4.241 If I use two signs with one and the same meaning [Bedeutung] then I express this by putting between them the sign “=”.
Thus “a = b” means that the sign “a” is replaceable by the sign “b”.
(If I introduce a new sign “b” by an equation, in which I stipulate that it should replace an already known sign “a”, then I write the equation – the definition – (like Russell) in the form: “a = b Def.”. The definition is a rule for signs.)
OK. Just stipulations here.
4.24 Names are simple symbols. I indicate them by single letters (“x,” “y,” “z”).
I write an elementary proposition as a function of names, in the form: “fx,” “ø(x,y),” etc.
Or else I indicate it by the letters p, q, r.
4.2211 Even if the world is infinitely complex, so that each fact consists of infinitely many states of affairs and each state of affairs is composed of infinitely many objects, even then there must be objects and states of affairs.
Well yes, there would be. If there are “objects” and “states of affairs” and “facts.”
4.221 It is obvious that by the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination.
Here the question arises of how the combination of propositions comes to be.
Or, if an “elementary proposition” is inconceivable, then it is obvious that “the analysis of propositions” as conceived so far is impossible or inconceivable. The question that “asks itself here” can have no real answer. Complex propositions, the origin of whose complexity we might wonder about, would not be complex (made up of elementary propositions) at all. So it isn’t a real question, by 4.1274. Black (p. 208): “The questions [i.e. ‘How can names combine to form a sentence?’ and ‘How can objects combine to form a state of affairs?’] are nowhere answered and it is hard to see how any answers, in W.’s view, could be expected. Here perhaps we have instances of irredeemable nonsense.”
Cf. 2.03.
So can there be such a thing? A proposition that cannot be contradicted, that contains no verb, but somehow asserts the existence of a state of affairs. Something of the form “chair” or “cat, mat” or “red, here, now” or “hard, blue,
4.128 Logical forms are unnumbered [number-less, but not in the sense of too numerous to count].
Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.
Black (p. 206) suggests ‘anumerical’ for zahllos (‘unnumbered’). He goes on: “It is nonsense to speak of counting logical forms. It is not clear what W. had in mind here: certainly in a universe containing a finite set of objects and a finite set of their combinations, a list could be made of distinct logical forms, which might then be counted. … Perhaps W. wanted to stress that ‘is a logical form’ is not an authentic predicate such as ‘is a star.’
My first reaction: Are logical forms without number (as Pears and McGuinness have it) because they cannot be counted, since their ‘existence’ is so dubious/problematic, or is it because they are more or less arbitrary inventions/conventions (like mathematical operations and stipulated first terms in series)?
4.1274 The question of the existence of a formal concept is nonsensical [unsinnig]. Because no proposition can answer such a question.
(Thus one cannot ask, e.g.: “Are there unanalysable subject-predicate propositions?”)
A formal concept, after all, is purely formal. If one existed, what would exist? Or not exist, on the contrary?
4.1273 If we want to express in the concept-script the general proposition: “b is a successor of a,” then we need for this an expression for the general term of the formal series: aRb, (Ex):aRx. xRb, (Ex,y):aRx. xRy. yRb, … The general term for a formal series can be expressed only by a variable, because the concept ‘term for this formal series’ is a formal concept. (This has been overlooked by Frege and Russell: because of this the way they want to express general propositions like the one above is false; it contains a vicious circle.)
We can determine the general term of a formal series by giving its first term and the general form of the operation that produces the next term from the proposition that goes before it.
Black (p. 203) points out that Wittgenstein seems to be attacking “Frege and Russell’s definition of the so-called ‘ancestral’ of a relation, which they use in their definition of a natural number.”
4.12721 With an object that falls under it, a formal concept is already given. Thus one cannot introduce as primitive ideas the objects of a formal concept and the formal concept itself. Thus one cannot (like Russell) introduce, e.g., the concept of a function and also special functions as primitive ideas; or the concept of number and specific numbers.
Yes, Russell seems to be making a mistake here about what it makes sense to call “primitive ideas.” So what is (or should be) primitive? The concept under which certain objects fall, or the objects themselves, which perhaps somehow bring the relevant concept with them? Or can there be no true primitiveness or foundation here?
4.1272 Thus the variable name “x” is the proper sign of the pseudo-concept object.
Wherever the word “object” (“thing,” “item,” etc.) is used rightly, it is expressed in the concept-script by a variable name.
For example in the proposition “there are two objects, such that …” by “(Ex,y)…”.
Wherever it is used otherwise, thus as a proper concept word, nonsensical [unsinnige] pseudo-propositions arise.
Thus one cannot, e.g., say “There are objects,” as one says “There are books.” Just as little can one say “There are 100 objects” or “There are א0 objects.”
And it is nonsensical [unsinnig] to speak of the number of all objects.
The same goes for the words “complex,” “fact,” “function,” “number,” etc.
They all signify formal concepts and are represented in the concept-script by variables, not by functions or classes. (As Frege and Russell believed.)
Expressions like “1 is a number,” “there is only one zero,” and all such are nonsensical [unsinnig].
(It is equally nonsensical [unsinnig] to say “there is only one 1,” as it would be nonsensical [unsinnig] to say: 2+2 is at
Quite a bit of Frege- and Russell-bashing going on here, it seems. But what concept-script is he talking about? His own, or the only possible correct one? In other words, is he stipulating how he wants these things to be done, or claiming that Frege and Russell are wrong in some more objective sense? Perhaps it comes to the same thing if he is here developing Frege's and Russell’s ideas as well as they can be developed. But in what sense, if any, is it nonsensical to say there are objects or that 1 is a number? Surely in teaching a child or doing philosophy we make such assertions often. They do not, presumably, count as propositions though for Wittgenstein. They are what he later called grammatical remarks, not (metaphysical) facts. To treat them as facts is to misuse them, i.e. to speak nonsense. Certainly attempts to specify the minimum number of objects there must be are badly mistaken, in Wittgenstein’s view. The Hebrew letter Aleph with the suffix 0 is used in mathematics, including in Principia Mathematica, says Wittgenstein in Letters to
Ostrow (p. 77): “In acknowledging the weakness of our grasp on “object” we are acknowledging the same about “complex,” “fact,” “function,” “number,” and so on.” On p. 78 he says: “We do not by means of this text arrive at new, superior accounts of “fact,” “object,” and “number.” What the Tractatus seeks instead is to lead us to regard in a new way our attempts to gain clarity about all such notions; it seeks to get us to go on differently in our efforts to know the world. We are called to go on without philosophy.”
4.1271 Each variable is the sign of a formal concept.
Because each variable presents a constant form, which all its values possess, and which can be conceived as a formal property of these values.
So a formal concept is purely formal, not really a concept at all? And formal properties are purely formal, lacking content?
4.127 A propositional variable signifies a formal concept and its values [signify] the objects that fall under this concept.
Black (p. 201) says that this is not strictly correct unless “signify the objects” means “refer to the objects in combination.” 3.313 has propositions as the values of a propositional variable, not names or other referring expressions.
4.126 In the sense of which we speak of formal properties, we can now also speak of formal concepts.
(I introduce this expression in order to make clear the basis of the confusion of formal concepts with proper concepts, which runs through the whole of the old logic.)
That something is an instance of a formal concept cannot be expressed through a proposition. Rather it shows itself in the sign of this object itself. (A name shows that it signifies an object, a numeral that it signifies a number, etc.)
Formal concepts cannot, in the way that proper concepts can, be presented by a function.
Because of their defining characteristics, formal properties are not expressed through functions.
The expression of a formal property is a feature of certain symbols.
The sign for the defining characteristics of a formal concept is therefore a characteristic feature of all symbols whose meaning falls under the concept.
The expression of a formal concept is therefore a propositional variable, in which only this characteristic feature is constant.
In the third sentence here I take Black’s suggestion (p. 199) of saying ‘is an instance of a formal concept’ rather than the more literal ‘falls under a formal concept as an object belonging to it,’ as
Cf. 4.122 and note that “the sense in which we speak of formal properties” might be no sense at all. Wittgenstein says that the term “Merkmal” (characteristic) here is taken from Frege’s terminology. See Letters to
Richard L. Mendelsohn The Philosophy of
4.1252 Series which are ordered according to internal relations I call formal series.
The series of numbers is ordered not by an external but rather by an internal relation.
Equally the series of propositions:
“aRb,”
“(Ex): aRx. xRb,”
“(Ey): aRx. xRy. yRb,” etc.
(If b stands in one of these relations to a then I call b a successor of a.)
The first part confirms my comment on 4.123. The second introduces a definition of “successor.”
4.1251 Here now the vexed question “whether all relations are internal or external” disappears.
“Relations” seems to have different senses: definitional/necessary/internal and factual/contingent/external. If this is so, then the vexed question looks like “Are all banks financial institutions or sides of rivers?” A question not worth asking. 4.1241 implies an internal connection between questions of sense (logical) and questions of form (metaphysical). The vexed metaphysical question of 4.125 seems to be the result of a mistake about logic/sense. Cf. the second paragraph of the foreword.
Black (p. 198) says that this might be a reference to G. E. Moore’s essay “Relations,” which attacks the views of Bradley and others on internal relations. Hegelian, idealist views on relations certainly were a concern of Russell’s.
Marie McGinn says that “This remark and the one following (4.1252) make a clear reference to Russell. Russell had argued against the intelligibility of internal relations and held that all relations are external.” (p. 178)
4.124 The holding of an internal property of a possible state of things will not be expressed through a proposition, but rather it expresses itself in the proposition that presents the state of things, through an internal property of this proposition.
It would be equally senseless to ascribe a formal property to a proposition as to deny it.
By 4.122, do “formal property” and “internal property” mean the same here? If so, then the second sentence/paragraph implies that the first is senseless. And does the second sentence really have a sense? Has “formal property” been defined?
4.123 A property is internal if it is unthinkable that its object should not possess it.
(This blue color and that stand in the internal relation of lighter and darker eo ipso. It is unthinkable that this pair of objects not stand in this relation.)
(Here the shifting use of the word “object” corresponds to the shifting use of the words “property” and “relation.”)
Marie McGinn (p. 182): “In the later philosophy, it is clear that Wittgenstein thinks that the colour-wheel is itself a part of the symbolism, in the sense that the ordered colour samples of the colour-wheel constitute an instrument of our language, by means of which the logical order of our colour concepts is presented. However, it is not clear that he held this view at the time of writing the Tractatus, where he seems to suggest that the logical order of colour-space will be revealed through the logical analysis of colour terms (see TLP 6.3751).” McGinn also discusses Remarks on Colour p. 34 in connection with this.
So, this is what is special about facial features: they have a kind of essentiality. The reference to shifting uses of words here might alert us to the possibilities that LW’s example does not really tell us anything about what he has been talking about till now (objects, etc. in a different sense) and that nothing really can be identified as what he has been talking about till now (objects, etc.). On the other hand, isn’t there a relation of darker/lighter internal to a pair of shades of blue? And a similar essential relation between earlier/later, left/right, and so on? The very necessity involved (seemingly) here makes them, perhaps, not relations proper (matters of fact), but don’t they indeed seem to be relations of a kind? Isn’t one essentially less than three? Perhaps LW wants us to see such apparent metaphysical truths as misunderstood points of logic, definition, stipulation, convention, or grammar.
4.1221 We can also call an internal property of a fact a feature of that fact. (In the sense in which we speak of facial features.)
Cf. references to physiognomy in the Investigations, perhaps. This sounds as though LW really means it, but we can call anything anything, after all, and is the word ‘features’ used in a special way in connection with faces?
4.122 We can talk in a certain sense of formal properties of objects and states of affairs or of properties of the structure of facts, and in the same sense of formal relations and relations of structures.
(Instead of structural property I say also “internal property;” instead of structural relation, “internal relation.”
I introduce these expressions in order to show the basis of the confusion between internal relations and proper (external) relations, which is very widespread among philosophers.)
The holding of such internal properties and relations, however, cannot be asserted through propositions, but rather it shows itself in the propositions which present the states of affairs and deal with the objects in question.
The last sentence here seems patently absurd (cf. 4.116: there is no excuse for trying to get something out of ‘impermissible’ sentences). And if internal relations are not proper relations, what are they? Not relations at all, one is tempted to think. And perhaps internal properties are not really properties at all, although LW does not say so here. Haven’t we seen already how hard it would be to think what external properties of objects, etc. might be? If now their internal properties and relations go up in smoke, what can be left of the objects and states of affairs themselves? Black (p. 195) points out that, by 3 and 4, formal properties are not really properties at all and cannot be talked about. Hence, in the first sentence, the expression “in a certain sense.” Of that sentence, Black says: “The sentence should be put into apposition with 4.12a, where we are told that logical form belongs to the unspeakable.”
On p. 57 McManus says that “the intent of the qualification ‘internal’ seems to be that it taketh away what the word ‘relation’ giveth.”
4.1213 Now we understand too our feeling that we have a correct logical apprehension only if everything is right in our sign-language.
For Auffassung here I have ‘apprehension,’ although ‘comprehension,’ ‘conception,’ and ‘view’ would also be all right.
My first reaction: So we are talking about concept-scripts and, perhaps more importantly, psychology here. LW aims to show us why we feel, mistakenly, that a perfect concept-script is essential to logic. We want a kind of unmistakeable means of presenting thoughts without ambiguity or interpretation. We want to make our meaning visible, so it will be as plain as the nose on one’s face. But meaning, what can be said, cannot be shown. Our quest is forlorn.
4.1212 What can be shown cannot be said.
OK, but is this a stipulation about a possible concept-script or a grammatical truism (like “colors cannot be spoken”)? Or something else? Cf. Schopenhauer on music: We could “just as well call the world embodied music as embodied will.” (WWR, v. 1, §52, pp. 262-3)
Music, like the phenomenal world, shows, as it were, the nature of the thing-in-itself. What this is cannot be said or translated into concepts. Nor can it be demonstrated or proved that music does this. The listener must simply hear the music and agree that it expresses the inner nature of the world. On that idea cf. the preface, where LW talks about being understood only by someone who has already had similar thoughts.
4.1211 Thus the proposition “fa” shows that it is about the object a, two propositions “fa” and “ga” show that they are both about the same object.
If two propositions contradict each other then their structure shows this; the same applies if one follows from the other. And so on.
In what sense is “fa” a proposition? Only according to the conventions of a concept-script. “Fa” stands in need of some interpretation, and only in a context of certain conventional understanding/interpretation does it show anything. Is LW assuming some transparent language of thought here? Is he describing how a possible concept-script might go? Is he talking nonsense? Or is he just talking about a notational system that would work well for us, given our understanding of these conventions?
Propositions show something that cannot be presented [darstellen] by language.
Ostrow (p. 107) notes that this “makes clear that it is the genuine proposition that shows logical form,” a job taken by some commentators to be done by the (pseudo-) propositions of logic. But couldn’t both do it?
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.
4.1 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 11th 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.”
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(xa)” – 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?
4.04 In a proposition there must be exactly as many things to differentiate as there are in the state of things it represents.
Both must possess the same logical (mathematical) multiplicity. (Compare Hertz’s Mechanics on dynamic models.)
The more a proposition comes to have in common with what it represents, the less distinguishable it is from it.
4.032 Only insofar as it is logically articulated is a proposition a picture of a state of things.
(Even the proposition “ambulo” is composite, because its stem with another ending, or its ending with another stem, gives another sense.)
A proposition must be composite then in order to be a proposition, a picture of a state of affairs, rather than a mere word or name. Apparently simple propositions are really complex, such as the Latin “ambulo” (I walk).
4.0312 The possibility of a proposition is based on the principle of the representation of objects by signs.
My fundamental thought is that the “logical constants” represent nothing. That the logic of facts does not allow of representation.
Ostrow (p. 87): “We are meant to see that, contrary to Frege’s contention, the logical functions cannot be construed along the lines of genuine (material) functions, that it makes no sense to suppose a domain of entities which form the special province of the logician. Nor is this a point directed merely at Frege. Russell is even more explicitly committed to the assumption of a definite logical subject matter, as is evident in his … claim that “the chief part of philosophical logic” is “the endeavor to see clearly the entities” that mathematics regards as indefinable (Principles xv).” On this, see note to 2.01. In Letters to
4.0311 A name stands for a thing, another for another thing, and they are connected with each other, so the whole – like a tableau vivant – stands for a state of affairs.
Why a tableau vivant and not a normal picture? For what does a tableau vivant stand? The picture, or the pictured? That is, a tableau vivant of the death of Socrates could be seen as a representation of the death of Socrates or of The Death of Socrates (a painting). Is Wittgenstein saying that a proposition is like a name, only for a state of affairs rather than for an object?
4.031 In a sentence a state of things is as it were put together by way of a test.
Instead of, This sentence has such and such a sense, one can say, This sentence represents such and such a state of things.
A proposition is here spoken of as an unasserted thought in Frege’s terms. It is a possible assertion, so to speak. Nordmann (pp. 108-114) discusses various possible translations of this remark, and their various implications. It is ambiguous in the German, the first sentence allowing for the interpretation that a sentence puts together a situation experimentally, or as an experiment, or for the sake of experiment, or in order to be put to the test.
4.03 A sentence must communicate a new sense with old terms.
A sentence communicates a state of things to us, so it must be essentially connected with the state of things.
And the connection is just that it is its logical picture.
A sentence says something only insofar as it is a picture.
So propositions picture states of things. This is not new. It must be essentially connected with the relevant state of things, which sounds metaphysical, but in fact the connection in question is precisely, merely, that it pictures it. Logically, whatever exactly that might mean.
4.027 It is of the essence of a sentence that it can communicate a new sense to us.
We can learn new words, and use these to mean new things, but the credit should go not to words but to the sentence. If I become strong by taking steroids, it is a mistake to think that the steroids are doing all the work. Rather, my body is such that it converts steroids to muscle. It is of the essence of a sentence that it can absorb new words and use them to make a new sense.
Could there be anything here that could be used to solve the 6.54 puzzle? (Not that I can see, but this would seem to be a good place, in terms of the number scheme, to look.)
Original comment: A new sense in the sense that this combination of signs has not been seen before, at least by us. But how do we know the meanings of words except through sentences? And we just do not understand sentences on their own, as even 4.026 can be taken to imply.
4.026 The meanings of simple signs (words) must be explained to us for us to understand them.
We make ourselves understood, though, with sentences.
Black (p. 172) offers this rather free paraphrase: “The meanings of words have to be explained for us, have to be shown, but once this has been done, we use propositions to make ourselves understood, to communicate thoughts.” It seems to me, though, that the meaning might be more that, while words need to be explained, the explanations offered can only take the form of sentences. Meaning and understanding take place in the medium of sentences, not words (even though, in a sense, sentences are made up of words). Sentences consist of words in the way that the human body consists of such things as carbon and water. You can break the one down into the other, but you cannot produce the greater simply by adding or mixing the ingredients.
Compare with 6.54. Wittgenstein there seems to contrast understanding a person's sentences with understanding the person, so that we can understand him yet see that his sentences are nonsensical. According to 4.026, though, we could only understand him by means of his sentences. If these sentences are nonsensical, it is obviously difficult to see how we could understand him by means of them.
My initial reaction: You need to learn the meanings of words, but once you know them you can understand new combinations of them in sentences. The sensible components of language are arbitrary and so must be learned, but the senses (meanings0 expressed by means of them are, what, already intelligible? This would be very different from the later Wittgenstein, perhaps even the Wittgenstein who comes later at 5.62, for instance. If “senses” are “intelligibilities” then this is uncontroversially true, I suppose, but hardly as informative as it sounds.
4.025 The translation of one language into another does not proceed by one’s translating each sentence of one into a sentence of the other, but only by translating the constituent parts of sentences.
(And the dictionary translates not only substantives but also verbs, adjectives, and conjunctions, etc.; and it treats them all the same way.)
Yes, but translation software does not work very well. Translation is not as simple or mechanical as 4.025 suggests. Wittgenstein, who helped with the translation of the Tractatus, surely knew this. Cf. Philosophical Investigations §§1-23.
4.024 To understand a proposition means to know what is the case if it is true.
(One can therefore understand it without knowing whether it is true.)
One understands it if one understands its constituent parts.
The first two sentences here seem straightforward enough. The last is problematic, because you might think you do not understand “The cow milks the boy” even though you understand the individual words. But knowing what milking (a cow) is does not tell us what is meant here. So we do not understand the constituent parts of this sentence. We understand parts of other sentences that look the same, that is all.
4.023 Reality must be fixed by a proposition except for a yes or a no.
Therefore it must describe reality completely.
A proposition is a description of a state of affairs.
As the description of an object goes by its external properties, so a proposition describes reality according to its internal properties.
A proposition constructs a world with the help of a logical scaffolding and therefore one can actually see in the proposition all the logical features of reality if it is true. One can draw conclusions from a false proposition.
So propositions must be quite definite or determinate about something (not the whole of reality, presumably, although maybe that) and not at all vague. A proposition describes the internal properties of a state of affairs. Why? And what are these? If internal properties are logical properties, then do propositions describe these? Presumably. And so a true proposition will describe the logic of a part of the world, of a state of affairs. Since it shows its sense, one will be able to see from it what this logic is. If the proposition is false one will have to think a bit, perhaps just by affixing a mental “not” to the picture presented by the proposition.
4.022 A proposition shows its sense.
A proposition shows what is the case if it is true. And it says that this is the case.
Puzzling, since a proposition considered as a sentence does not show its sense, and considered as a proposition or understood thought then the concept of showing does not seem to fit it. A proposition, we might say, is a sense. 4.022 suggests that a proposition is like a Fregean assertion sign followed by a literal picture, one that is impossible to misinterpret because it requires no interpretation. It (somehow) shows its sense (correct interpretation). Is this a reduction of Frege’s philosophy of language?
Others are puzzled by this remark too. Black (p. 165) quotes Wisdom calling it “a mistake.”
4.021 A proposition is a picture of reality: Because I know the state of things it represents if I understand the proposition. And I understand the proposition without its sense having been explained to me.
Tricky. How can I know or be acquainted with a state of things/state of things that does not exist (consider false propositions)? I think 4.021 must be taken as a tautology. To know the state of things a proposition represents simply is (i.e. means) understanding the proposition.
4.02 We see this from our understanding the sense of a proposition without its being explained to us.
Splutter! We might understand a string of pictographs (women drink beer, say, or bird fly to pharaoh) but we hardly understand a sentence in the same way. We need to know the meanings of the signs. The same is true with pictographs, of course, but they could sometimes be guessed. We could, I suppose, guess the meaning of a sentence, but what could this show us about the essence of propositions? The reason we can understand the sense of a proposition without its being explained to us is that we know the correct use of its signs. In this I include letters as well as words and punctuation marks, since “The dog went Hav! Hav!” is intelligible (that’s the sound the dog made) whereas “The dog went hav hav” would take more guesswork (does “hav hav” mean “pee pee”? is it a place?, etc.). Consideration of the use of writing, including hieroglyphic writing, in fact seems to show that the essence of propositions is not picturing in any simple sense at all. And neither 4.016 nor 4.02 actually denies this.
Proops (pp. 103-105) argues that Wittgenstein is in fact referring back to 4.01 here, when he says ‘this.’ He bases this claim on the fact that it does not make much sense otherwise, and in the Prototractatus 4.02 refers to 4.01 and some related remarks. Presumably Wittgenstein inserted other material without noticing that he needed to change the wording of 4.02.
4.016 In order to understand the essence of the proposition, let us consider hieroglyphic writing, which depicts the facts it describes.
And from it came the alphabet, without losing the essence of picturing.
Real (Egyptian) hieroglyphic writing is in fact alphabetic and does not simply depict, image, or map the facts it describes. We might imagine the kind of writing Wittgenstein describes here, but it is possible that he knows we could not get very far this way. Writing does seem to have started with pictographs, but of course spoken language came before this, and is thought to have emerged from gestures (in the beginning was the deed, all very later Wittgensteinian). So it might be true that the (written) alphabet came from pictographs, and hence that (written) sentences began this way. This tells us nothing philosophically, surely, since logic is not concerned with such empirical matters. But the history lesson might be helpful all the same, as a kind of metaphor. The idea seems to be that the essence of propositions is to represent.
4.015 The possibility of all similes, of all the imagery of our language, rests on the logic of picturing.
The clause “of all the imagery of our language” is Wittgenstein’s translation.
This clearly looks to be a key statement for the picture theory. Language is pictorial or representative, and the possibility of its being so depends on the logic of representation. So: the logic of representation is fundamental to the possibility of similes (representation?), which might in turn be taken to be a prerequisite for representation itself.
But is this resting or necessity or dependence meant to be metaphysical (factual)? Presumably not. It is logical. So the image of resting, etc. is quite misleading here. Can the logic of picturing really be anything other than the possibility of picturing? Does anything rest on anything else? Is anything at all really being said?
4.0141 In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and that there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again – by means of the first rule – construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. And the rule is the law of projection which projects the symphony into the language of the musical score. It is the rule of translation of this language into the language of the gramophone record.
This is all Wittgenstein’s translation. See Letters to
I have wondered whether the last sentence could possibly be a joke. What could the rule be by which one reads music from a score? Of course people do this, just as we can read aloud from a printed script. But I'm not sure what there is apart from the printed word and the sounds we make. There is something, seemingly, but what is hard to say. Rules are not easy to understand, and nothing here seems to help very much.
4.014 A gramophone record, a musical thought, musical notation, and sound waves, all stand to one another in that internal picturing relation that holds between language and world.
The logical form is common to all of them.
(As in the fairytale with the two youths, their two horses and their lilies. They are all in a certain sense one.)
‘Logical form’ is suggested by Black (p. 163) for logische Bau, which literally means something more like
If they are one then they do not really have anything in common. They simply are the same thing. And yet they are not really the same thing. A musical score and a musical recording are not the same, although both may be referred to as, say, Beethoven’s Fifth. They have a kind of interchangeability, though, and insofar as they are interchangeable (which is by no means completely) they are one. But the interchangeability is purpose-dependent, seemingly. In the fairy story it is symbolic, and depends on our being able to see it as such. It is not, it seems, real in a platonic, metaphysical sense.
The fairytale in question appears to be the story “Golden Children” by the brothers Grimm. See Nordmann p. 114, note 47, where Jim Klagge is credited with this discovery. In this story, Nordmann says, “two youths, two horses, and two lilies mirror each other and yet, in a fairy-tale sense, are “literally” one.” In another case of two being one, he says that “the definite article points to Goethe’s Märchen, which revolves around a lily and a youth who are in many ways one.”
