reality, a form that is common to both. At the same time, a clear understanding of this idea makes evident that we have no holds on that form apart from our capacity to make true and false statements about the world.”

See comment on 4.442 for Proops on this. On pp. 40-42 he gives reasons for rejecting Anscombe’s account of what “verb” means for Wittgenstein/Frege here. Proops (p. 41, note 122) points to Begriffsschrift § 2 as a likely source of Wittgenstein’s belief that Frege’s assertion sign (|-) marks something as an assertion, when in fact, as Frege explains elsewhere, it is the vertical stroke that does this, the horizontal stroke merely marking a potentially assertable proposition, what Wittgenstein appears to be calling an assumption. Proops (pp. 50-57) notes that Wittgenstein links talk of the ‘assumption’ in his Notebooks (January 11^th 1915, pp. 37-38) with a yardstick: “Could we not ask: What has to be added to that yardstick in order for it to assert something about the length of the object? (The yardstick without this addition would be the ‘assumption’ [Annahme].” A yardstick marks a certain length, as if in readiness for objects one yard long (Proops assumes, for the sake of argument, that it has no finer gradations marked), but does not actually say of its own accord that this or that object is one yard long. Similarly, an unasserted proposition marked only by a horizontal stroke stands, as it were, ready to be asserted as a proposition, but does not assert itself. We might then wonder what needs to be added to it to make it an assertion, an actual proposition rather than mere content. But this content must already have sense. I cannot even consider asserting something unless it is already a proposition. Proops (p. 56): “The Annahme is treated as the notational embodiment of the “showing” aspect of the proposition (picking out a situation while saying nothing about it), while the assertion sign is treated as embodying the proposition’s “truth-claiming” or “saying” aspect (saying of the possible situation thus picked out that it actually obtains). I have wanted to suggest that Wittgenstein’s critique of the assertion sign is best seen as part of an attack on the coherence of such a conception of the proposition.” See 4.022. Proops (p. 57): “In the end, then, the thought that a proposition cannot assert its own truth is best seen not as a direct criticism of any view that Frege or Russell actually hold, but as the denial of a crucial presupposition of the coherence of the notion of logical assertion.”

Marie McGinn (p. 50): “The judgement stroke is not itself a function, but it is only by placing the name of a truth-value in the context of a judgement stroke that we move from naming an object to expressing something with the bipolarity which Wittgenstein takes to be the defining feature of sense. This is what Wittgenstein means when he says that Frege believes the verb of a proposition is “is true” or “is false”: it is only when we assert, by means of the judgement stroke, that the proposition designates the True that we achieve something with the essential bipolarity of a proposition.”

4.0621 But it is important that the signs “p” and “~p” can say the same thing. Because it shows that the sign “~” corresponds with nothing in reality.

That negation occurs in a proposition is still no characteristic [or sign: Merkmal] of its sense (~~p=p).

The propositions “p” and “~p” have opposite senses, but one and the same reality corresponds to them.

This seems pretty straightforward. If "p" could mean anything (as it surely could) then "~p" could mean anything too. In that sense "~" has no meaning at all. If I know that a movie review contains the word "not" then I really know nothing about the reviewer's verdict. If I know that it contains the words "masterful editing" or "woeful acting" then I do know something, in contrast, even though I realize that the full review might assert or deny that the movie contains good editing or bad acting. At least I know that the review talks about editing or acting. The sign "~" is unlike (at least some) other signs in this way. Presumably Wittgenstein is criticizing someone else's thoughts on the negation sign here, and that someone is probably Frege.

4.062 Can’t one make oneself understood with false propositions as one has till now with true ones? Just as long as one knows that they are meant to be false. No! Because a proposition is true if things are as we say they are by means of it; and if by “p” we mean ~p, and things are as we mean, then “p” in the new sense is true and not false.

So the meaning of “p” depends on us, as does its truth. This sounds very antirealist, but it is only true in a sense, not absolutely. The quality of a movie depends on the movie, but the truth of my judgment that it is “great” depends, among other things, on whether I am being sarcastic. Truth and falsity might be, as it were, poles of each proposition, but they are not equal. There is, one might say, an orientation toward truth in language. What proposition one utters depends on (is?) what one means, although note that LW uses the plural ‘we’ (wir) here, so he is not suggesting the possibility of a private language.

Are we meant to think of the Tractatus as possibly trying to get the truth across through false sentences? Presumably we are not meant to conclude that this is what is going on. Its sentences are said to be nonsensical, not false. But perhaps we are encouraged to consider the possibility before dismissing it. This is roughly what Wittgenstein thought of Weininger's work (that it expressed a great truth, so long as it was all negated).

4.061 If one does not notice that a proposition has a sense independent of the facts, then one can easily believe that true and false are relations, with the same rights, between signs and the signified.

One could then say, e.g., that “p” signifies in the true way what “~p” signifies in the false way, etc.

Isn’t what “one could say” here quite correct? Don’t p and ~p refer to the same fact or state of affairs, according to the TLP itself? On this, see below. The point now is that a proposition’s having a sense does not depend on any fact (cf. 2.0211). Logic is not metaphysics. Sense is independent of truth/reality. What then of the picture theory? What of 4.03? Perhaps there is a sense in which propositions are independent of facts and another in which they are not.

Marie McGinn (p. 44) on 4.061-4.063: “[Wittgenstein’s] aim is to show that insofar as Frege holds that true and false propositions designate distinct but equivalent entities, the True and the False, he fails to make the relation between sense and truth and falsity perspicuous. In treating the Bedeutung of true sentences as an equivalent and distinct object from the Bedeutung of false sentences, Wittgenstein believes that Frege fails to make it clear that each proposition with sense essentially has two poles—a true pole and a false pole—each of which excludes the other.”

4.06 Only thus can a sentence be true or false, in that it is a picture of reality.

Correspondence theory of truth again, presumably not being endorsed though, given Frege’s criticism of it and W’s own explicit rejection of it later (and, indeed, perhaps implicitly immediately above). It (or something very like it, cf. Glock) seems to be being endorsed here, but it is so only if “a picture of reality” means something, which presupposes that comparing a proposition with reality is an idea with sense. But has this idea been given any sense yet?

4.05 Reality is compared with a sentence.

Cf. 2.223. Why not “a proposition [or sentence] is compared with reality,” as you might expect? Perhaps to prompt the idea that we cannot really get between language and reality in order to then compare the one with the other. If it is not clear what it is to, or how we, compare x with a proposition, then it is equally unclear what it means to compare x with reality or the world. Cf. Frege’s ideas about the correspondence theory of truth.

4.0412 On the same grounds, the idealist explanation of seeing spatial relations by reference to “spatial spectacles” is inadequate because it cannot explain the multiplicity of these relations.

The idealist sounds rather Kantian here, at least on one popular reading of Kant. Black (p. 177) quotes Russell’s “Philosophical Importance” p. 491 saying that “The categories of Kant are the coloured spectacles of the mind,” but adds that Wittgenstein might have been thinking of Meinong or Husserl rather than Kant.

What is the multiplicity of spatial relations? Perhaps W’s general idea here and in 4.0411 is that what is general cannot be reduced to a single (or simple?) formula or explanation without distortion or implicit generailty.

4.0411 Should we want to express, e.g., what we express with “(x) fx” by placing an affix before “fx” – something like “Gen. fx”, it would not suffice – we would not know what was being generalized. Should we want to indicate it by an affix “a” – something like “f(x_a)” – it would still not suffice – we would not know the scope of the generality-sign.

Should we want to try it by the introduction of a mark in the argument place – something like “(A, A).F (A, A)” – it would not suffice – we could not fix the identity of the variables. Etc.

All these ways of symbolizing do not suffice, because they do not have the necessary mathematical multiplicity.

In other words, if we want to say “For all x, f is true of x” then the best way to do this is the standard way. Saying “Generally [or universally] f is true of x” does not say whether the generality applies to f or to x. Say “fx” means x is fierce. Then does “Gen. fx” say that fierce things are generally x, or that x’s are generally fierce? Saying “f(x-all)” doesn’t help either, because the “all” might apply only within the parentheses or more widely. And so on. The only way to do it is as we do.

It might be objected, since these days the more common way to represent “for all x” is “Ax” (with the A inverted) rather than “x”, that Wittgenstein, taken at face value here, is quite wrong. On its own “(x) fx” says nothing and has nothing to recommend it over any other possible notation. What matters is the use we make of the notation. In 4.0411 Wittgenstein points out possible ambiguities and misunderstandings that could arise if different notations were used. But any notation can be misapplied. Wittgenstein presumably realizes this and wants to minimize the chances of misapplication. On the other hand, perhaps these remarks should not be taken at face value.

4.041 Of course one cannot in turn picture this mathematical multiplicity itself. One cannot get outside it to make a picture.

The idea of “of course” (natürlich) here seems not to fit. Why should this be obvious? Isn’t there an implication here that 4.04 has gone beyond what can be said? Not because it pictures the mathematical multiplicity in question (though doesn’t it?) but because if 4.04 is possible then this picturing would seem at least not obviously un-picturable. And how could one know that 4.04 were true unless 4.041 were false?