A Referential Theory of Truth and Falsity

Ilhan Inan

• Publisher: Routledge
• Year: 2022
• ISBN:
  9781000580938
• Edition: 1
• Topic: Philosophie
• Subtopic: Langue en philosophie

This book proposes a novel theory of truth and falsity. It argues that truth is a form of reference and falsity is a form of reference failure.

Most of the philosophical literature on truth concentrates on certain ontological and epistemic problems. This book focuses instead on language. By utilizing the Fregean idea that sentences are singular referring expressions, the author develops novel connections between the philosophical study of truth and falsity and the huge literature in in the philosophy of language on the notion of reference. The first part of the book constructs the author's theory and argues for it in length. Part II addresses the ways in which the theory relates to, and is different from, some of the basic theories of truth. Part III takes up how to account for the truth of sentences with logical operators and quantifiers. Finally, Part IV discusses the applications and implications of the theory for longstanding problems in philosophy of language, metaphysics, and epistemology.

A Referential Theory of Truth and Falsity will appeal to researchers and advanced students working in philosophy of language, epistemology, metaphysics, and linguistics.

Part I The Referential Theory of Truth and Falsity

1 Introducing the Referential Theory

DOI: 10.4324/9781003165705-3

How could it be that the notion of truth, a notion we use daily with no difficulty, turns out to be so problematic? What aspect of language masks the deep grammar of this popular notion? I believe the answer lies within the way in which syntax evolved. With the rise of modern syntax there emerged a very basic unit of language that we now call a “declarative sentence” (henceforth “sentence” unless otherwise stated). Among all the meaningful expressions that we can construct in language, a sentence is the only linguistic entity whose utterance in a context allows us to say something that is true or false. Understanding what truth is, is to understand what a sentence is. That may sound like a trivial task, but it isn’t. What is a sentence? How and why did sentence become the very basic unit of language? What purpose did it serve in speech and thought? These are not questions that have straightforward answers. Simply saying that a sentence is a linguistic tool by which we make assertions is no progress. What is an assertion? An answer to this question will have to appeal to the notion of truth. What a sentence is, is an issue as problematic as the notion of truth itself, and one cannot give a philosophically satisfying explication of the notion of a sentence without having to appeal to the notion of truth. We, of course, know that a sentence is made up of meaningful parts that typically stand for things. We use names, demonstratives, and pronouns to refer to objects, we use general terms to refer to kinds, we use predicative terms to refer to actions, properties, and relations. Through our ability to construct such semantic units we succeed in thinking and talking about those entities. If parts of a sentence stand for things, then what does a sentence stand for? Is a sentence a referring expression? This is a mindboggling question. It appears that a normal adult who has mastered a language typically does not consider this question, the issue does not come up. It took a creative and innovative philosopher who constructed the most influential theory of language, namely Frege, to raise it, and once it was raised, we realized that we have no clear semantic intuitions about whether or not sentences are referring expressions. It is not easy to answer in the positive, for once you entertain the idea that a sentence is a linguistic device to make reference, a host of new problematic issues arise. What kind of entity could be the referent of a true sentence? What could be a suitable referent of a false sentence, if there is one? How about negative sentences, disjunctions, conditionals, existential statements, do they also have referents when they express truths? If a sentence is a referring expression, then it will turn out that it is a singular term, but why can it not occupy the subject position of a larger sentence? After meditating on these problems for a while, you may end up wanting to deny that a sentence is a referential device. You are then already buried in philosophical thinking. Our raw pre-philosophical semantic intuitions do not dictate anything on this issue. This is exactly where language hides one of its essential features. If it turns out that sentences are referential devices just like descriptions, then we have failed to see a very basic aspect of language that we have been using for thousands of years. I propose that some of the mysteries regarding the notion of truth lie here. It is our failure, despite Frege’s valuable effort, to come to realize that a sentence is a referring expression that has led to a mystification of the notion of truth. One reason why this Fregean idea did not find much support in the philosophical tradition is, I believe, due to Frege himself. After somewhat unconvincingly arguing that sentences are referring expressions, Frege claimed that the referent of a sentence must always be one of two peculiar objects that he named “the True” and “the False”. This is where his theory goes astray.¹ Once we deny that sentences refer to these weird objects, and search for an alternative, then a very simple and intuitive theory of truth and falsity will emerge. To what does a sentence that expresses a truth refer? What, for instance, is the referent of the sentence “the Earth is round”? Now one intuitive way to answer this question is to consider the referents of the logical parts of the sentence, and then apply the principle of compositionality to get to the referent of the whole sentence. The subject part of the sentence refers to the Earth, and the predicate part refers to the property of roundness. The whole sentence then refers to the entity that is composed of those parts: the Earth’s being round. Some may wish to call this a “fact”, others who find the ontology of facts problematic may use another name for it. Either way we should acknowledge that our use of language is deeply committed to the existence of such entities. It is common linguistic practice to use such phrases as referential devices in the subject position of a sentence, as, for instance, when one says, “the Earth’s being round is part of what causes day and night.” Whether one takes it as a fact or not, the Earth’s being round, whatever kind of entity it might be, is one that we normally consider to possess such causal powers. The descriptive phrase “the Earth’s being round” is nothing but a nominalization of the sentence “the Earth is round”. This, I believe, gives us the most plausible alternative to Frege’s theory of Truth: Every sentence in the simple subject/predicate form, a is F, when it expresses a truth, refers to a’s being F. Some may wish to call such an entity a “fact”; I will prefer to call it a “state” given some of the common connotations of the former term.

How about falsity? To what does a sentence expressing a falsity refer? What, for instance, is the referent of the sentence “the Earth is flat”? Again, by applying compositionality we may say that it refers to the Earth’s being flat. This time we have a problem. Though the term the Earth’s being round can occupy the subject position of a larger sentence that expresses a truth, the same is not the case for the Earth’s being flat. Any sentence that we construct which has this term in the subject position followed by a suitable first-order predicate will not express a truth, as for instance when one says “the Earth’s being flat will cause our ship to fall off its edge”. The reason is clear: The Earth is round, and given that it is, the sentence that expresses this truth refers to the Earth’s being round; the Earth is not flat, and given that it isn’t, the phrase the Earth’s being flat, purports to refer to the Earth’s being flat, but fails, since there is no such entity. This is similar to how we can succeed or fail in our attempt to refer to some object by a name. We may name an object, say “Neptune”, and then use the name to refer to it, but we may also attempt to name an object, say “Vulcan”, but fail, if there is no such object. Even when a name fails to refer, its semantic function is still to refer. Similarly, a sentence is a referring expression, regardless of whether it expresses a truth or falsity. When the sentence does in fact express a truth, it succeeds in referring, but when it expresses a falsity, it fails. This implies then that the notion of truth is a subspecies of our more general notion of reference, which in effect implies that the notion of falsity, is a subspecies of our more general notion of failure of reference. Such a view has not been very popular among philosophers. One reason for this, of course, is the reluctance of philosophers to take sentences as referential devices. Interestingly, however, even those who have accepted this Fregean dictum have not explored the idea that truth is a form of reference. This may have to do with a prejudice concerning falsity. Those who have held that sentences are referring expressions thought that not just sentences that express truths, but those which express falsehoods, must also have referents. On Frege’s theory, for instance, a sentence having a referent is independent of its being true or false; either way we get a referent, but a different one.² Alternatively one may take a sentence to refer to a proposition, in which case the referent to a sentence will be the same independent of its being truth or false.³ Another option can be found in Barwise and Perry (1983), who have developed a theory of semantics based on the idea that sentences refer to situations whether they express truths or not. None of these views are compatible with the idea that truth is a form of reference. That is because in all these theories a sentence having a referent does not imply that it expresses a truth, and that is exactly what you need in order to show that truth is a form of reference. At the time when fact ontology was popular in the early 20th century we see the first hints of the idea that a true sentence refers to a fact.⁴ This, of course, brings about the obvious question of what a false sentence refers to. From the identity theory one can get to the thesis that a sentence refers to a proposition either way, but only when that proposition is true is it identical with a fact.⁵

An alternative account of falsity can be derived from some versions of the correspondence theory, viz., that a sentence that expresses a falsehood refers to a possible state of affairs that is not actualized. This, of course, runs into the problem of how to account for sentences that express propositions that are necessarily false. Do such sentences simply lack referents? Or do they refer to impossible states of affairs? Putting aside these problematic ontological issues, none of these views are compatible with the dictum that truth is a form of reference. We need to do away with the prejudice that a sentence that expresses a falsity must also have a referent. Interestingly, this very simple account of falsity, to my knowledge, has never been explored. Even if a truth-theorist ends up rejecting such a theory of falsity, one would expect them to at least address it explicitly and refute it by argument. My diagnosis of the lack of discussion of such a theory of falsity is that the literature on the topic concentrates so much on truth that it neglects falsity. Of course, we all care to know what truth is, and that may be taken to be the primary object of our inquiry. This, however, should not imply that philosophizing about falsity is futile. This is not a good strategy for two reasons. First because to understand certain aspects of some object of inquiry, a good approach is to explore the conditions under which that thing is absent, and falsity is one way in which truth is absent. An analogous case concerns the concept of existence. It seems to me that what led Frege and Russell to discover that existence is a second-order predicate was the result of their efforts to try give an account of how we may deny the existence of something without falling into a contradiction. It may well be that understanding non-existence is the best path leading into an understanding of existence; if so, in order to understand what truth is, perhaps what we should do is to first understand what falsity is. It may be that only when you are convinced that falsity is a form of failure of reference would you become convinced that truth is a form of successful reference.

Perhaps an even more important reason why we should philosophize about falsity is because a theory of truth does not always entail a theory of falsity. It appears that philosophers are inclined to think that once we know everything about truth, then all there is to know about falsity should automatically follow. That is why despite the fact that there are so many theories of truth, we hardly come across something called “a theory of falsity”, and there are hundreds of books and thousands of articles containing the notion of “truth” in their title, but many fewer ones containing the notion of “falsity”. For some theories of truth it may not matter; that is, a theory of falsity can directly be derived from the theory of truth. But for others this may not be so. For instance, the Fregean view that a sentence is true just in case it refers to the True tells us nothing about falsity. One may construct radically different theories of falsity compatible with it. Frege offered one, but I shall argue later that Frege should have at least considered the idea that falsity may simply be failure of reference to the True. A much more controversial example is Deflationism: Does deflationism about truth imply deflationism about falsity? I shall later provide some reason why it doesn’t. There may be an asymmetry between the notions of truth and falsity in terms of their prudential use in language. I shall argue that in the early stages of the evolution of language the concept of falsity played a far more important role in our use of language than truth did.

A theory of falsity does not immediately fall onto our laps even for some versions of the correspondence theory of truth. The claim that a proposition is true just in case it corresponds to a fact, by itself, does not give us all we wish to know about falsity. Holding that a proposition is false just in case it does not correspond to a fact leaves it open whether it corresponds to something other than a fact. Furthermore, saying that it corresponds to nothing is not very illuminating unless we give an explanation of what that means. What is worse is that in some versions of the correspondence theory a false proposition also corresponds to a fact. Russell, for instance, held that not just a true proposition but the false proposition we get by negating it also corresponds to the very same fact.⁶ Things are not different when we replace the notion of correspondence with that of reference to get a referential theory of truth. The simple claim that a sentence that expresses a truth refers to a fact does not automatically tell us what falsity is. It by itself does not entail that falsity is failure of reference.⁷

A theory of truth may be called a referential theory if its primary thesis is that truth is a subspecies of the more general notion of reference. An essential component of such a theory will have to be that falsity is a subspecies of our more general notion of failure of reference. There could be a multitude of such theories; for instance, if we endorse one part of Frege’s theory and hold that all true sentences refer to the same entity, the True, but reject the other part and hold that all false sentences fail to refer, we would end up with a referential theory of truth. One could also replace this odd Fregean entity with something else, such as Davidson’s Great Fact, or the mereological sum of everything. On all such accounts it would follow that a sentence expresses a truth just in case it refers. Such referential theories of truth are different from the one that I advocate, since they are based on what I take to be a very counterintuitive idea that all true sentences are coreferential. The referential theory I discuss and argue for in this book is also based on the simple idea that truth is a form of reference, but it also commits itself to the view that a sentence that expresses a truth describes, specifies and individuates its unique referent. Here then is the referential theory expressed as the conjunction of the following five theses:

• Thesis of Sentential Reference: A declarative sentence occurrence (that is a sentence type that occurs in a certain context) is a singular referring expression.
• Referential Theory of Truth: Truth is a form of reference, i.e. a sentence occurrence is true just in case it uniquely refers.
• Referential Theory of Falsity: Falsity is a form of failure of reference, i.e. a sentence occurrence is false just in case it fails to refer.
• Coreferentiality Thesis for Sentences: A sentence occurrence is coreferential with its nominalization.
• State Theory of Sentential Reference: The referent of a true sentence occurrence is the unique state that is specified by the content of that sentence.

I should note from the very start that the referential theory does not attempt to define or provide a semantic analysis of our concepts of truth and falsity; rather it tries to explicate them in terms of our more general concept of reference. Truth and falsity are primitives, they do not call for semantic analysis. The thesis that truth is a form of reference should be approached with caution; what it says is that the concept of truth is a subspecies of our more general concept of reference when applied to sentences. If at the end of the day you are convinced that this is the case, you will have learned something new about the concept of truth as well as the concept of reference. For this to happen it need not be the case that you had a better understanding of the concept of reference to start off with. It may have been the other way around. To make an analogy, we have the concept of purple, and we have the concept of lavender, and both of them may be taken to be primitive color concepts, but even so, the concept of lavender is a subspecies of our more general concept of purple. If one has acquired these concepts but does not know that lavender is in fact a shade of purple, they will have learned something new when they are told that it is so. Whether they initially had a better understanding of the concept purple than they had of lavender, or vice versa, makes little difference, either way they will have learned something new. On the surface it appears that truth is a more popular concept than the concept of reference, and it may seem that ordinary users of language have a better understanding of truth than they have of reference. This may only be in appearance though, for even if the person on the street seldom makes use of the concept of reference by that name, they frequently make use of notions such as thinking about and talking about which are nothing but our ordinary ways of expressing the notion of reference in two of its varieties, namely speaker’s reference and mental reference. But even if the notion of reference is less well understood than the notion of truth, the referential theory could still give one a better understanding of both of them.

The Thesis of Sentential Reference acts as the basic presupposition of the referential theory. If you deny it, then the theory does not get off the ground, for all the remaining four theses presuppose it. This thesis does n...