Wittgenstein on truth: Some remarks on Paragraphs 134–137 of Philosophical Investigations

The main aim of this text is to explicate what paragraphs 134–137 of Philosophical Investigations say about truth. I start, however, with a discussion of the remarks on truth contained in the Tractatus because the thoughts expressed in the former should be read in the context of the thoughts expressed in the latter. According to my interpretation of paragraphs 134–137 of the Investigations , Wittgenstein aims to show that the relationship between the concept of truth and the concept of a proposition may consist in the fact that truth and falsity, in certain language games, are constitutive elements of what a proposition is, but it must be added that these concepts cannot be comprehended independently from each other. I also come to the conclusion that in his opinion the concept of truth is expressed in various ways in our language, it being conveyed by such expressions as “… is true” and “this is how things are: …,” and that this shows that while asserting that something is true one can emphasize, on the one hand, that it is a proposition that says that things are a certain way, and on the other, just the fact that things are thus and so .


Introduction
Wittgenstein made relatively few direct remarks on the concept of truth, but this does not mean that the problem of truth is merely a peripheral issue in the context of his philosophy: On the contrary, it is related to the question of the nature of propositions, which lies at the heart of both his earlier and later approaches.
In the present text, I would like to limit myself to discussing what paragraphs 134-137 of Philosophical Investigations have to say about truth.Nevertheless, it is almost impossible to interpret these parts of the text properly without invoking thoughts expressed in Wittgenstein's earlier writings.This is because-as he himself points out in the Preface to the Investigations-the remarks contained there should be read in the context of those contained in the Tractatus: Four years ago, however, I had occasion to reread my first book (the Tractatus Logico-Philosophicus) and to explain its ideas.Then it suddenly seemed to me that I should publish those old ideas and the new ones together: that the latter could be seen in the right light only by contrast with and against the background of my older way of thinking.(Wittgenstein, 2009, p. 4) For this reason, I begin with a short presentation of Wittgenstein's approach to truth as contained in the Tractatus, before turning to a discussion of § § 134-137 of the Investigations.My considerations regarding these paragraphs lead me to a number of conclusions.The first of these is that Wittgenstein formulates neither a theory, nor a definition of truth.The second is that he aims to show what relations hold between the concept of truth and the concept of a proposition.The third is that the relationship between these two concepts may consist, inter alia, in the fact that truth and falsity, in certain language games, are constitutive elements of what a proposition is, but it must be added that these concepts (truth, proposition) cannot be comprehended independently from each other.Finally, my fourth conclusion is that the concept of truth is expressed in various ways in our language, it being conveyed, inter alia, by such expressions as "… is true" and "this is how things are: …," and that this shows that while asserting that something is true one can emphasize, on the one hand, that it is a proposition that says that things are a certain way, and on the other, just the fact that things are thus and so.I end my text with considerations on three further issues: the question of how Wittgenstein approaches the problem of truth-bearers, the question of whether he ought to be considered an adherent of the redundancy conception of truth, and the question of what is new in the approach to truth contained in the Investigations compared to that contained in the Tractatus.

the tractatus on truth
In the Tractatus, Wittgenstein offers, inter alia, the following remarks on the subject of truth: […] The verb of the proposition is not "is true" or "is false"-as Frege thought-but that which "is true" must already contain the verb.(Wittgenstein, 1922, 4.063) […] One could e.g., believe that the words "true" and "false" signify two properties among other properties, and then it would appear as a remarkable fact that every proposition possesses one of these properties.This now by no means appears self-evident, no more so than the proposition "All roses are either yellow or red" would sound even if it were true.Indeed our proposition now gets quite the character of a proposition of natural science and this is a certain symptom of its being falsely understood.(Wittgenstein, 1922, 6.111)A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions.(Wittgenstein, 1922, 4.4) Before I present the thoughts expressed in the quotes above that I take to be most essential for the present discussion, I wish to make an important terminological remark.The English word "proposition" in the translation of the Tractatus corresponds to the German word "Satz" as used in the book's original version.Of course, this German word can be translated variously in different contexts, but it must be emphasized that, basically, the word "Satz" refers to a linguistic entity, not an abstract object such as is expressed by or through a sentence.So, this German word could be appropriately rendered in English by the term "sentence" in many contexts.Moreover, the elucidations in the Tractatus clearly show that Wittgenstein uses the word "Sätze" to refer to meaningful sentences (cf. 3.11, 3.12, 3.141, 4.001).1 Here, I wish to point out that these terminological findings also apply to the use of the word "Satz" in the Investigations: it is used in a way that denotes a meaningful sentence.So, the word "proposition" in the English translation of the Investigations should not be understood as referring to a certain abstract object that is expressed by some sentences.In this text, I also employ the word "proposition" to designate a meaningful sentence, and for this reason the words "proposition" and "sentence" are used interchangeably in many contexts below.
Wittgenstein's statement in the Tractatus that the verb of the proposition is not "is true," and that the verb must already be contained in that which is true, says that the concept of truth applies only to such things as already contain predicates.It may also be interpreted as suggesting that, in fact, the expression "is true" does not play the role of a predicate that is predicated of propositions.In my opinion, both of these points lead to the conclusion that, according to Wittgenstein, the logical form of such propositions as "John's statement is true" should not be represented by the scheme "S is P" ("P(s)").It is also compatible with Wittgenstein's conviction that propositions do not name states of affairs, but describe them (cf.Wittgenstein, 1922Wittgenstein, , 3.1432, 3.144;, 3.144;Diamond, 2002).
The main idea expressed in the second quotation above is negative in character: Wittgenstein wishes to deny that truth and falsity are just certain properties among other properties.That approach to truth and falsity-the one he is criticizing-treats the statement that every proposition is either true or false as if it were itself a statement belonging to the natural sciences, and this in turn shows that the approach must be confused.
Proposition 4.4 says that every proposition "is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions" (Wittgenstein 1922).This, in turn, implies that every proposition can be represented by a truth-table, and truth-tables-as is commonly known-are composed of, inter alia, the signs "T" and "F," which have the same meaning as the words "true" and "false" (cf.Diamond 2003).So, the concepts of truth and falsity are constitutive for the concept of a proposition: One cannot comprehend what a proposition is if one does not grasp the concepts of truth and falsity.At the same time, it seems that the converse also holds: the concepts of truth and falsity cannot be grasped independently of the concept of a proposition.According to Wittgenstein, the signs which express these concepts do not stand for any objects: It is clear that to the complex of the signs F and T no object (or complex of objects) corresponds; any more than to horizontal and vertical lines or to brackets.There are no logical objects.(Wittgenstein, 1922, 4.441) This remark suggests that the concept of a proposition cannot be defined in terms of the concepts of truth and falsity, although grasping the latter is essential if we are to grasp the former.If truth and falsity were objects of any kind, they could be-in some sense-independent of any proposition, and for that reason their names could be used in a definition of the concept of a proposition; but, of course, they are not objects, and the concept of a proposition cannot be defined in that way. 2 2 Many commentators have interpreted the remarks on truth contained in the Tractatus as expressing a correspondence conception of truth (Black, 1964, p. 90;Hacker, 1981, p. 100;Hacker, 1986, p. 119;Stenius, 1981, p. 117).It should be added, however, that Hacker later changed his point of view on this issue: "But if we construe correspondence theories of truth as holding that being true is a relational property of sentences or propositions, then, despite these affinities, the Tractatus does not propound a correspondence theory of truth" (Baker & Hacker, 2005, p. 352).According to Glock, in the Tractatus Wittgenstein adopts a position similar in some respects to the correspondence conception of truth.This position is called the obtainment theory of truth and is characterized as follows: "The obtainment theory can be seen as a synthesis of correspondence, semantic and deflationary theories.It does justice to the idea that whether a sentence is true depends solely on what is the case.And it combines a ... semantic explanation of the relation between a sentence and what it ... says with a ... deflationary account of the agreement between what the sentence says and what ... is the case if it is true" (Glock, 2006, p. 347).However, in my opinion, the above-considered propositions from the Tractatus and the following remark from the Notebooks "'p' is true, says nothing else but p" (Wittgenstein, 1979, p. 9) should not be interpreted as an expression of a certain theory of truth, because as Wittgenstein himself points out in the Tractatus, "Philosophy is not a theory but an activity.… The result of philosophy is not a number of philosophical propositions" (1922, 4.112).
How Should We read the Sentence "'p' is true = p"?Now I shall turn to § § 134-137 of Philosophical Investigations.I would like to begin my discussion of Wittgenstein's remarks on truth contained therein by pointing out that the main topic of this part of the Investigations is the question of the general form of the proposition.In these paragraphs, Wittgenstein is mainly concerned with criticism of his earlier (Tractarian) views on the general form of the proposition.So, it would be a mistake to treat his remarks on truth contained in § § 134-137 of the Investigations as an attempt to explain this concept in terms of the concept of a proposition.Thus, commentators who claim-contra Horwich's suggestions (cf.Horwich, 2012, p. 110)-that in these paragraphs Wittgenstein is not aiming to explain the concept of truth in terms of the previously defined concept of a proposition are right (cf.Bronzo, 2019, McFarland, 2020, Vision, 2005).Of course, that does not mean that paragraphs 134-137 are not written with the intention of elucidating the concept of truth in some way, and that this aim is not achieved at all in these paragraphs.
Having explained what the main topic of § § 134-137 is, I now wish to turn to the most frequently discussed part of the text of these paragraphs: 'p' is true = p 'p' is false = not-p.(Wittgenstein 2009: § 136) The remark quoted here is a commentary on the statement that the sentence "a proposition is whatever can be true or false" (Wittgenstein, 2009, § 136) is equivalent to the following Tractarian formulation of the general form of the proposition (Wittgenstein, 1922, 4.5): "Such and such is the case" ("Es verhält sich so und so"). 3Wittgenstein formulates this remark with the aim of elucidating the meaning of the expressions "is true" and "is false," but, of course, does not assume that the concept of a proposition is independent of the concepts of truth and falsity.In my view, to properly understand the meaning of this remark two issues need to be addressed: the role played by the sign "=" in this part of the Investigations, and the question of how expressions corresponding to sentences enclosed in quotation marks should be understood.
It might seem that, in the scheme presented above, "=" is actually playing the role of a sign for equivalence (cf.Vision, 2005).Given that "'p' is true" is the scheme for a proposition, and "p" is a propositional variable, it seems natural to construe the sign which joins the former with the latter this way.However, in my opinion, this natural and, indeed, almost irresistible interpretation is mistaken.Firstly, it should be noted that, in his late writings, Wittgenstein uses not only a certain sign for identity, but also a certain sign for equivalence: for example, in Remarks on the Foundations of Mathematics (1991, pp. 178, 396).This puts into question the thesis that it is obvious that, in § 136, he is using the sign "=" to express equivalence.Secondly, in Philosophical Grammar, Wittgenstein calls the formula "~~p = p" a rule of grammar (1978, p. 89), whereas in Remarks on the Foundations of Mathematics he calls a similar formula a proposition-this being the formula "~~p ≡ p," which differs from the former in that it contains a sign for equivalence instead of one for identity (1991, p. 178).This shows, in my opinion, that Wittgenstein's use of a sign for identity between expressions that are schemas of propositions, not names, is not accidental.Thirdly, the following part of the text of Remarks on the Foundations of Mathematics shows that the schema under consideration does not so much express some true equivalence as elucidate the meaning of the expression "is true": For what does a proposition's 'being true' mean?'p' is true = p.(That is the answer) (Wittgenstein, 1991, p. 117 (Appendix III, § 6)) Based on these three arguments, the following interpretative hypothesis can be formulated: The scheme "'p' is true = p" is a grammatical remark which expresses a grammatical rule, and the use of the sign "=" shows that instead of asserting that "p" is true one can simply assert that p, because both statements assert the same thing (cf.Wittgenstein, 2001, p. 106). 4 Let us now turn to our second question, namely, that of how expressions corresponding to sentences enclosed in quotation marks should be understood (this issue is considered by Baker & Hacker, 2005, Bartunek, 2019, and Vision, 2005).Of course, one cannot consider this one outside of the context in which it can be posed.For example, in case of the proposition "The sentence 'Paris is bigger than Rome' is italicized," it is clear that enclosing the sentence in quotation marks serves to refer to a particular token of the sentential type "Paris is bigger than Rome," and that this particular token is being treated merely as an inscription of a certain shape, whereas in the case of the proposition "The sentence 'You are my Sun' is not an especially original metaphor," this serves to represent a certain meaningful English sentence, and not to refer to a certain inscription.So, one has to consider what role quotation marks play in the scheme "p" is true = p.Indeed, Wittgenstein addresses this issue explicitly in Philosophical Grammar: So is it correct to write "'p' is true," "'p' is false"; mustn't it be "p is true" (or false)?The ink mark is after all not true; in the way in which it's black and curved.Does "'p' is true" state anything about the sign "p" then?... It can also be put thus: The proposition "'p' is true" can only be understood if one understands the grammar of the sign "p" as a propositional sign; not if "p" is simply the name of the shape of a particular ink mark.In the end one can say that the quotation marks in the sentence "'p' is true" are simply superfluous.(Wittgenstein, 1978, pp. 123-124) He is claiming that the quotation marks in sentences of the form "'p' is true" do not serve to form the name of a sentence understood merely as an inscription.In the sentence "'Paris is bigger than Rome' is true," the expression "'Paris is bigger than Rome'" does not just refer to an inscription; rather, it represents a meaningful sentence.Moreover, Wittgenstein adds that the quotation marks in sentences of this type are, in the end, dispensable.This last remark does not appear in the Investigations.Why not?I think that the main reason is that such expressions as "Paris is bigger than Rome is true" are not-as Baker and Hacker (2005, p. 347) emphasize-grammatically correct.In the Investigations, Wittgenstein (2009, § 195, § 197) the propositional variable enclosed in quotation marks.So, the scheme would have the following form: p is true = p.recognizes that our ordinary ways of speaking are in perfect order, even if they sometimes suggest to us misleading interpretations of them.According to him, it is basically not the task of philosophy to reform language-that is, to introduce such a way of speaking, such a notation, as would be less vulnerable to misinterpretation, but rather to understand how we in fact use our language.Thus, in the case under consideration here, the point is not to substitute the sentence "'Paris is bigger than Rome' is true" with a certain artificial-sounding expression-for example, with the expression "Paris is bigger than Rome is true," which might not then suggest that when one asserts that it is true that something is the case one is ascribing the property of being true to some object.The point is to see that the use of our original formulation-namely, "'Paris is bigger than Rome' is true"-differs in principle5 from the standard use of sentences of the form "S is P," because the expression "'Paris is bigger than Rome'," which is a constituent of this expression, does not function in this case as the name of some object, and the expression "is true" does not in fact refer to some property or other.The fact that this is so can be shown by invoking the grammatical rule contained in paragraph 136: i.e., the schema "'p' is true = p."If by means of a proposition of the form "'p' is true" one states the same as one does by means of a proposition of the form "p," then the use of the former does not presuppose that in such a case the sentence enclosed in quotation marks is referring to some object, or that the property of being true is being ascribed to this object.However, in order to better understand what the difference between the use of sentences of the form "'p' is true" and a standard use of sentences of the form "S is P" consists in, we need to discuss the remarks subsequently contained in § § 136-137 of the Investigations.

How Does the Concept of truth relate to the Concept of a Proposition?
In § 136 of the Investigations, Wittgenstein contrasts two ways of relating concepts to each other.On the one hand, a given concept can fit another one, and on the other hand, it can belong to another one.According to the author of the Investigations, the use of the expressions "is true" and "is false" may be constitutive for some language-games in which we form propositions-that is, the use of these expressions belongs to the concept of a proposition expressed in these games, rather than merely fitting it: And what a proposition is, is in one sense determined by the rules of sentence formation (in English, for example), and in another sense by the use of the sign in the language-game.And the use of the words "true" and "false" may also be a constituent part of this game; and we treat it as belonging to our concept 'proposition', but it doesn't 'fit' it.(Wittgenstein, 2009, § 136) How, then, should we understand the two pictures to which Wittgenstein appeals in this part of his text: i.e., the picture of fitting and the picture of belonging?My own view is that two concepts fit each other, but one does not belong to the other, when their ranges are not necessarily related.For example, the concept of redness fits the concept of a rose because some roses are red, but they do not have to be red or not red.The same goes for the concepts of a cat and a being living on Earth: They fit each other because even though all cats live on Earth, there might have been some that did not live there.By contrast, those included in the pairs proposition and truth, rule and agreement, and integer and parity are such that grasping one of the relevant pair requires that we grasp the other.(In the case of some pairs of this sort, the converse relationship also holds.)Wittgenstein says, of concepts that are related in this way, that one belongs to the other.Someone who does not grasp the concept of truth will also not grasp the concept of a proposition, and someone who does not understand the concept of a proposition will also not understand the concept of truth.Likewise, a person who does not grasp the concept of agreement will not grasp the concept of a rule.In the case of two concepts that merely fit each other, grasping one of these concepts is not necessary for understanding the other one.One can possess the concept of a rose without being in possession of the concept of redness, and vice versa.
So in what way should we seek to elucidate the sense of Wittgenstein's statement that the use of the words "true" and "false" belongs to our concept of a proposition?6One way of explaining what the belonging of the use of these words to the concept of a proposition consists in has already been presented above.According to the Tractatus, every proposition can be written in the form of a truth-table; and truth-tables are composed of the symbols "T" and "F," which have the same meaning as the words "true" and "false" (1922, 4.31).Thus, when it comes to expressing propositions in such a notation, the use of these words belongs in a quite literal way to the concept of a proposition.However, some light is shed on what the belonging of the use of the words "true" and "false" to the concept of a proposition consists in by, above all, the following remark from the Investigations: And to say that a proposition is whatever can be true or false amounts to saying: We call something a proposition if in our language we apply the calculus of truth functions to it.(Wittgenstein, 2009, § 136) In this part of the text, Wittgenstein expresses the thought that propositions are something to which we apply truth functions.As is well known, truth functions are those functions whose arguments and values are the truth-values truth and falsity.This elucidation of the concept of a proposition shows that the latter presupposes the concepts of truth and falsity, and-in that sensethe use of the words "true" and "false" belongs to the concept of a proposition.That is, in order to understand any complex proposition, one has to know how its truth-value depends on the truth-values of its components, and in the case of elementary propositions, one has to know their truth conditions and, thereby, their conditions for being false.Of course, this should not be construed as Wittgenstein's claiming that the concept of a proposition can be fully explained in terms of the concepts of truth and falsity; his point is only that without understanding these concepts, one will not be able to grasp our concept of a proposition (cf.Bronzo, 2019).
the Grammar of the Expression "Is true" In § 137 of the Investigations, Wittgenstein qualifies his statement according to which the use of the words "true" and "false" belongs to, but does not fit, the concept of a proposition.He points out that, in some sense, one can recognize that the use of these words fits propositions.He explains what this kind of fitting amounts to as follows: In that sense "true" and "false" could be said to fit propositions; and a child might be taught to distinguish propositions from other expressions by being told "Ask yourself if you can say 'is true' after it.If these words fit, it's a proposition."(And in the same way one might have said: Ask yourself if you can put the words "This is how things are:" in front of it.)(Wittgenstein, 2009, § 137) The fit he is talking about in this remark consists simply in the fact that if the words "is true" can be said after uttering some expression, these words fit this expression and, in that case, this expression is a proposition.In other words, the expression "is true" fits propositions because if one concatenates any proposition enclosed in quotation marks with this expression, one will obtain a meaningful whole. 7he quoted excerpt from § 137 is also important as regards the main topic of our discussion for another reason.In this part of his text, Wittgenstein considers two expressions, "is true" and "This is how things are:" and points out that they play a similar role in our language.The possibility of concatenating them with a given expression shows that this expression is a proposition.Of course, there are some differences between their uses.The former can be placed after a proposition; moreover, for Wittgenstein as it seems, it can be put after a proposition that is enclosed in quotation marks.Meanwhile the latter, "This is how things are:" can be put before a proposition, and-in addition-before a proposition which is not enclosed in quotation marks.These expressions differ also in the following respect: that from the point of view of ordinary grammar, the former is a predicate, but the latter not.If we take into account the division of expressions into syntactic categories, we can characterize the former as a sentence-forming functor with a name as its argument, and the latter as one with a sentence as its argument.It should also be added that the latter is used as an operator, and plays a similar role to the expression "it is true that." In order to better understand the differences between the uses of the expressions "is true," "This is how things are:" and "it is true that," it is worth recalling again the following remark from the Investigations: And to say that a proposition is whatever can be true or false amounts to saying: We call something a proposition if in our language we apply the calculus of truth functions to it.(Wittgenstein, 2009, § 136) One can say that when we utter a proposition of the form "'p' is true," we assert that, in this case, the calculus of truth functions is applied to an expression of the form "p" in the following way: The sign "T" occurring in this truth-table is the truth-connective "it is true that."By contrast, when we utter a proposition of the form "This is how things are: p," we are simply applying the calculus of truth functions to an expression of the form "p" in the way presented above.This difference in use might be recognized as fundamental, were it not for the fact that Wittgenstein emphasizes that "[t]he proposition "'p' is true" can only be understood if one understands the grammar of the sign "p" as a propositional sign" (Wittgenstein, 1978, pp. 123-124).Thus, when we use a proposition of the form "'p' is true," we are not only asserting that, in this case, the calculus of truth functions is applied to an expression of the form "p" in that way, but are also simply applying the calculus of truth functions to an expression of this form in that way; the fact that Wittgenstein recognizes the schema "'p' is true = p" as a rule of grammar shows that from his point of view it is an adequate interpretation of the role played in our language by propositions of the form "'p' is true."So, if one accepts Wittgenstein's point of view on the sense of propositions of the form "'p' is true," then the differences in use of the expressions "is true," "this is how things are:" and "it is true that" can be interpreted as resulting from this: that propositions having the forms "'p' is true," "This is how things are: p," and "It is true that p" merely emphasize different facets of the same underlying fact-this being that it is true that p-and not from their saying anything fundamentally different from one another.Statements of the first type emphasize, first of all, that we are in the business of asserting how things are by means of propositions, whereas statements of the second and third types stress the idea that when we say that it is true that things are thus and so, we are saying how things are.
Even so, the fact that different aspects can be emphasized by propositions of those kinds does not mean that, for Wittgenstein, the uses of, for example, the following propositions fundamentally differ from one another: 1. "'Paris is bigger than Rome' is true." 2. "This is how things are: Paris is bigger than Rome." 3. "It is true that Paris is bigger than Rome."It must therefore be acknowledged that the grammatical differences indicated above are not of any fundamental significance. 8It turns out that, in some contexts, the concept of truth is expressed by an expression that looks like a predicate-i.e., by the expression "is true"-but which is in fact being used in a different way from ordinary predicates.Since, as I have already pointed out, the use of this expression is similar to the use of the expressions "this is how things are:" and "it is true that," one can say that from the point of view of grammar in Wittgenstein's sense of the term, it plays the role of an operator, even though it looks like a predicate.This means that it is not an expression of the kind that we use to ascribe some property to something, and hence that truth is not a property; its use consists in the fact that the result of its being applied to any given proposition is a proposition having the same content as the original proposition.9It is worth emphasizing here that one of the most important ideas of both Wittgenstein's early and his late philosophy is the conviction that the external similarity of various expressions may hide essential differences in their use: Of course, what confuses us is the uniform appearance of words when we hear them in speech, or see them written or in print.For their use is not that obvious.Especially when we are doing philosophy!(Wittgenstein, 2009, § 11) Applying this general observation to the issue under discussion here leads to the conclusion that the external similarity of the expression "is true" to ordinary predicates in no way entails that it need actually play the role of a predicate.As Wittgenstein points out, its use differs fundamentally from the use of ordinary predicates (cf.Diamond, 2003).
a Wittgensteinian Perspective on the Problem of truth-Bearers and the redundancy Conception of truth The considerations above regarding Wittgenstein's remarks on truth raise two further issues: firstly, the question of how Wittgenstein approaches the problem of truth-bearers, and secondly, that of whether he ought to be considered an adherent of the redundancy conception of truth.(The second issue is discussed by several commentators (see Baker & Hacker, 2005, Bartunek, 2019, Diamond, 2003, Horwich, 2016, McFarland, 2020, Vision, 2005)).
My attempt to answer these issues will, in a way, be tantamount to giving a summary of my preferred interpretation of paragraphs 134-137 of Philosophical Investigations.
The issue of so-called "truth-bearers" is often treated as one of the most important problems connected with the concept of truth (Künne, 2003, pp. 15-16).Put very briefly, it is about what kind of entities the property of being true should be attributed to.Some philosophers argue that the property of being true belongs to propositions (Horwich, 1990, Künne, 2003), others that it belongs to statements (cf.Strawson, 1971), while still other ones claim that it belongs to sentences (cf.Quine, 1986, pp. 10-12, Tarski, 1944), and yet still others claim that it belongs to ordered triples of sentences, times, and persons (see Davidson, 1967).It is noteworthy that the proponents of all these solutions make a common assumption to the effect that truth is a property.The source of this assumption is, ostensibly, the fact that the external form of many statements asserting that it is true that things are thus and so has the form "S is P"-i.e., that of a subject-predicate sentence-and on this basis it is concluded that their mode of employment is not fundamentally different from that of other subject-predicate sentences, which are used to ascribe properties to objects.
In my opinion, it is this very assumption that is problematic for Wittgenstein.At the same time, it should be emphasized that it would be a mistake to formulate his objections to it as amounting to the claim that the property of being true does not exist.To properly understand the essential point of his concerns and reservations, it can be helpful to recall those remarks in which he seeks to explain the real nature of his criticisms of various philosophical claims and positions: If I speak of a fiction, then it is of a grammatical fiction.(Wittgenstein, 2009, § 307) The decisive movement in the conjuring trick has been made, and it was the very one that seemed to us quite innocent.(Wittgenstein, 2009, § 308) The object of Wittgenstein's criticism being considered in these comments is a certain sort of grammatical fiction that consists in misunderstanding the grammar of those propositions that say something is true.The fiction consists in construing the use of those sentences as substantially similar to the use of other subject-predicate sentences.It is treating propositions of the form "'p' is true" in this manner that is "[t]he decisive movement in the conjuring trick," and this movement seems quite innocent to us.So what does Wittgenstein's rejection of this grammatical fiction really signify?As I have already said, it does not amount to the claim that the property of being true does not exist.Rather, it should be expressed in the following terms: The expression "is true" is not being used as a genuine predicate, and for this reason the question "To what property does this expression refer to?" has no sense.
What, then, are the consequences for the problem of so-called "truthbearers" of rejecting this assumption?In my judgement, there are two possible alternatives when the assumption is to be dispensed with.Where the first of these is concerned, it needs to be demonstrated that the question "To what kind of entities should the property of being true be attributed?" is meaningless.As to the second, the problem of truth-bearers somehow needs to be reformulated.That this question is meaningless can be easily seen if one realizes that while the expression "is true" is, from the point of view of standard grammar, a predicate, it is used rather as an operator than as an ordinary predicate.This interpretation of Wittgenstein's approach to the problem of truth-bearers is supported by the following quotation: The words "true" and "false" are two words on which philosophy has turned, and it is very important to see that philosophy always turns upon nonsensical questions.(Wittgenstein, 2001, p. 106) Could the issue of truth-bearers be formulated in some other way, so that it would make sense?In my opinion, the answer is "yes," and the reformulated question might run something like this: By what means do we assert (or express) the truth?In principle, the truth is asserted (or expressed) by means of meaningful sentences, i.e., propositions, although in some cases it is asserted (or expressed) by means of such expressions as, for example, "yes" and "no."Thus, the solution to the problem of truth-bearers so construed turns out to be quite trivial, and this fact is in line with Wittgenstein's remark that "[i]f someone were to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them" (Wittgenstein, 2009, § 128).
I shall now turn to the second question to be addressed here, i.e., that of whether we should regard Wittgenstein as an adherent of the redundancy conception of truth.To put the matter briefly, according to the latter conception the concept of truth is redundant and, in fact, does not play any vital role at all when it comes to understanding our language.10This is often explained in the following terms: All sentences with the expressions "is true" and "it is true that" can be substituted-without any loss of sense-with sentences in which these expressions do not occur.Wittgenstein, as it seems, does not endorse the first statement, which says that the concept of truth is redundant (cf.Diamond, 2003), but he does-seemingly paradoxicallyagree with the second, to the effect that one can do away with the phrases "is true" and "it is true that" altogether.The fact that he agrees with the latter is evidenced by the following passages: 'p' is true = p 'p' is false = not-p.(Wittgenstein, 2009, § 136) For what does a proposition's 'being true' mean?'p' is true = p.(That is the answer) (Wittgenstein, 1991, p. 117 (Appendix III, § 6)) Discussion of these words is made easier once it is realized that the words "true" and "false" can be done away with altogether.Instead of saying "p is true" we shall say "p," and instead of "p is false" we shall say, "not-p."(Wittgenstein, 2001, p. 106) What the above quotations clearly show is that, for Wittgenstein, the phrase "is true" can be eliminated from our language without diminishing the latter's expressive resources.This does not mean, however, that he views the concept of truth as redundant, or as not playing any significant role in our language.This more nuanced interpretation of Wittgenstein's approach to the concept of truth is well supported by the following passages: And the use of the words "true" and "false" may also be a constituent part of this game; and we treat it as belonging to our concept 'proposition,' but it doesn't 'fit'.(Wittgenstein, 2009, § 136) That is, instead of the notions of truth and falsity, we use proposition and negation.That we can do this is a useful hint, but it does do away with the puzzles connected with truth and falsity.* Wittgenstein recognizes, firstly, that the use of the words "true" and "false" belongs to the concept of a proposition, such that it is impossible to fully explain what a proposition is without invoking the concepts of truth and falsity. 11Secondly, in his view the fact that one can use the notions of truth and falsity instead of the notions of proposition and negation does not allow us to avoid "the puzzles connected with truth and falsity."And finally, thirdly, Wittgenstein points out that a kind of reverse operation can be performed.That is to say, instead of using the notions of negation, conjunction, etc., one can use just the notions of truth and falsity. 12On the basis of these three points it must be concluded, I think, that according to Wittgenstein the concepts of truth and falsity cannot be explained in terms of a prior understanding of the notions of a proposition and its negation.Here, the expression "prior understanding" means no more and no less than such an understanding as does not itself refer to the concepts of truth and falsity (cf.Bronzo, 2019).In other words, for Wittgenstein, neither of the concepts from the pair consisting of that of a proposition and that of truth is more basic than the other-neither of these concepts is prior to the other one.
To sum up, if the redundancy conception of truth boils down to just the claims that (1) "'p' is true = p" is a rule of grammar in the Wittgensteinian sense of the term and (2) the phrase "is true" can be eliminated from our language without diminishing its means of expression, then Wittgenstein's remarks on truth may be considered to be in line with it.However, if this conception assumes that the concept of truth is actually redundant and can be fully explained in terms of some more basic concepts-for example, in terms of the concept of a proposition or the concept of the content of a proposition-then Wittgenstein's approach to truth cannot be so construed.
What Is the Difference between the Investigations' Approach to truth and that of the tractatus?
Is there any significant novelty in the remarks on truth in paragraphs 134-137 of the Investigations compared to the Tractatus' account of truth?The answer to this question is, "Yes."The main source of this novelty is a different approach to the issue of the general form of the proposition.According to the Tractatus, since the "[g]eneral form of proposition is: Such and such is the case" (Wittgenstein, 1922, 4.5), the concepts of truth and falsity belong to every proposition (cf.Wittgenstein, 1922, 6.111).On the other hand, Wittgenstein in the Investigations recognizes that the search for the general form of the proposition is completely futile (cf.2009, § 65), and that the concept of a proposition is a family-resemblance concept-"these phenomena have no one thing in common in virtue of which we use the same word for all-but there are many different kinds of affinity between them" (2009, § 65).Therefore, in the Investigations Wittgenstein does not claim that the concepts of truth and falsehood simply belong to the concept of a proposition, but he points out that in many cases when we use propositions, the use of the words "true" and "false" belong to the use of these propositions.Whether the use of these words belongs to propositions or not depends on what language-game we are playing.When we take into account such a game as that presented in § 8 of the Investigations, i.e., the game of giving orders like "fourth-slab-there," "this-there," we may be inclined to consider such utterances as propositions, but the concepts of truth and falsehood will not apply to the propositions belonging to this language-game.On the other hand, these concepts would undoubtedly be applied to the propositions belonging to the game which would consist in describing the activities of the participants of the above-mentioned language-game; these concepts can also be applied to the propositions belonging to the game presented in § 48 of the Investigations.To sum up, since in the Investigations Wittgenstein rejects the explanation of the essence of a proposition in terms of its general form and points out that whether or not the concept of truth belongs to a given proposition depends on how that proposition is used in a given languagegame, he recognizes that to clarify the concepts of truth and proposition it is necessary to grasp the similarities and differences between those languagegames that include the use of the words "true" and "false" and those that do not.However, as I have already mentioned, the author of the Investigations agrees with the author of the Tractatus, that basically the concept of truth and the concept of a proposition are closely related.