Dewey and Russell's debate over the status of logic in the twentieth-century is, by now, well-trodden ground for scholarly inquiry. However, Dewey's novel theory of propositions, first articulated in his 1938 Logic: The Theory of Inquiry, has received comparatively less attention than the debate that touched upon it. The paucity of interest among philosophers of language is probably due to a variety of reasons, such as the theory's unorthodox character and, what at least appears to be, its naive simplicity when (...) compared to other more common (syntactic and pragmatic) theories of propositions. In this paper, I would like to examine the three most extensive treatments, one by the late H.S. Thayer, another by Tom Burke, and the most recent exposition by Larry Hickman, with the intention of reviving scholarly interest in Dewey's theory of propositional form. Another objective of the present project is to situate Dewey's theory relative to more contemporary theories and debates about propositional form in the philosophy of language literature. (shrink)
Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that (...) depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another. (shrink)
Contemporary epistemology has assumed that knowledge is represented in sentences or propositions. However, a variety of extensions and alternatives to this view have been proposed in other areas of investigation. We review some of these proposals, focusing on (1) Ryle's notion of knowing how and Hanson's and Kuhn's accounts of theory-laden perception in science; (2) extensions of simple propositional representations in cognitive models and artificial intelligence; (3) the debate concerning imagistic versus propositional representations in cognitive psychology; (4) recent (...) treatments of concepts and categorization which reject the notion of necessary and sufficient conditions; and (5) parallel distributed processing (connectionist) models of cognition. This last development is especially promising in providing a flexible, powerful means of representing information nonpropositionally, and carrying out at least simple forms of inference without rules. Central to several of the proposals is the notion that much of human cognition might consist in pattern recognition rather than manipulation of rules and propositions. (shrink)
Wittgenstein presents in the Tractatus a variable purporting to capture the general form of proposition. One understanding of what Wittgenstein is doing there, an understanding in line with the ‘new’ reading of his work championed by Diamond, Conant and others, sees it as a deflationary or even an implosive move—a move by which a concept sometimes put by philosophers to distinctively metaphysical use is replaced, in a perspicuous notation, by an innocent device of generalization, thereby dispersing the clouds of (...) philosophy that formerly surrounded the concept. By asking how Wittgenstein supposed his variable to work, and what work he imagined it was fit for, the paper questions the adequacy of that understanding. (shrink)
An attractive semantic theory presented by Richard K. Larson and Peter Ludlow takes a report of propositional attitudes, e.g 'Tom believes Judy Garland sang', to report a believing relation between Tom and an interpreted logical form constructed from 'Judy Garland sang'. We briefly outline the semantic theory and indicate its attractions. However, the definition of interpreted logical forms given by Larson and Ludlow is shown to be faulty, and an alternative definition is offered which matches their intentions. This (...) definition is then shown to imply that Tom does not know his own mind, a result without intuitive support. A third definition is offered to deal with this problem. (shrink)
The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, such as (...) of The Morning Star and The Evening Star (section 1). Given the second members of the pairs, the modes of presentation, it is quite natural to allow exportation everywhere. There is no need for essentialism. (One also can have non-essentialistic modal logic if one grants analyticity or the like.) (section 2). Given that the second member of the pair need only be one that is satisfied by the entity that is the first member (and need not be specificative), the method has no difficulties when one is concerned only with discriminations (and not specifications) (section 3). When this method is combined with the Frege-Carnap method of descriptions, fictional entities can be accommodated; Goodman''s unicorn-picture and the like can be brought within a Tarskian semantics; and Geach''s difficulties with intentional identity appear to be handled (section 4). Given the author''s ordered pair construals, there appears to be no additional need for notional construals; i.e., the author''s one unified method appears satisfactory for dealing with both traditionalde re (relational) andde dicto (notional) construals. The Paradox of the Knower and the like do not appear formulatable against the author''s approach. (section 5). The author also argues against the basic principles behind the Church-Langford translation argument (section 6). (shrink)
A form (or pattern) of inference, let us say, explicitlysubsumes just such particular inferences as are instances of the form, and implicitly subsumes thoseinferences with a premiss and conclusion logically equivalent to the premiss and conclusion of an instanceof the form in question. (For simplicity we restrict attention to one-premiss inferences.) A form ofinference is archetypal if it implicitly subsumes every correct inference. A precise definition (Section 1)of these concepts relativizes them to logics, since different logics classify different inferences ascorrect, (...) as well as ruling differently on the matter of logical equivalence which entered into the definitionof implicit subsumption. When relativized to classical propositional logic, we find (Section 2) thatall but a handful of `degenerate' inference forms turn out to be archetypal, whereas matters are verydifferent in this respect for the case of intuitionistic propositional logic (Sections 3 and 4), and an interestingstructure emerges in this case (the poset of equivalence classes of inference forms, with respect tothe equivalence relation of implicitly subsuming the same inferences). Thus a more accurate, if excessivelylong-winded title would be 'Archetypal and Non-Archetypal Forms of Inference in Classical andIntuitionistic Propositional Logic'. Some left-overs are postponed for a final discussion (Section 5).The overall intention is to introduce a new subject matter rather than to have the last word on thequestions it raises; indeed several significant questions are left as open problems. (shrink)
Interpreted Logical Forms (ILFs) are objects composed of a syntactic structure annotated with the semantic values (objectual content) of each node of the structure. We criticize the view that ILFs are the objects of propositional attitude verbs such as believe, as this is developed by Larson and Ludlow (1993). Our critique arises from a tension in the way that sen-.
We prove completeness and decidability results for a family of combinations of propositional dynamic logic and unimodal doxastic logics in which the modalities may interact. The kind of interactions we consider include three forms of commuting axioms, namely, axioms similar to the axiom of perfect recall and the axiom of no learning from temporal logic, and a Church–Rosser axiom. We investigate the influence of the substitution rule on the properties of these logics and propose a new semantics for (...) the test operator to avoid unwanted side effects caused by the interaction of the classic test operator with the extra interaction axioms. (shrink)
The propositional fragment L 1 of Leniewski's ontology is the smallest class (of formulas) containing besides all the instances of tautology the formulas of the forms: (a, b) (a, a), (a, b) (b,). (a, c) and (a, b) (b, c). (b, a) being closed under detachment. The purpose of this paper is to furnish another more constructive proof than that given earlier by one of us for: Theorem A is provable in L 1 iff TA is a thesis (...) of first-order predicate logic with equality, where T is a translation of the formulas of L 1 into those of first-order predicate logic with equality such that T(a, b) = FblxFax (Russeltian-type definite description), TA B = TA TB, T A = TA, etc. (shrink)
In this paper, I explore the question of whether the expected consequences of holding a belief can affect the rationality of doing so. Special attention is given to various ways in which one might attempt to exert some measure of control over what one believes and the normative status of the beliefs that result from the successful execution of such projects. I argue that the lessons which emerge from thinking about the case ofbelief have important implications for the way we (...) should think about the rationality of a number of other propositional attitudes,such as regret, desire, and fear. Finally,I suggest that a lack of clarity with respect to the relevant issues has given rise to a number of rather serious philosophical mistakes. (shrink)
This book makes a stimulating contribution to the philosophy of language and philosophy of mind. It begins with a spirited defense of the view that propositions are structured and that propositional structure is "psychologically real." The author then develops a subtle view of propositions and attitude ascription. The view is worked out in detail with attention to such topics as the semantics of conversations, iterated attitude ascriptions, and the role of propositions as bearers of truth. Along the way important (...) issues in the philosophy of mind are addressed. (shrink)
Most contemporary philosophical discussions of intentionality start and end with a treatment of the propositional attitudes. In fact, many theorists hold (tacitly if not explicitly) that all attitudes are propositional attitudes. Our folk-psychological ascriptions suggest, however, that there are non-propositional attitudes: I like Sally, my brother fears snakes, everyone loves my grandmother, and Rush Limbaugh hates Obama. I argue that things are as they appear: there are non-propositional attitudes. More specifically, I argue that there are attitudes (...) that relate individuals to non-propositional objects and do so not in virtue of relating them to propositions. I reach this conclusion by not only showing that attempted analyses of apparently non-propositional attitudes in terms of the propositional fail, but that some non-propositional attitudes don't even supervene on propositional attitudes. If this is correct, then the common discussions of intentionality that address only propositional attitudes are incomplete and those who hold that all intentional states are propositional are mistaken. (shrink)
A prospective introduction -- The received view -- Troubles with the received view -- Are propositional attitudes relations? -- Foundations of a measurement-theoretic account of the attitudes -- The basic measurement-theoretic account -- Elaboration and explication of the proposed measurement-theoretic account.
Eliminative materialism is a popular view of the mind which holds that propositional attitudes, the typical units of our traditional understanding, are unsupported by modern connectionist psychology and neuroscience, and consequently that propositional attitudes are a poor scientific postulate, and do not exist. Since our traditional folk psychology employs propositional attitudes, the usual argument runs, it too represents a poor theory, and may in the future be replaced by a more successful neurologically grounded theory, resulting in a (...) drastic improvement in our interpersonal relationships. I contend that these eliminativist arguments typically run together two distinct capacities: the folk psychological mechanisms which we use to understand one another, and scientific and philosophical guesses about the structure of those understandings. Both capacities are ontologically committed and therefore empirical. However, the commitments whose prospects look so dismal to the eliminativist, in particular the causal and logical image of propositional attitudes, belong to the guesses, and not necessarily to the underlying mechanisms. It is the commitments of traditional philosophical perspectives about the operation of our folk psychology which are contradicted by?new evidence and modeling methods in connectionist psychology. Our actual folk psychology was not clearly committed to causal, sentential propositional attitudes, and thus is not directly threatened by connectionist psychology. (shrink)
Reprinted in Philosophy of Religion: An Anthology, Wadsworth 2013, 6th edition, with an additional section entitled, "Reasons for the Common View," eds Michael Rea and Louis Pojman. What is propositional faith? At a first approximation, we might answer that it is the psychological attitude picked out by standard uses of the English locution “S has faith that p,” where p takes declarative sentences as instances, as in “He has faith that they’ll win”. Although correct, this answer is not nearly (...) as informative as we might like. Many people say that there is a more informative answer. They say that, at the very least, propositional faith requires propositional belief. More precisely, they say that faith that p requires belief that p or that it must be partly constituted by belief that p. This view is common enough; call it the Common View. I have two main aims in this paper: (i) to exhibit the falsity of the Common View and the paucity of reasons for it, and (ii) to sketch a more accurate and comprehensive account of what propositional faith is. (shrink)
Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such (...) as the aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)
Folk psychological realism is the view that folk psychology is true and that people really do have propositional attitudes, whereas anti-realism is the view that folk psychology is false and people really do not have propositional attitudes. We argue that anti-realism is not worthy of acceptance and that realism is eminently worthy of acceptance. However, it is plainly epistemically possible to favor either of two forms of folk realism: scientific or non-scientific. We argue that non-scientific realism, while (...) perhaps unpopular among philosophers of mind, is a distinct form of realism from scientific realism, and that it is not yet knowable whether scientific or non-scientific realism is true. We also outline how adopting realism, but remaining neutral between scientific and non-scientific realism, offers fresh insights into such topics as instrumentalism, supervenience, the language of thought hypothesis, and elimin-ativism. (shrink)
Syntactical treatments of propositional attitudes are attractive to artificial intelligence researchers. But results of Montague (1974) and Thomason (1980) seem to show that syntactical treatments are not viable. They show that if representation languages are sufficiently expressive, then axiom schemes characterizing knowledge and belief give rise to paradox. Des Rivières and Levesque (1988) characterize a class of sentences within which these schemes can safely be instantiated. These sentences do not quantify over the propositional objects of knowledge and belief. (...) We argue that their solution is incomplete, and extend it by characterizing a more inclusive class of sentences over which the axiom schemes can safely range. Our sentences do quantify over propositional objects. (shrink)
Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of (...) extensions of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4. (shrink)
Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing (...) in OBJECTS OF THOUGHT. (shrink)
We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...) (.. B..) infer A = B. The paper respondes to a criticism of an earlier paper by James Freeman . (shrink)
Anderson and Belnap devise a model theory for entailment on which propositional identity equals proposional coentailment. This feature can be reasonably questioned. The authors devise two extensions of Anderson and Belnap’s model theory. Both systems preserve Anderson and Belnap’s results for entailment, but distinguish coentailment from identity.
We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.
We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...) (.. B..) infer A = B. The paper is a response to a paper by James Freeman to an earlier paper by us. (shrink)
Argument-forms exist which are valid over finite but not infinite domains. Despite understanding of this by formal logicians, philosophers can be observed treating as valid arguments which are in fact invalid over infinite domains. In support of this claim I will first present an argument against the classical pragmatist theory of truth by Mark Johnston. Then, more ambitiously, I will suggest the fallacy lurks in certain arguments for physicalism taken for granted by many philosophers today.
‘Is being one only one? – The Argument for the Uniqueness of Platonic Forms’ Abstract: Each Form is unique in number; no two numerically distinct Forms can share the same nature. Plato argues for this claim in Republic X. I identify the metaphysical principles Plato presupposes in the premises of the argument, by examining the reasoning behind them, and offer a reconstruction of the argument showing the principles in use. I argue that the metaphysical significance of the argument’s (...) conclusion is to establish that if a Form F were not unique, if there were many Forms F, their nature would alter along with their number: a Form cannot recur without change in its constitution. This is why there can be only one Form for each character in the world. (shrink)
In at least some cases of future directed propositional hoping, facts about the hoper become puzzling if one supposes that the object of hoping is a future tensed proposition. These facts are easily explained by the alternative suppostion that the hoper accepts a future tensed proposition but bears the hopingattitude toward a disjunctively tensed proposition. Parallel remarks apply to past directed and present directed prepositional hoping. Thus, at least some instances of hoping have as their objects disjunctively tensed rather (...) than purely tensed propositions. Propositional remembering may possibly resemblepropositional hoping in this respect. (shrink)
Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as (...) he called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)
This paper presents an account of the manner in which a proposition’s immediate structural features are related to its core truth-conditional features. The leading idea is that for a proposition to have a certain immediate structure is just for certain entities to play certain roles in the correct theory of the brute facts regarding that proposition’s truth conditions. The paper explains how this account addresses certain worries and questions recently raised by Jeffery King and Scott Soames.
The paper presents an interpretation of the thinking behind the early Wittgenstein's "general form of the proposition." It argues that a central role is played by the assumption that all domains of discourse are governed by the same laws of logic. The interpretation is presented partly through a comparison with ideas presented recently by Michael Potter and Peter Sullivan; the paper argues that the above assumption explains more of the key characteristics of the "general form of the proposition" than Potter (...) and Sullivan suppose, including, in particular, its claim that the bases from which all other propositions are derived must be elementary propositions. (shrink)
The problem of the ‘Unity of the Proposition’ is the problem of explaining the difference between a content-expressing declarative sentence and a ‘mere list’ of referents. The prevailing view is that such a problem is to be solved metaphysically, either by reducing our ontology to exclude propositions or universals, or by explaining how it is possible for a certain kind of complex entity – the ‘proposition’– to ‘unify’ its constituents. I argue that these metaphysical approaches cannot succeed; instead the only (...) viable approach is linguistic, identifying features of the (type–) sentence itself that enable it to express a content. Thus the problem of the ‘Unity of the Proposition’ (distinguishing sentences from lists) is distinct from the problem of ‘propositional unity’ (explaining how the constituents of propositions form a unified content). I suggest that, while the latter problem is not pressing, the former does not permit of an answer which applies in generality in all languages; we can only fully explain the Unity of the Proposition for single languages or groups of similar languages. (shrink)
This book is about beliefs, language, communication and cognition. It deals with the fundamental issue of the interpretation of the speaker's utterance expressing a belief and reporting on beliefs of other people in the form of oratio obliqua. The main aim of the book is to present a new account of the problem of interpreting utterances expressing beliefs and belief reports in terms of an approach called Default Semantics.
It is widely agreed that perceptual experience is a form of intentionality, i.e., that it has representational content. Many philosophers take this to mean that like belief, experience has propositional content, that it can be true or false. I accept that perceptual experience has intentionality; but I dispute the claim that it has propositional content. This claim does not follow from the fact that experience is intentional, nor does it follow from the fact that experiences are accurate or (...) inaccurate. I end by considering the relationship between this question and the question of whether experience has non-conceptual content. (shrink)
A major issue in political philosophy is the extent to which one or another version of nationalism or, by contrast, cosmopolitanism, is morally justified. Nationalism, like cosmopolitanism, may be understood as a position on the status and responsibilities of nation states, but the terms may also be used to designate attitudes appropriate to those positions. One problem in political philosophy is to distinguish and appraise various forms of nationalism and cosmopolitanism; a related problem is how to understand the relation (...) of patriotism to each. Nationalists may tend to be patriots, but need not be; patriots may tend to be nationalists, but need not be. Like nationalism, patriotism may also be considered in propositionalforms or in related attitudinal forms; but unlike nationalism and cosmopolitanism, patriotism can exist in the form of an emotion: roughly, love of one’s country. This paper characterizes nationalism, cosmopolitanism, and patriotism in both forms and argues for a conception of patriotism on which it is both distinct from nationalism and compatible with certain kinds of cosmopolitanism. It also suggests that, in qualified forms, nationalism and cosmopolitanism may overlap in what they require of their proponents. (shrink)
According to proponents of the face-value account, a beliefreport of the form ‘S believes that p’ is true just in case the agentbelieves a proposition referred to by the that-clause. As againstthis familiar view, I argue that there are cases of true beliefreports of the relevant form in which there is no proposition that thethat-clause, or the speaker using the that-clause, can plausibly betaken as referring to. Moreover, I argue that given the distinctiveway in which the face-value theory of belief-reports (...) fails, there ispressure to give up the metaphysical thesis that belief is apropositional attitude. I conclude by suggesting that we allownon-propositional entities to be amongst the relata of thebelief-relation, and make some speculative remarks concerning whatsuch entities might be like. (shrink)
The paper deals with the question of the structure of knowledge and the precise relationship between propositional "knowledge that" and dispositional "knowledge how." In the first part of my essay, I provide an analysis of the term 'knowing how' and argue that the usual alternatives in the recent epistemological debate – knowing how is either a form of propositional or dispositional knowledge – are misleading. In fact it depends on the semantic and pragmatic context of the usage of (...) this term whether 'knowing how' refers to a type of dispositional knowledge, to propositional knowledge, or to a hybrid form of both. Only in the first case, can one say that dispositional know how cannot be reduced to any form of propositional knowledge. Yet, this case is the most interesting one to consider in the investigation of the nature of knowledge, if one assumes that knowing that p presupposes "having found out that p." Having found something out, however, presupposes certain acts of epistemic inquiry and corresponding epistemic abilities. Examined more carefully, it is shown that the dispositional knowledge-how is a necessary condition for propositional knowledge-that, hence propositional knowledge-that is a species of the dispositional knowledge-how. Accordingly, dispositional knowledge has to be understood as being at the very core of our notion of knowledge, including propositional knowledge. (shrink)
I have shown (to my satisfaction) that Leibniz's final attempt at a generalized syllogistico-propositional calculus in the Generales Inquisitiones was pretty successful. The calculus includes the truth-table semantics for the propositional calculus. It contains an unorthodox view of conjunction. It offers a plethora of very important logical principles. These deserve to be called a set of fundamentals of logical form. Aside from some imprecisions and redundancies the system is a good systematization of propositional logic, its semantics, and (...) a correct account of general syllogistics. For 1686 it was quite an accomplishment. It is a pity that Leibniz himself did not fully appreciate what he had achieved. It does seem to me that this was due in part, as the Kneales urge (Note 4), to his having kept the focus of his attention on traditional syllogistics. It is a great pity that he did not polish GI 195–200 for publication. The publication of GI 195, 198, and 200 would have most likely promoted further research. MAJR- Humanities, Social Sciences and Law. (shrink)
One major obstacle in providing a compositional semantics for natural languages is that it is not clear how we should deal with propositional attitude contexts. In this paper I will discuss the Interpreted Logical Form proposal , focusing on the case of belief. This proposal has been developed in different ways by authors such as Harman (1972), Higginbotham (1986,1991), Segal (1989) and Larson and Ludlow (1993). On this approach, the that-clause of a belief report is treated as a singular (...) term, referring to the interpreted logical form (ILF) of its embedded sentence. The ILF of a sentence is made up of two parts : a syntactic representation of the sentence at the level of logical form, and an assignment of semantic values to parts of the representation. Thus, given a belief report such as. (shrink)
Taking Wittgenstein's love of music as my impetus, I approach aporetic problems of epistemic relativity through a round of three overlapping (canonical) inquiries delivered in contrapuntal (higher and lower) registers. I first take up the question of scepticism surrounding 'groundless knowledge' and contending paradigms in On Certainty (physics versus oracular divination, or realism versus idealism) with attention given to the role of 'bedrock' certainties in providing stability amidst the Heraclitean flux. I then look into the formation of sedimented bedrock knowledge, (...) or practices of knowing, by comparing Wittgenstein's remarks on animal habituation and initiate training into human forms of life. In the latter case, mastery of techniques—our common education—secures agreement in judgment. Finally, I entertain Wittgenstein's obscure references to Einstein's Relativity in Zettel, showing initiate training as a way of 'setting the clocks' with variable degrees of certainty, relative to the language-games played. Together, these three approaches help us to stop the 'endless circling' when philosophers try to address knowledge questions through the logic of object and designation, or verification of correspondence between propositions and things. Instead, attention moves to the way we educate our children and how we employ agreements and bedrock certainties in practices. (shrink)
According to the standard definition, a first-order theory is categorical if all its models are isomorphic. The idea behind this definition obviously is that of capturing semantic notions in axiomatic terms: to be categorical is to be, in this respect, successful. Thus, for example, we may want to axiomatically delimit the concept of natural number, as it is given by the pre-theoretic semantic intuitions and reconstructed by the standard model. The well-known results state that this cannot be done within first-order (...) logic, but it can be done within second-order one. Now let us consider the following question: can we axiomatically capture the semantic concept of conjunction? Such question, to be sure, does not make sense within the standard framework: we cannot construe it as asking whether we can form a first-order (or, for that matter, whatever-order) theory with an extralogical binary propositional operator so that its only model (up to isomorphism) maps the operator on the intended binary truth-function. The obvious reason is that the framework of standard logic does not allow for extralogical constants of this type. But of course there is also a deeper reason: an existence of a constant with this semantics is presupposed by the very definition of the framework1. Hence the question about the axiomatic capturability of concunction, if we can make sense of it at all, cannot be asked within the framework of standard logic, we would have to go to a more abstract level. To be able to make sense of the question we would have to think about a propositional ‘proto-language’, with uninterpreted logical constants, and to try to search out axioms which would fix the denotations of the constants as the intended truth-functions. Can we do this? It might seem that the answer to this question is yielded by the completeness theorem for the standard propositional calculus: this theorem states that the axiomatic delimitation of the calculus and the semantic delimitation converge to the same result.. (shrink)
The debate between representationalists and anti-representationalists as I construe it in this chapter is a debate about whether truth-conditions are or should be assigned directly to natural language sentences (NLSs) – the anti-representationalist view – or whether they are or should be assigned instead to mental representations (MRs) that are related in some appropriate way to these NLSs. On the representationalist view, these MRs are related to NLSs in virtue of the fact that the MRs are the output of an (...) interpretive process that has as its input both representations of the lexico-syntactic structure of the NLSs and relevant non-linguistic assumptions that are accessible in the current conversational context. On this conception, language interpretation is a process of developing sentential forms into fully propositionalforms, and it is these propositionalforms that are the primary bearers of truth-conditional content, and are candidates for model-theoretic interpretation, not the NLSs themselves. (shrink)
We may have a bit of a handle on roughly what kinds of entities the Platonic Forms are. We can think of them as analogous to a number of notions in contemporary philosophy that are denominated “Platonic abstracta”, e.g., propositions, concepts, mathematicals, and the like. We may think them queer, but we have some idea what their queerness consists in. We may even believe that some of these kinds of entities actually exist.
We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined (...) classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)
Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional (...) identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation. (shrink)
Empathy is often described as an evolutionary tool that helps humans manoeuvre between the complexities of our social hierarchy. As it allows us to understand other people's intentions, it is often categorized as an element of social cognition that can lead to a form of know-how. This paper will argue that empathy can lead to more than know-how. Using data from psychology and neuroscience, I will sketch empathizing as a reliable process. On the assumption of reliabilism, I will (...) show that empathizing as a generally reliable process can produce justified beliefs and thus that the empathizing process can lead to propositional knowledge. In passing I shall reveal some flaws in an influential line of research on empathy in psychology, which in turn exposes a more fundamental, conceptual, problem with empirical research on. (shrink)
In this article, I examine the ramified-type theory set out in the first edition of Russell and Whitehead's Principia Mathematica. My starting point is the ?no loss of generality? problem: Russell, in the Introduction (Russell, B. and Whitehead, A. N. 1910. Principia Mathematica, Volume I, 1st ed., Cambridge: Cambridge University Press, pp. 53?54), says that one can account for all propositional functions using predicative variables only, that is, dismissing non-predicative variables. That claim is not self-evident at all, hence a (...) problem. The purpose of this article is to clarify Russell's claim and to solve the ?no loss of generality? problem. I first remark that the hierarchy of propositional functions calls for a fine-grained conception of ramified types as propositionalforms (?ramif-types?). Then, comparing different important interpretations of Principia?s theory of types, I consider the question as to whether Principia allows for non-predicative propositional functions and variables thereof. I explain how the distinction between the formal system of the theory, on the one hand, and its realizations in different epistemic universes, on the other hand, makes it possible to give us a more satisfactory answer to that question than those given by previous commentators, and, as a consequence, to solve the ?no loss of generality? problem. The solution consists in a substitutional semantics for non-predicative variables and non-predicative complex terms, based on an epistemic understanding of the order component of ramified types. The rest of the article then develops that epistemic understanding, adding an original epistemic model theory to the formal system of types. This shows that the universality sought by Russell for logic does not preclude semantical considerations, contrary to what van Heijenoort and Hintikka have claimed. (shrink)
This note sketches how a theory of procedural semantics may offer a solution to the problem of the unity of the proposition. The current revival of the notion of structured meaning has made the problem of propositional unity pressing. The problem, stated in its simplest form, is how an individual a and a property F combine into the proposition P that a is an F; i.e. how two different kinds of objects combine into a third kind of object capable (...) of having properties that neither of its constituents could have. Constraints imposed on P include that P must be capable of being true/false, being known/believed to be true/false, and occurring as argument of propositional connectives, such as entailment. (shrink)
In what follows, I will first try to show that both anti-realist and realist intensionalist truthconditional accounts of internal metafictional sentences (i.e., sentences of the form "in the story S, p") are unsatisfactory. Moreover, I will claim that this does not mean that propositional truthconditional accounts of those sentences are to be dispensed with; simply, one has to provide a non-intensionalist propositional truthconditional account of those sentences. Finally, I will show that this account is fully compatible with a (...) realist interpretation of those sentences' truthconditions according to which at least some of those sentences commit one to fictional entities. (shrink)
Aristotle assesses as valid three first figure syllogisms, each of which contains at least one premiss expressing a de re contingency. In fact, all three of these moods (namely, Barbara-QQQ, Barbara-XQM, and Barbara-LQM) are invalid. Utilizing the concept of ampliation, this paper shows how the mood Barbara-QQQ must be refined if it is to be deemed valid. It can then become clear as to how Barbara-XQM and Barbara-LQM can be disambiguated and ultimately validated. In treating all three moods, some theses (...) from S4 will be exploited in the context of distinguishing de dicto and de re modes of attributing possibility and necessity. Various Aristotelian propositionalforms and rules of inference, including argumentation by ecthesis, will shape the presentation. The viability of Aristotle’s views on the convertibility of universal negative apodeictic propositions will emerge as decisive in evaluating the success of his modal syllogistic. (shrink)
The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical (...) form, known as its finest splitting. In this paper we explain these ideas; relate the approaches of Rodrigues and Parikh to each other; and briefly report some recent results of Kourousias and Makinson on the extent to which AGM belief change operations respect relevance. Finally we suggest a further refinement of the notion of relevance by introducing a parameter that allows one to take epistemic as well as purely logical components into account. -/- A version of this was published in the /Journal of Applied Logic/ (Elsevier). (shrink)
We study the monadic fragment of second order intuitionistic propositional logic in the language containing the standard propositional connectives and propositional quantifiers. It is proved that under the topological interpretation over any dense-in-itself metric space, the considered fragment collapses to Heyting calculus. Moreover, we prove that the topological interpretation over any dense-in-itself metric space of fragment in question coincides with the so-called Pitts' interpretation. We also prove that all the nonstandard propositional operators of the form q (...) $\mapsto \exists$ p (q $\leftrightarrow$ F(p)), where F is an arbitrary monadic formula of the variable p, are definable in the language of Heyting calculus under the topological interpretation of intuitionistic logic over sufficiently regular spaces. (shrink)
We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from (...) implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics. (shrink)
In this book Haridimos Tsoukas, one of the most imaginative organization theorists of our time, examines the nature of knowledge in organizations, and how individuals and scholars approach the concept of knowledge. -/- Tsoukas firstly looks at organizational knowledge and its embeddedness in social contexts and forms of life. He shows that knowledge is not just a collection of free floating representations of the world to be used at will, but an activity constitutive of the world. On the one (...) hand the organization as an institutionalized system does produce regularities that can can be captured via propositionalforms of knowledge. On the other, the organization as practice, as a lifeworld, or as an open-ended system produce stories, values, and shared traditions which can only be captured by narrative forms of knowledge. -/- Secondly, Tsoukas looks at the issue of how individuals deal with the notion of complexity in organizations: Our inability to reduce the behaviour of complex organizations to their constituent parts. Drawing on concepts such as discourse, narrativity, and reflexivity, he adopts a hermeneutical approach to the issue. -/- Finally Tsoukas examines the concept of meta-knowledge, and how we know what we know. Arguing that the underlying representationalist epistemology of much of mainstream management causes many problems, he advocates adopting a more discursive approach. He describes what such an epistemology might be, and illustrates it with examples from organization studies and strategic management. -/- An ideal introduction to the thinking of a leading organizational theorist, this book will be essential reading for academics, researchers, and students of Knowledge Management, Organization Studies, Management Studies, Business Strategy, and Applied Epistemology. (shrink)
LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$ (both of bounded arity). Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O(n3 + d) which are refutable in LK by depth d + 1 proof of size exp(O(log2 n)) but such that every depth d refutation must have the size at least exp(nΩ(1)). The sets Td (...) n express a weaker form of the pigeonhole principle. (shrink)
Plato on Knowledge and Forms brings together a set of connected essays by Gail Fine, in her main area of research since the late 1970s: Plato's metaphysics and epistemology. She discusses central issues in Plato's metaphysics and epistemology, issues concerning the nature and extent of knowledge, and its relation to perception, sensibles, and forms; and issues concerning the nature of forms, such as whether they are universals or particulars, separate or immanent, and whether they are causes. A (...) specially written introduction draws together the themes of the volume, which will reward the attention of anyone interested in Plato or in ancient metaphysics and epistemology. (shrink)
The Peri ide^on (On Ideas) is the only work in which Aristotle systematically sets out and criticizes arguments for the existence of Platonic forms. Gail Fine presents the first full-length treatment in English of this important but neglected work. She asks how, and how well, Aristotle understands Plato's theory of forms, and why and with what justification he favors an alternative metaphysical scheme. She examines the significance of the Peri ide^on for some central questions about Plato's theory of (...)forms--whether, for example, there are forms corresponding to every property or only to some, and if only to some, then to which ones; whether forms are universals, particulars or both; and whether they are meanings, properties or both. Fine also provides a general discussion of Plato's theory of forms, and of our evidence about the Peri ide^on and its date, scope, and aims. While she pays careful attention to the details of the text, she also relates it to contemporary philosophical concerns. The book will be valuable for anyone interested in metaphysics ancient or modern. (shrink)
There is a mystery at the heart of Plato’s Parmenides. In the first part, Parmenides criticizes what is widely regarded as Plato’s mature theory of Forms, and in the second, he promises to explain how the Forms can be saved from these criticisms. Ever since the dialogue was written, scholars have struggled to determine how the two parts of the work fit together. Did Plato mean us to abandon, keep, or modify the theory of Forms, on the (...) strength of Parmenides’ criticisms? Samuel Rickless offers something that has never been done before: a careful reconstruction of every argument in the dialogue. He concludes that Plato’s main aim was to argue that the theory of Forms should be modified by allowing that forms can have contrary properties. To grasp this is to solve the mystery of the Parmenides and understand its crucial role in Plato’s philosophical development. (shrink)
Scholars of Plato are divided between those who emphasize the literature of the dialogues and those who emphasize the argument of the dialogues, and between those who see a development in the thought of the dialogues and those who do not. In this important book, Russell Dancy focusses on the arguments and defends a developmental picture. He explains the Theory of Forms of the Phaedo and Symposium as an outgrowth of the quest for definitions canvassed in the Socratic dialogues, (...) by constructing a Theory of Definition for the Socratic dialogues based on the refutations of definitions in those dialogues, and showing how that theory is mirrored in the Theory of Forms. His discussion, notable for both its clarity and its meticulous scholarship, ranges in detail over a number of Plato's early and middle dialogues, and will be of interest to readers in Plato studies and in ancient philosophy more generally. (shrink)
The explanatory gap and theknowledge argument are rooted in the conflationof propositional and phenomenal knowledge. Thebasic knowledge argument is based on theconsideration that ``physical information'' aboutthe nervous system is unable to provide theknowledge of a ``color experience'' (Jackson,1982). The implication is that physicalism isincomplete or false because it leaves somethingunexplained. The problem with Jackson'sargument is that physical information has theform of highly symbolic propositional knowledgewhereas phenomenal knowledge consists in innateneurophysiological processes. In addition totheir fundamental epistemological differences,clinical, anatomical, pathological (...) and brainimaging studies demonstrate that phenomenal andpropositional knowledge are fundamentallydifferent neurobiological processes. Propositional knowledge is phylogeneticallynew, highly symbolic, culturally acquired,exclusively human and expressible in differentnatural and artificial languages. By contrast,phenomenal knowledge (i.e.: knowingwhat-it-is-like to see a color) consists inqualitative experiences and phenomenal conceptsthat provide an internal, language-independentreference to the properties of objects and theneeds of the organism. Language andpropositional knowledge are exclusively humanattributes implemented in specific regions ofthe dominant hemisphere. This contrastssharply with the phylogenicallysensory areas that are common to animals andhumans, which implement qualitativeexperiences. Experiences are hard-wiredneurobiological processes that can neither betransmitted nor re-created through thesymbolism of propositions. Thus, I concludethat the fallacy in the explanatory gap and inthe knowledge argument is a fallacy ofequivocation that results from ignoringfundamental neurobiological differences betweenphenomenal and propositional knowledge. (shrink)
Propositional identity is not expressed by a predicate. So its logic is not given by the ordinary first order axioms for identity. What are the logical axioms governing this concept, then? Some axioms in addition to those proposed by Arthur Prior are proposed.
In this paper, after outlining the methodological role Wittgenstein's appeal to language-games is supposed to play, I examine the picture of language which his discussion of such games and their relations to what Wittgenstein calls forms of life suggests. It is a picture according to which language and its employment are inextricably connected to wider contexts—they are embedded in specific natural and social environments, they are tied to purposive activities serving provincial needs, and caught up in distinctive ways of (...) life which creatures of a certain sort enjoy. In the remainder of the paper, I consider whether Wittgenstein's emphasis on the link between language and the circumstances surrounding its use points in the direction of an influential view widespread in contemporary philosophy of language, namely, semantic contextualism. I examine carefully a number of passages which scholars have appealed to in support of the claim that Wittgenstein advances contextualism and argue that they in fact provide no such support. The connection which Wittgenstein sees between what is expressed in the use of words and the circumstances in which they are used is not the connection the contextualist insists on. (shrink)
A number of philosophers are committed to the view that sense experiences, in so far as they have contents, have propositional contents, but this is more often tacitly accepted than argued for in the literature. This paper explains the propositional account and presents a basic case in support of it in a simple and straightforward way which does not involve commitment to any specific philosophical theory of perception.
This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial (...) simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area. (shrink)
Descartes' arguments against the substantial form -- Aquinas' introduction of the substantial form -- Suarez's defense of the substantial form -- Sanchez's skeptical humanist attack -- The mechanical alternative to substantial forms -- Cartesian science and the principles of Aristotelian mechanics -- Atoms, modes, and other heresies -- Descartes' metaphysical alternative to substantial forms.
In this book, Malcolm presents a new and radical interpretation of Plato's earlier dialogues. He argues that the few cases of self-predication contained therein are acceptable simply as statements concerning universals, and that therefore Plato is not vulnerable in these cases to the Third Man Argument. In considering the middle dialogues, Malcolm takes a conservative stance, rejecting influential current doctrines which portray the Forms as being not self-predicative. He shows that the middle dialogues do indeed take Forms to (...) be both universals and paradigms, and thus to exemplify themselves. The author goes on to consider why Plato should have been unsuccessful in avoiding self-predication. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual. The author concludes with the claim that reflection on the ambiguity of the notion of the "Standard Yard" may help us to appreciate why Plato failed to distinguish Forms as universals from Forms as paradigm cases. (shrink)
Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newtonâ€™s unpublished texts (and the views of his mentor, Isaac Barrow) shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtapositionâ€”the putting-together in spaceâ€”of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all (...) quantity (which is what measurement makes known) is ultimately related to spatial extension. I use this conception of Newtonâ€™s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia (beginning in Sect. 2 of Book I). The placementof Keplerâ€™s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)
Recently we have learned how experiment can have a life of its own. However, experiment remains epistemologically disadvantaged. Scientific knowledge must have a theoretical/propositional form. To begin to redress this situation, I discuss three ways in which instruments carry meaning: 1. Scientific instruments can carry tremendous loads of meaning through association, analogy and metaphor. 2. Instrumental models of complicated phenomena work representationally in much the same way as theories. 3. Instruments which create new phenomena establish a new field of (...) material possibilities. I suggest that scientists employ a "visual/physical/material logic," analogous to propositional logic, which establishes relations between different material forms. (shrink)
Ineffability, method, and ontology, by G. Bergmann.--The glory and the misery of Ludwig Wittgenstein, by G. Bergmann.--Stenius on the Tractatus, by G. Bergmann.--Naming and saying, by W. Sellars.--The ontology of Wittgenstein's Tractatus, by E. D. Klemke.--Material properties in the Tractatus, by H. Hochberg.--Wittgenstein's pantheism: a new light on the ontology of the Tractatus, by N. Garver.--Science and metaphysics: a Wittgensteinian interpretation, by H. Petrie.--Wittgenstein on private languages, by C. L. Hardin.--Wittgenstein on private language, by N. Garver.--Wittgenstein and private languages, by (...) W. Todd.--The private-language argument, by H.-N. Castañeda.--Wittgenstein on privacy, by J. W. Cook.--"Forms of life" in Wittgenstein's Philosophical investigations, by J. F. M. Hunter.--Privacy and language, by M. S. Gram.--On language games and forms of life, by F. Zabeeh.--Wittgenstein on meaning and use, by J. F. M. Hunter.--Wittgenstein on phenomenalism, skepticism, and criteria, by A. Oldenquist.--Tractarian reflections on saying and showing, by D. W. Stampe.--Wittgenstein and logical necessity, by B. Stroud.--Negation and generality, by H. Hochberg.--Facts, possibilities, and essences in the Tractatus, by H. Hochberg.--Arithmetic and propositional form in Wittgenstein's Tractatus, by H. Hochberg.--Selected bibliography (p. 543-546). (shrink)