The Society tor Exact Philosop-hy was founded :in·l97D at a meeting held at McGill University in Montreal on 4-5 November at which was organised iby Mario Bunge. Funding for the meeting iwas provided by SDiii the International Union of Hsistory and Philosophy of cience (vson..

previous theories and the relevance of those criticisms to the new accounts. Additionally, we have included a new section at the end, which gives some directions to literature outside of formal semantics in which the notion of mass has been employed. We looked at work on mass expressions in psycholinguistics and computational linguistics here, and we discussed some research in the history of philosophy and in metaphysics that makes use of the notion of mass.

(although the FOF, unlike the CNF, is still a theorem). The correct version of Problem 62 is (following the format of (Pelletier, 1986)): Natural FOF Negated Conclusion CNF (Ax)r(Pet~(Px m Pf(x))) m Pf(f(x))] Pet Px+ P f(f(x)) + -Pa..

In ‘On Denoting’ and to some extent in ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie’, published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous elimination (or contextual defi nition) of defi nite descriptions, but also a series of considerations against understanding defi nite descriptions as singular terms. At the end of ‘On Denoting’, Russell believes he has shown that all the theories that do treat defi nite descriptions as singular terms fall (...) logically short: Meinong’s, Mally’s, his own earlier (1903) theory, and Frege’s. (He also believes that at least some of them fall short on other grounds—epistemological and metaphysical—but we do not discuss these criticisms except in passing). Our aim in the present paper is to discuss whether his criticisms actually refute Frege’s theory. We fi rst attempt to specify just what Frege’s theory is and present the evidence that has moved scholars to attribute one of three different theories to Frege in this area. We think that each of these theories has some claim to be Fregean, even though they are logically quite different from each other. This raises the issue of determining Frege’s attitude towards these three theories. We consider whether he changed his mind and came to replace one theory with another, or whether he perhaps thought that the different theories applied to different realms, for example, to natural language versus a language for formal logic and arithmetic. We do not come to any hard and fast conclusion here, but instead just note that all these theories treat defi nite descriptions as singular terms, and that Russell proceeds as if he has refuted them all. After taking a brief look at the formal properties of the Fregean theories (particularly the logical status of various sentences containing nonproper defi - nite descriptions) and comparing them to Russell’s theory in this regard, we turn to Russell’s actual criticisms in the above-mentioned articles to examine the extent to which the criticisms hold.. (shrink)

Although resolution-based inference is perhaps the industry standard in automated theorem proving, there have always been systems that employed a different format. For example, the Logic Theorist of 1957 produced proofs by using an axiomatic system, and the proofs it generated would be considered legitimate axiomatic proofs; Wang’s systems of the late 1950’s employed a Gentzen-sequent proof strategy; Beth’s systems written about the same time employed his semantic tableaux method; and Prawitz’s systems of again about the same time are often (...) said to employ a natural deduction format. [See Newell, et al (1957), Beth (1958), Wang (1960), and Prawitz et al (1960)]. Like sequent proof systems and tableaux proof systems, natural deduction systems retain.. (shrink)

There are two different things that are thought of when the issue of compositionality is considered. One concerns a generalized notion of “what is a complex item made of?” A second view of compositionality comes mostly from linguistic semantics. In this conception, the question is whether there is a certain relationship that holds amongst the properties of members of a structure. In the language case, the property that is usually of interest is the meaning of arbitrary members of the syntactically (...) given structure. The fundamental idea behind holism is to give some sort of priority to a “whole” in preference to the “parts” of that whole, and this plays out differently in different areas where the term is used. (shrink)

Many different kinds of items have been called vague, and so-called for a variety of different reasons. Traditional wisdom distinguishes three views of why one might apply the epitaph "vague" to an item; these views are distinguished by what they claim the vagueness is due to. One type of vagueness, The Good, locates vagueness in language, or in some representational system -- for example, it might say that certain predicates have a range of applicability. On one side of the range (...) are those cases to which the predicate clearly applies and on the other side of the range are those cases where the negation of the predicate clearly applies. But there is no sharp cutoff place along the range where the one range turns into the other. Most examples of The Good are those terms which describe some continuum -- such as bald describes a continuum of the ratio of hairs per cm2 on the head. But not all work this way. Alston (1968) points to terms like religion invoking a number of criteria the joint applicability of which ensures that the activity in question is a religion and the failure of all to apply ensures that it is not a religion. But when only some middling number of the criteria are fulfilled, the term religion neither applies nor fails to apply. Some accounts of "family resemblance" and "open texture" might also fit this picture. Such a view is often called a "representational account of vagueness". Another conception of vagueness, The Bad, locates vagueness as a property of discourses, of memories, and of certain philosophers and their papers, etc. This sort of vagueness occurs when the information available does not allow one to tell, for example, that a certain sentence is true, but also does not allow one to determine that it is false. It occurs when the information available does not allow one to claim that a predicate applies to a name, but also does not allow one to claim that the negation of the predicate applies to that name.. (shrink)

In this paper I intend to discuss a series of views about substance. I take as my starting point certain things locke says about substance, argue that there are a number of logico-linguistic pecularities in his view, claim that the basic intuition is correct but that locke's final pronouncements are wrong, canvass three other possible but incorrect attempts to accommodate this correct intuition, and then sketch what I take to be the proper way to embrace the intuition. Finally I indicate (...) what changes in lockean doctrine would be needed if Locke wanted to hold the correct doctrine of substance. My conclusion is: not many.The places where Locke is most explicit about his views on substance are the Letters to Stillingfleet. The value of these letters as against Locke views in the Essay has been sometimes depreciated, but it seems clear that the views expressed in the Letters are merely a making explicit the views held in the Essay. (shrink)

The central concern of Knowledge in a Social World is to restore the notion of Truth to the rightful place of glory that it had before the onslaught of those pragmatic, cultural-studying, social constructing, critical legalistic and feministic postmodernists (PoMo’s, for short). As G sees it, these PoMo’s have never put forward any “real” arguments for their veriphobia; and, well, how could they, since their position is committed to the “denial of Truth” and hence committed to denying that there is (...) any such thing as a valid or a sound argument. Instead, according to G, they have artfully inculcated various types of considerations so that a defender of Truth now must swim against the entire flow of academe to even stand a chance of making his or her voice heard. G finds six overlapping currents in this wash of anti-veritas ideas, listing them in his §1.3 and devoting a further section to each of them in turn (§1.4–§1.9). These currents spring up in various later parts of the book for further discussion, but even in these places G refers the reader back to the material in Chapter 1 as refuting them. (Insofar as a current that is not based on any consideration of Truth, validity, or soundness is susceptible of refutation.) I think it is fair to say that G does not really intend that his comments about the anti-veritas ideas will be taken as definitive by the veriphobes, but rather that he believes the strength of his positive account in the rest of the book (which accords Truth a central role) will sway all neutral readers into a belief of the usefulness of Truth in an account of social knowledge. Still, I think many readers…even veriphiles…will find the considerations that G brings against the six currents to be disappointingly short. I want to consider some of the currents in the stream of PoMo ideas. As I said, G’s six currents overlap at various points, and each of the currents has sub-flows. This means that we might put.... (shrink)

I was asked to develop a course “Philosophy and Cognitive Science” to be taught for the first time in Spring 1995 in the Philosophy Department at the University of Alberta. Since my cognitive science-related interests are focussed more towards philosophy mixed with artificial intelligence (A I) and linguistics than towards (say) neuroscience or anthropology, I decided to slant the course in t hat direction. The departmental intent was that this should be an upper-level course, but with no spe cific prerequisite (...) courses. This meant that while there was a “three previous courses in philosophy ” prerequisite, the students could not be expected to have taken any particular course, as (say) a phil osophy of mind course or a logic course. Further, I had in mind that the course would be part of an initiative to create an undergraduate program in Cognitive Science at the University of Alberta, and s o I encouraged students from linguistics, computer science, and psychology who had taken courses in their department like “Language and Mind”, “Introduction to AI”, and “Introduction to Cognit ive Science” to take this course even without the philosophy background. This resulted in the class consisting of about a quarter each philosophy, psychology and computer science majors, with the re st being drawn from linguistics, education, and anthropology. And although this distribution of stud ents arguably lessened the philosophical sophistication of both the lectures and the class discussion, I (and the students, I believe) found the perspectives brought to the topic by these other students to be fascinating and quite provocative. (shrink)

Psychologism in logic is the doctrine that the semantic content of logical terms is in some way a feature of human psychology. We consider the historically influential version of the doctrine, Psychological Individualism, and the many counter-arguments to it. We then propose and assess various modifications to the doctrine that might allow it to avoid the classical objections. We call these Psychological Descriptivism, Teleological Cognitive Architecture, and Ideal Cognizers. These characterizations give some order to the wide range of modern views (...) that are seen as psychologistic because of one or another feature. Although these can avoid some of the classic objections to psychologism, some still hold. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (shrink)

This volume showcases an interplay between leading philosophical and linguistic semanticists on the one side, and leading cognitive and developmental psychologists on the other side. The topic is a class of outstanding questions in the semanticists on the one side, and leading cognitive and developmental psychologists on the other side. The topic is a class of outstanding questions in the semantic and logical theories of generic statements and statements that employ mass terms by looking to the cognitive abilities of speakers (...) and of child language-learners. (shrink)

A certain direction in cognitive science has been to try to “ground” public language statements in some species of mental representation. A central tenet of this trend is that communication – that is, public language – succeeds (when it does) because the elements of this public language are in some way correlated with mental items of both the speaker and the audience so that the mental state evoked in the audience by the use of that piece of public language is (...) the one that the speaker wanted to evoke. The “meaning”, therefore, of an utterance – and of the parts of an utterance, such as individual sentences and their parts, the individual words, etc. – is, in this view, some mental item. Successful communication requires that there be widespread agreement amongst speakers of the same public language as to the mental entities that are correlated with any particular public words. Such a view of meaning is variously called “internalist” or “cognitive” or “subjectivist” or “solipsistic” or (sometimes) “representationalist” (these terms having, however, further connotations which set them apart from one another in other ways), and can be found in a wide variety of writers who do not agree on many other things. It is opposed to views that take the meaning of an utterance to be an item of “reality,” however defined. In different writers this latter view is called “externalist” or “objectivist” or “realist” or (sometimes) “represent-ationalist,” always with the idea that there is something other (or at least, more) than the mental state of speakers and hearers that determines meaning. The literature is rife with arguments between internalists vs. externalists, subjectivists vs. objectivists, cognitivists vs. realists, on such topics as “truth” and “synonymy” and “twin earth” and “arthritis” (to mention only a few).. (shrink)

Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in (...) which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning. (shrink)

Some utterances of sentences such as ‘Every student failed the midterm exam’ and ‘There is no beer’ are widely held to be true in a conversation despite the facts that not every student in the world failed the midterm exam and that there is, in fact, some beer somewhere. For instance, the speaker might be talking about some particular course, or about his refrigerator. Stanley and Szabó (in Mind and Language v. 15, 2000) consider many different approaches to how contextual (...) information might give meaning to these ‘restricted quantifier domains’, and find all of them but one wanting. The present paper argues that their considerations against one of these other theories, considerations that turn on notions of compositionality, are incorrect. (shrink)

Topics discussed include Aristotle's semantics, individuation, essentialism, causation, & being. Contents: The Aporematic Approach to Primary Being in Metaphysics Z. Aristotle's Semantics & a Puzzle Concerning Change. Aristotle & Individuation. Singular Statements & Essentialism in Aristotle. What is Aristotle's Theory of Essence?. Aristotle on the Proximate Efficient Cause of Action. Causes as Necessary Conditions: Aristotle, Alexander of Aphrodisias & J.L. Mackie.

Contrary to the claims of owen, frede, and many other platonic scholars, there is a straight forward way to explicate plato's "sophist" as having 'heteron' first be understood as "non-identical" and after 257b or so be understood as "incompatible." this should encourage scholars who prefer the "incompatibility" reading but don't see how to get the required change of meaning.

1: Linguistic and Epistemological Background 1 . 1 : Generic Reference vs. Generic Predication 1 . 2 : Why are there any Generic Sentences at all? 1 . 3 : Generics and Exceptions, Two Bad Attitudes 1 . 4 : Exceptions and Generics, Some Other Attitudes 1 . 5 : Generics and Intensionality 1 . 6 : Goals of an Analysis of Generic Sentences 1 . 7 : A Little Notation 1 . 8 : Generics vs. Explicit Statements of Regularities..

In the last ten years or so, talk of “possible worlds” has become decidedly more fashionable from a logical point of view. And here fashion is well-justified: both from a logical and from a metaphysical point of view, the work of Saul Kripke on the concept of a possible world is as challenging as any contributions since the time of Leibniz himself. It is only fair, then, and indirectly flattering, to complain that Kripke is limiting himself as a major philosopher (...) in ways which Leibniz saw to be essential to balanced philosophy. We confine ourselves in this paper to just two crucial dimensions of philosophical depth when it comes to the concept of possible worlds. On the one hand, Leibniz saw the concept as one which raises very usefully many traditional problems of ethics, including those of free will and theodicy. On the other hand, Leibniz saw that questions about possible worlds may call for a radical approach to sane ontology. Such an approach, “revisionary metaphysics,” systematically reinterprets rather than dogmatically regurgitates the convictions of Plain Men and Theoretical Physicists about—to take a favorite example of Kripke’s—this single table’s being made of many distinct molecules. (shrink)

The Principle of Semantic Compositionality (sometimes called Frege''s Principle) is the principle that the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined. This principle has been extremely influential throughout the history of formal semantics; it has had a tremendous impact upon modern linguistics ever since Montague Grammars became known; and it has more recently shown up as a guiding principle for a (...) certain direction in cognitive science.Despite the fact that The Principle is vague or underspecified at a number of points — such as what meaning is, what counts as a part, what counts as a syntactic complex, what counts as combination — this has not stopped some people from viewing The Principle as obviously true, true almost by definition. And it has not stopped other people from viewing The Principle as false, almost pernicious in its effect. And some of these latter theorists think that it is an empirically false principle while others think of it as a methodologically wrong-headed way to proceed. (shrink)

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

Ternary exclusive or is the truth function that is true just in case exactly one of its three arguments is true. This is an interesting truth function, not definable in terms of the binary exclusive or alone, although the binary case is definable in terms of the ternary case. This article investigates the types of truth functions that can be defined by ternary exclusive or, and relates these findings to the seminal work of Emil Post.

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non‐conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would lead (...) to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model‐theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction. The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logic‐based formalizations of belief revision, syntactic and model‐theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more “entrenched” than others in the face of contradiction are also discussed from the perspective of induction and theory revision. (shrink)

This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are "synonymous" or "translationally equivalent." We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals (...) are drawn concerning the possibility of having two logical systems that are "empirically distinct" but are both translationally equivalent to a common logic. (shrink)

Different researchers use "the philosophy of automated theorem p r o v i n g " t o cover d i f f e r e n t concepts, indeed, different levels of concepts. Some w o u l d count such issues as h o w to e f f i c i e n t l y i n d e x databases as part of the philosophy of automated theorem p r o v i n g . (...) Others wonder about whether f o r m u l a s should be represented as strings or as trees or as lists, and call this part of the philosophy of automated theorem p r o v i n g . Yet others concern themselves w i t h what k i n d o f search should b e embodied i n a n y automated theorem prover, or to what degree any automated theorem prover should resemble Prolog. Still others debate whether natural deduction or semantic tableaux or resolution is " b e t t e r " , a n d c a l l t h i s a part of the p h i l o s o p h y of automated theorem p r o v i n g . Some people wonder whether automated theorem p r o v i n g should be " h u m a n oriented" or "machine o r i e n t e d " — sometimes arguing about whether the internal p r o o f methods should be " h u m a n - I i k e " or not, sometimes arguing about whether the generated proof should be output in a f o r m u n d e r s t a n d a b l e by p e o p l e , and sometimes a r g u i n g a b o u t the d e s i r a b i l i t y o f h u m a n intervention in the process of constructing a proof. There are also those w h o ask such questions as whether we s h o u l d even be concerned w i t h completeness or w i t h soundness of a system, or perhaps we should instead look at very efficient (but i n c o m p l e t e ) subsystems or look at methods of generating models w h i c h might nevertheless validate invalid arguments. A n d a l l of these have been v i e w e d as issues in the philosophy of automated theorem proving. Here, I w o u l d l i k e to step back from such i m p l e m e n t - ation issues and ask: " W h a t do we really think we are doing when we w r i t e an automated theorem prover?" My reflections are perhaps idiosyncratic, but I do think that they put the different researchers* efforts into a broader perspective, and give us some k i n d of handle on w h i c h directions we ourselves m i g h t w i s h to pursue when constructing (or extending) an automated theorem proving system. A logic is defined to be (i) a vocabulary and formation rules ( w h i c h tells us w h a t strings of symbols are w e l l - formed formulas in the logic), and ( i i ) a definition of ' p r o o f in that system ( w h i c h tells us the conditions under which an arrangement of formulas in the system constitutes a proof). Historically speaking, definitions of ' p r o o f have been given in various different manners: the most c o m m o n have been H i l b e r t - s t y l e ( a x i o m a t i c ) , Gentzen-style (consecution, or sequent), F i t c h - s t y l e (natural deduction), and Beth-style (tableaux).. (shrink)