Semantic theories have a role in the justification of systems of formal logic. Dummett holds that Frege used his work on sense and reference to justify his formal system in exactly the way that logicians today use what is explicitly described as a semantic explanation. Indeed, Dummett sees Frege's work as providing the foundations for all current work in semantics of natural language Dummett, a, Dummett does not just claim that Frege had a semantic theory; he claims that he had a realist semantic theory.
Dummett, Michael | Internet Encyclopedia of Philosophy
The semantic theory is realist because the prototype of a term's semantic value is the object designated by a name: Philosophy of Language , a, From Frege's perspective, if an expression lacks a semantic value, then that really is a failure: If a declarative sentence lacks a truth-value, that is because something has gone wrong: Dummett holds that it was an important turning point when Frege described a sentence as a proper name for a truth-value.
He thinks that, at this point, Frege lost sight of an important insight embodied in the context principle: Once a sentence is treated as just a proper name, and a truth-value as just another object, there is no acknowledgement that there is something special about the role of a sentence in language Dummett, a, Dummett is also unsatisfied by Frege's account of sense. We have seen that, for Frege, several people may grasp the sense of one word or of one thought, and that just as the sense of a name denotes an object, the sense of a thought denotes a truth-value.
But what is involved in grasping a sense? Frege's answer is that senses are neither part of the world of spatio-temporal objects, nor do they exist inside the minds of individuals. They belong to a "third realm", a timeless world, to which all of us have access. Dummett is far from endorsing the suggestion that thoughts occupy a third realm beyond time and space. He describes this doctrine as a piece of "ontological mythology", the term "mythology" here being used in a purely pejorative sense Dummett, a, Dummett thinks that these two loose ends should be tied together.
Rather than being content to describe the act of understanding as involving a mysterious connection between our minds and timeless entities known as senses, we should focus on the practice of using sentences in a language. This, in turn requires us to think about the purpose of classifying sentences as true or false, and that requires that we think about the purposes for which we use a language Dummett, a, The result of this process might be to vindicate Frege's semantics, or it might vindicate the intuitionist position. Dummett's most influential contribution to philosophy can be understood as an attempt to resolve this unfinished business.
Along with his historical work, Dummett is known for his on-going work on a grand metaphysical project. The aim of this project is to find a means of resolving a number of debates, each of which has a common form but a different subject matter. In each debate, there is a realist, and an anti-realist, and they differ concerning which logical principles they apply to statements of the type that are under dispute—as it may be, statements of arithmetic, statements about the past, about the future, about the physical world, about possible worlds, and so forth.
To decide in favor of anti-realism in one instance does not mean that one must always decide in favor of anti-realism, and the same is true for realism. Some of Dummett's papers deal with arguments that are quite specific to one particular debate—for example, he discusses the charge that anti-realism about the past is ultimately self-defeating, since what is now the present will be the past Dummett, "The Reality of the Past", in his , and he has advanced an argument about the nature of names for non-existent natural-kinds that is intended to undercut David Lewis's argument for the thesis that all possible worlds are real Dummett, "Could There Be Unicorns?
However, he is best known for advancing a generic line of argument that the anti-realist in any particular debate could appeal to. That does not mean that he thinks that the anti-realist will always be successful. In his valedictory lecture as Wykeham Professor of Logic, he stated:. I saw the matter, rather, as the posing of a question how far, and in what contexts, a certain generic line of argument could be pushed, where the answers 'No distance at all' and 'In no context at all' could not be credibly entertained, and the answers 'To the bitter end' and 'In all conceivable contexts' were almost as unlikely to be right.
Dummett's most complete statement of the nature of such metaphysical debates, and the means by which they can be resolved was The Logical Basis of Metaphysics Dummett, b. According to Dummett, to find out how to resolve metaphysical disputes, we must find out how to justify a logic—that is, a set of principles of inference.
Logic is the study of validity—an inference is valid if, and only if, the truth of the premises guarantees the truth of the conclusion. The logician wants to be able to recognize such truth-preserving inferences by their structure. More precision can be achieved by presenting inferences in a formal system Dummett, b, , and precision comes to be of vital importance when we are trying to choose between rival logical systems.
The logician wants to be able to recognize, from the structure of one set of sentences, that the members of another set of sentences are true. One method of validating rules of inference is by means of a semantic theory. In such a theory, every expression is assigned a semantic value, and an account is offered of how the semantic value of a complex expression is based upon the semantic value of its components.
The aim of the semantic theory is to explain how the parts of a sentence determine the truth-value of that sentence Dummett, b, , as was explained above. At this point, it may be helpful to focus upon a particular inference and a particular semantic theory. Suppose that we assign the following semantic values to symbols in the following way. P and Q stand for atomic sentences, which have either the value true , or the value false , and never both values. The symbol " x v y ", where x and y are replaced by symbols which stand for atomic sentences has the value true when at least one of those atomic sentences has the value true.
Otherwise, it has the value false. Next, we consider the following argument:. To validate this inference, we must show that if 1 and 2 are true, then the conclusion, P, must also be true. If 2 is true, then Q is false. If Q is false, then if 1 is true, it must be in virtue of the truth of P, since if both P and Q were false, 1 could not be true. So we must suppose that P is true, and that is what we were trying to demonstrate. In this case, the semantic theory used incorporated the principle of bivalence: For reasons explained in sections 2. There is no one simple alternative to the principle of bivalence.
One could depart from bivalence in virtue of having more than two truth-values, or in virtue of admitting that there are sentences without a truth-value, or in virtue of believing that we have no guarantee that all sentences will have one of the two values true or false. Just as there are many alternatives to bivalence, there are many alternatives to classical logic. Although Dummett's work on deduction has its roots in the debate over intuitionism, it does not necessarily follow that, in every case, the alternative logic advocated by a Dummett-style anti-realist would be intuitionistic logic.
The correct logical principles should become clear once the correct semantic theory is established. Of course, in this case, it probably was not necessary to offer a semantic theory in order to convince the reader of the validity of the inference. Indeed, the astute reader might well wonder whether such a procedure can serve to justify a logical law at all. Did we not invoke logical laws when explaining how the inference under discussion was justified? The answer is that we did—but this need not render the justification circular.
Dummett is clear that he is not trying to show how deductive practices could be justified to someone who is completely skeptical about the possibility of deduction; rather, he is considering how we might decide whether a particular rule of inference, which is accepted by some logicians but not by others, is justifiable. As long as no logical law that is under dispute is used in the semantic theory, it will be possible to offer a justification that does not beg the question. It is important to note that the set of logical laws that are used in the semantic theory need not be co-extensive with the set of logical laws that are justified thereby Dummett, b, Dummett devotes considerable attention to establishing a procedure that can be used to show that a law is beyond dispute, a procedure that he terms "third-grade proof-theoretic justification.
It is not possible to explain the procedure in full here, only to outline the basic principles on which the procedure is based. As we have seen, logic deals with our ability to recognize that one set of sentences implies that all the members of some other set of sentences are true, in virtue of the structure of the sentences. The task of a system of formal logic is to display the structure, or form, in virtue of which such inferences are possible.
Within such a system, the principal operator in a sentence indicates which other sentences may be derived from that sentence, possibly in conjunction with other sentences. As well as elimination rules, a logical constant also has introduction rules. Dummett is in agreement with Belnap's thesis is that if we can show, for some rule, that adding this rule to a language involves only a conservative extension, then we have a reason for supposing that the addition of this rule has been justified Dummett, b, The assumption that, when we have a sentence containing a logical constant, that sentence could have been derived using the introduction rule for the constant, is referred to by Dummett as "the fundamental assumption".
It is necessary to consider, for each logical constant whose introduction and elimination rules we wish to justify, whether the fundamental assumption is correct for it. Consider, for example, disjunction, " v "—that is, the logical constant which is more or less equivalent in meaning to "or". The standard introduction rule for disjunction is that, if one can assert P, one can assert "P v Q", and if one can assert Q, then one can assert "P v Q". To decide whether the fundamental assumption is true in this case, it is necessary to consider whether, if I see a child running across the street and say "A boy or a girl is running across the street," it is always true that I could have looked more closely, and been in a position to say either "A boy is running across the street," or "A girl is running across the street.
Even if we accept the fundamental assumption, not every alleged logical rule involves making merely a conservative extension to the language.
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Here, we are applying an elimination rule that does not involve a merely conservative extension of the language, because it could be that the truth of "Q" was not used in deriving either of the two conditional statements. The technical apparatus for examining whether adding some constant to the language involves a conservative or non-conservative extension is known as "proof-theory". It was pioneered by Gerhard Gentzen.
Dummett's third-grade proof theoretic justification builds on the work of Dag Prawitz. Dummett's requirements are, in fact, more stringent than that adding an operator to a language involve a merely conservative extension of the language, because it is necessary to take into account that two or more operators each of which, taken on its own, involves a conservative extension might, taken together, involve a non-conservative extension, Dummett, b, , but we cannot discuss all those details fully here.
It must be remembered that Dummett is not arguing that we should accept only those logical laws which can be justified by these means—rather, he is suggesting that these logical laws are the ones which can be taken for granted when trying to justify more controversial principles. Logical constants that are justified by third-grade proof-theoretic justification are above reproach.
Other logical constants may be justified, if at all, by a semantic theory. Proof-theoretic justification is not sufficient to settle disputes about logical laws: The set of logical laws that are justified by a semantic theory need not be the same as the set of logical laws that are appealed to in explaining that theory Dummett, b, So, we settle a debate about a logical law by offering a semantic theory—but that just pushes the problem back one stage further; we must still consider how to settle debates about rival semantic theories.
Dummett's answer is that just as a logic may be justified by a semantic theory, a semantic theory may, in turn be justified by being made the basis of a meaning-theory. A meaning-theory is an explanation of the skill that anyone who understands a language has. As language-users, we are faced, continually, with sentences that we have never before encountered.
- Trans-Canada Chronicle : A Bicycle Ride Pacific to Atlantic 4,400 miles.
- The Foundations of Arithmetic.
- CLEAR GREY SKIES.
- Michael Dummett (1925—2011).
- .
- A Year In Time;
It seems that there must be some set of rules of which we have implicit knowledge, which enable us to deduce the meaning of new sentences. Dummett is by no means alone in seeking for such a theory: One suggestion, which Davidson has advocated strongly, is that a meaning-theory would specify a set of rules from which we could derive, for any sentence, a knowledge of the conditions under which that sentence is true. The suggestion is that, if you know of some sentence of a foreign language that the sentence is true if the cat is on the mat, and false if the cat is not on the mat, then you know that the sentence in question means "The cat is on the mat.
Dummett endorses the proposal that this is the best suggestion currently on offer for constructing a meaning-theory Dummett, b, , and notes that such a theory must be built on foundations laid by Frege. However, he distinguishes between a strong and a weak sense in which truth can be the central notion of a meaning-theory.
In the strong sense, meaning is to be explained in terms of truth-conditions, as above, and it is simply taken for granted that we know what truth is. If truth is central to the meaning-theory only in the weak sense, then although knowledge of the meaning of a sentence is equated with knowledge of its truth-conditions, some further explanation is offered of what it is for a sentence to be true Dummett, b , For example, an intuitionist would say that to understand some mathematical formula, it is necessary to be able to distinguish between those mathematical constructions which do and those which do not constitute proofs of the formula in question: If truth is central to the meaning-theory in the strong sense, however, grasp of truth-conditions is not explained in terms of any more fundamental notion: The connection between a semantic theory and a meaning-theory should now be apparent.
Both the realist and the anti-realist offer semantic theories that explain how the semantic value of a sentence is determined by the semantic value of its parts. A meaning-theory of the type favored by Dummett will explain how, when we see what words are used in a sentence and the order in which they are put together, we are enabled to understand the truth-conditions for that sentence.
The realist, adhering to the principle of bivalence, supposes that all the sentences will be determinately true or false.
The anti-realist, on the other hand, can bring other notions into play to explain what it is for a sentence to be true. So, the logic is justified by a semantics; the semantics is justified by a meaning-theory. How is the meaning-theory to be justified? A meaning-theory is judged to be successful according to whether it provides us with a satisfactory explanation of what it is to understand a language.
It is important to note that Dummett requires that the meaning-theory provide us with a genuine explanation of what understanding is. He points out that while it is, no doubt, correct to say that someone understands the meaning of "Davidson has a toothache" if, and only if, they know that an utterance of this sentence is true if, and only if, Davidson has a toothache, this account fails to provide us with a non-circular explanation of what it is to understand the utterance.
We want to be told exactly what it is to know that such an utterance is true. Meaning-theories of this type are classified by Dummett as "modest", and he urges other philosophers to set about the harder task of providing more ambitious meaning-theories, meaning-theories that are, in his terminology, "full-blooded. We are now in a position to consider the "generic line of argument" that Dummett considers can be advanced by the anti-realist.
This argument makes use of the Wittgensteinian principle that meaning is use.
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Dummett takes this to mean that there can be no element in linguistic understanding that is not manifested in the way a word is used in practice. When we recognize that a sentence is true, we are manifesting that we have a certain ability—the ability to recognize that the sentence has been verified.
The same holds when we recognize that a sentence has been decisively refuted. According to an anti-realist meaning-theory in which justification is central , the ability to recognize when a sentence has been decisively confirmed or refuted is constitutive of knowing the meaning. Dummett terms this a justificationist semantics. According to the realist, knowledge of how a sentence may be confirmed or refuted is answerable to a prior knowledge of the meaning. Dummett is aware that the realist suggestion is far more intuitively compelling.
However, he argues that it may yet prove to be mistaken. He offers several arguments, of which I will summaries one. Suppose that realism is correct. In that case, our ability to agree about what things are yellow is dependent upon our shared understanding of what makes it true that something is yellow. It would therefore be possible that, tomorrow, everything which is yellow becomes orange and vice versa, and that, at the same time, we all undergo a collective psychological change, so that things which are really yellow now appear to us to be orange, and vice versa.
In other words, a major change would have taken place in reality, and yet none of us would notice it. Given that we had not altered the truth-conditions of sentences involving "yellow" and "orange", we would now be making many false utterances using these words. Yet this widespread falsity would pass entirely unnoticed; indeed, it would be entirely inconsequential. Our assertions would be fulfilling perfectly every purpose that they have, and yet would be false. If we admit this possibility, it seems incorrect to say, as Dummett thinks we should, that truth is the goal of our assertions.
Truth and falsity would have lost their connection with practice. Alternatively, one might argue that we would still be making true statements using "yellow" and "orange", but that the meanings of the words "yellow" and "orange" would have been altered. In that case, meaning has been altered, even though there is no observable difference in the practice, and so meaning has lost its connection with practice.
For the anti-realist, this possibility cannot arise, because there is no gap between what makes an assertion correct, and the most direct means that we have of checking that assertion. Dummett does allow that there will be indirect means of confirming a sentence, that is, methods for showing that, had we applied our most direct, or canonical method of verification, it would have been successful Dummett, b, It is by this type of argument that Dummett hopes to persuade us to rethink our attachment to realism.
Of course, he does not think that we will know whether to be a realist or an anti-realist about a specific subject matter until we have a well-worked out meaning-theory. He does not assert that in all cases the correct meaning-theory will be an anti-realist one.
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The fundamental difference between the two lies in the fact that, whereas a means of deciding a range of mathematical statements or any other effective mathematical procedure, if available at all, is permanently available, the opportunity to decide whether or not an empirical statement holds good may be lost: The most extreme form of anti-realism would be the theory that a statement about the past is rendered true or false only by evidence available to the speaker at the time of asserting it.
This would imply that if the only evidence for the occurrence of an event is that some individual remembers it, and that individual takes the memory to their grave, then when the witness dies it ceases to be true that the event took place. Dummett therefore rejects this most extreme form of anti-realism about the past as being too solipsistic. Dummett, , For this reason, Dummett accepts that some concession must be made to realism when it comes to dealing with statements about the past.
What metaphysical groundings for linguistic content were considered? The volume opens with Deborah Modrak's essay on Plato's theory of definition, which is a useful tour through the dialogues' methods and assumptions. Modrak argues that Plato is tacitly committed to a two-tiered account of definition and, by extension, reference.
At the first tier are 'names and senses as expressed in linguistic definitions and the referents of words' At the second, we find the same names and their true definitions. The second-tier primary referents of these names are the Forms, whereas their secondary referents are ordinary objects. Most obviously, one wonders whether Plato would welcome the Fregean terminology of sense and reference or the distinction between primary and secondary referents.
Ademollo's second question concerns sentence signification: The question of the signification of the sentence continues to occupy medieval thinkers, as Margaret Cameron shows in her especially clear and useful contribution. Cameron focuses on Abelard and the Stoics, noting that, although there is no evidence the Stoics influenced Abelard, they arrive at similar positions and for similar reasons.
Both are 'anti-realists' who want to introduce the notion of a proposition in pursuit of a deflationary metaphysics. Both analyze away categorical statements 'dogs are mammals' as disguised conditionals 'if something is a dog, it is a mammal'. In the case of the Stoics, this allows them to do away with general concepts For his part, Abelard has no problem with concepts, which makes one wonder why the Stoics would think that merely going conditional would 'remove any reference to a generic object' Most interesting is the peculiar ontological status propositions are supposed to have.
Abelard and the Stoics both argue for the need to posit 'the sayable' as something more than tokens of sounds or marks on a page even as they try to keep their metaphysics as lean as possible. Peter Adamson and Alexander Key's focus is the medieval Arabic tradition They present their chapter as describing the clash between the 'autochthonous and pre-existing Arabic bipartite theory of meaning' and the Aristotelian tripartite theory, which arrives on the Arab scene in the seventh century. The bipartite Arab theory countenances vocal form and mental content only, while the Aristotelian view adds a third element: The set-up is a bit odd.
As Adamson and Key point out, the two traditions are only superficially incompatible Only idealists would insist on the absence of the third member of the tripartite view. What is at stake is, among other things, whether logic is indeed universal or contingent on the particular features of the Greek language Joke Spruyt and Catarina Dutilh Novaes provide an informative treatment of medieval theories of syncategoremata.
Focusing on the thirteenth and fourteenth centuries, they aim to contrast medieval treatments with contemporary views on the logical constants. As they note, medieval syncategoremata include more than the logical constants; at times, the category seems to be a grab bag of everything that is neither subject nor predicate. It is hard to evaluate this claim without knowing what Spruyt and Novaes think " significatio " and "meaning" mean.
In any case, the dissimilarities are more instructive. Nor do they worry much about giving a precise demarcation of the class of syncategoremata. Spruyt and Novaes claim that this 'fluidity' 'may serve as inspiration for an open-ended conception of logical constants' Gyula Klima's ambitious 'Semantic Content in Aquinas and Ockham' uses historical figures to mount a philosophical argument.
In brief, Klima's thesis is that any position on the identity of concepts that allows for the Cartesian evil demon scenario or the Putnamian brain in a vat scenario must be false. Following Claude Pannacio, Klima argues that Ockham distinguishes between semantic content what a term refers to and phenomenal content the set of phenomenal features one uses to recognize something as falling under a kind. For Ockham, semantic content is fixed by causation, whereas phenomenal content is just whatever phenomenal features the subject happens to pick up on.
Klima argues that Ockham's position entails a contradiction, for Ockham counts two concepts as the same just in case they have the same phenomenal content.
But then Ockham has to say that we and an envatted person call him 'Vatman' make the same judgment when we say that 'Vatman is a brain in a vat'. The way out of the contradiction and out of the skeptical scenario is hyper-externalism, which Klima, on the basis of nine quoted words, purports to find in Aquinas. It is also beautifully conceived and executed. For those who want to know what philosophical analysis is, this is among the best example ever produced.
Its vision, though complicated in details, is simple and compelling. But he did succeed in laying the foundation for the stunning advances in mathematical logic in the 20th century that themselves provided frameworks for modern theories both of computation and of linguistically encoded information. How does he fit in with Frege? This work is a kind of bookend, if you like, to Frege, who initiated a tradition which came to be known as analytic philosophy.
One is the distinction between necessary and contingent truth. A necessary truth is one that is true, and would have remained so no matter what possible state the world was in. A contingent truth is one that is true, but could have been false. For example, it is true that we are talking today, but we could have decided otherwise, in which case the claim that we are talking would have been false. This distinction between necessary and contingent truths is traditionally illustrated by saying that the truths of logic and mathematics are necessary, whereas those of natural and social science are contingent.
The second distinction is between those truths we can know a priori, just by thinking about them, and other truths, knowledge of which requires empirical observation and experiment for confirmation. As before, this distinction — between a priori and a posteriori truths — is traditionally illustrated by saying that our logical and mathematical knowledge is a priori, whereas our empirical, scientific knowledge is a posteriori. Why should that be so? Well, that brings us to the third distinction — between analytic and synthetic truths. An analytic truth is a sentence made true simply by what the words mean — bachelors being unmarried, for example.
By contrast, a synthetic truth is made true by corresponding to facts in the world. Throughout most of the 20th century this distinction between the meanings of two classes of sentences was assumed to explain the coincidence of the necessary with the a priori, and the contingent with the a posteriori. If a statement is made true by its meaning alone, then of course it would have remained true even if the facts of the world had been different, and of course it can be known without empirical confirmation, since understanding what it means is enough to know that it is true.
Contrary to what had been assumed, there are necessary truths knowable only by experience — including many important scientific truths — and there are contingent truths that can be known a priori. Moreover, this difference is not reducible to differences in linguistic meaning or convention. The reason this is important is that it falsified an assumption crucial to the self-conception of philosophy that had grown up in the first half of the 20th century — the assumption that philosophical truths are all analytic, necessary and a priori.
It brought back the idea that things in the world have discoverable essences, which are properties not just physically required but metaphysically necessary for their existence. Some of these properties are discoverable by science. But these may not exhaust the essential properties of human beings. It employs terms we use in everyday life that vary their referents from speaker to speaker and use to use.
What makes this interesting is that logic has always aimed, since Frege, at producing systems of proof that are mechanically checkable, so there can be no dispute about whether or not something counts as a proof. It was always thought that in order to do this you had to abstract away from natural language, and eliminate all context-sensitive words, the referents of which change from one context to another.
Kaplan shows that this is not so, which is a great achievement. The effect is to give us more interesting logical languages which begin to approach languages like English in their expressive power. By applying the techniques developed for understanding the original logical languages to these richer, more English-like systems, we achieve an understanding of these systems that gives us a kind of understanding of English and other natural languages by proxy.
That is all to the good. Even though he succeeds, he still has to abstract away from, and ignore, important aspects of the meanings of context-sensitive sentences in English.