’s glue logic for computing logical form dynamic. This allows us to model a dialogue agent’s understanding of what the update of the semantic representation of the dialogue would be after his next contribution, including the effects of the rhetorical moves that he is contemplating performing next. This is a pre-requisite for developing a model of how agents reason about what to say next. We make the glue logic dynamic by using a dynamic public announcement logic ( pal ). We (...) extend pal with a particular variety of default reasoning suited to reasoning about discourse—this default reasoning being an essential component of inferring the pragmatic effects of one’s dialogue moves. We add to the pal language a new type of announcement, known as ceteris paribus announcement, and this is used to model how an agent anticipates the (default) pragmatic effects of his next dialogue move. Our extended pal validates certain intuitive patterns of default inference that existing pal s for practical reasoning do not. We prove that the dynamic glue logic has a pspace validity problem, and as such is no more complex than pal with multiple $${\square}$$ operators. (shrink)

Wittgenstein initially endorsed but then abandoned, by the time of “Some Remarks on Logical Form”, the view that elementary propositions are logically independent. In this paper it is argued that the doctrine of logical independence is in fact inconsistent with the intuitions and examples that motivated the picture theory of the Tractatus Logico-Philosophicus. This leaves the question of whether the logical independence of elementary propositions can be reconciled with the theory itself; the paper explores some interpretations of the early Wittgenstein (...) with which this is, and others with which it is not, consistent. (shrink)

With their book Logical Pluralism, Jc Beall and Greg Restall have elaborated on their previous statements on logical pluralism. Their view of logical pluralism is centred on ways of understanding logical consequence. The essay tries to come to grips with their doctrine of logical pluralism by highlighting some points that might be made clearer, and questioning the force of some of Beall’s and Restall’s central arguments. In that connection seven problems for their approach are put forth: (1) The Informal Common (...) Core Problem, (2) The Formal Common Core Problem, (3) The Superior Judge Problem, (4) The Problem of the Conditional, (6) The Problem of an Unsettled Concept of Consequence, (7) The Methodological Problem, (8) The General Logical Form Problem. It seems that the case for logical pluralism is far from clear. It is even unclear what exactly logical pluralism is and where is stops. It is also unclear if logical pluralism could be stated as it is, if it were true. So far universalism seems to be the better position to take. (shrink)

There is a long-standing debate whether propositions, sentences, statements or utterances provide an answer to the question of what objects logical formulas stand for. Based on the traditional understanding of logic as a science of valid arguments, this question is firstly framed more exactly, making explicit that it calls not only for identifying some class of objects, but also for explaining their relationship to ordinary language utterances. It is then argued that there are strong arguments against the proposals commonly put (...) forward in the debate. The core of the problem is that an informative account of the objects formulas stand for presupposes a theory of formalization; that is, a theory that explains what formulas may adequately substitute for an inference in proofs of validity. Although such theories are still subject to research, some consequences can be drawn from an analysis of the reasons why the common accounts featuring sentences, propositions or utterances fail. Theories of formalization cannot refer to utterances qua expressions of propositions; instead they may refer to sentences and rely on additional information about linguistic structure and pragmatic context. (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)

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico-philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary (...) propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question whyWittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form. (shrink)

These are not just tricks or puzzles, but are intimately connected with some of the liveliest and most basic philosophical disputes about logical form, ...

A standard view of the semantics of natural language sentences or utterances is that a sentence has a particular logical structure and is assigned truth-conditional content on the basis of that structure. Such a semantics is assumed to be able to capture the logical properties of sentences, including necessary truth, contradiction and valid inference; our knowledge of these properties is taken to be part of our semantic competence as native speakers of the language. The following examples pose a problem for (...) this view of semantics. (shrink)

The standard view of logical form is that logical forms are synthetic structures which are the forms of sentences and of other linguistic entities. This is often associated with a more general linguistic view of logic which is articulated in different ways by various authors. This paper contains a critical discussion of such linguistic approaches to logical form, with special emphasis on Quine’s formulation of a logical grammar in Philosophy of Logic. An account of logical forms as higher-order properties, which (...) essentially builds on Frege’s analysis of quantification as higher-order predication, is suggested at the end. (shrink)

Carruthers’ argument depends on viewing logical form as a linguistic level. But logical form is typically viewed as underpinning general purpose inference, and hence as having no particular connection to language processing. If logical form is tied directly to language, two problems arise: a logical problem concerning language acquisition and the empirical problem that aphasics appear capable of cross-modular reasoning.

In Kant’s logical texts the reference of the form of the judgment to an “unknown = x” is well known, but its understanding remains far from consensual. Due to the universality of all concepts, the subject as much as the predicate, in the form S is P, is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, particularly in the text on the “logical use of the understanding”, this Kantian (...) interpretation of the subject-predicate relation leads to the question about the relations that must hold between intuition and concept in the judgment. In contrast to intuition, if no concept, due to its universal character, refers immediately to an object, how should we understand the relations of subject and predicate to one another, as well as their relations to intuition, which corresponds to the very special individuality of that object in general = x? In the Kant-Literatur, the relations between intuition and concept in the judgment have been considered in diverse theoretical backgrounds, mainly in Fregean logic and in the logic of Port-Royal. Although so markedly different, these two solutions to the problem above seem to share a common thesis, in so far as they claim, though in different ways, a predicative character to those relations. If the analytic tradition recognizes in the relation between x and the concept S the marks of a propositional function Sx, in turn, the interpretation elaborated from the background of Port-Royal recognizes in this relation the minor premise x is S implicit in the judgment every S is P. This being the case, if it were possible to prove, on the contrary, that the relations between intuition and concept in the judgment could only be of a non-predicative character, then a third solution would be open to us, a solution that could enable us to track down the sense of the conceptions of judgment and logical form in the CPR. In applying this argumentative strategy, it is of the utmost importance to insist on the specificity of Kant’s notion of extension, in order to prove its irreducibility to the Port-Royal notion of extension as well as to the modern one. (shrink)

Book Information Logical Form and Language. Edited by G. Preyer and G. Peter. Clarendon Press. Oxford. 2002. Pp. x + 512. Hardback, £55. Paperback, £19.99.

Donald Davidson has prepared a new edition of his classic 1980 collection of Essays on Actions and Events, including two additional essays. In this seminal investigation of the nature of human action, Davidson argues for an ontology which includes events along with persons and other objects. Certain events are identified and explained as actions when they are viewed as caused and rationalized by reasons; these same events, when described in physical, biological, or physiological terms, may be explained by appeal to (...) natural laws. The mental and the physical thus constitute irreducibly discrete ways of explaining and understanding events and their causal relations. -/- Among the topics discussed are: freedom to act; weakness of the will; the logical form of talk about actions, intentions, and causality; the logic of practical reasoning; Hume's theory of the indirect passions; and the nature and limits of decision theory. The introduction, cross-references, and appendices emphasize the relations between the essays and explain how Davidson's views have developed. -/- . (shrink)

First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.

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)

Vernacularism is the view that logical forms are fundamentally assigned to natural language expressions, and are only derivatively assigned to anything else, e.g., propositions, mental representations, expressions of symbolic logic, etc. In this paper, we argue that Vernacularism is not as plausible as it first appears because of non-sentential speech. More specifically, there are argument-premises, meant by speakers of non-sentences, for which no natural language paraphrase is readily available in the language used by the speaker and the hearer. The speaker (...) can intend this proposition and the hearer can recover it (and its logical form). Since they cannot, by hypothesis, be doing this by using a sentence of their shared language, the proposition-meant has its logical form non-derivatively, which falsifies Vernacularism. We conclude the paper with a brief review of the debate on incomplete definite descriptions in which Vernacularism is assumed as a suppressed premise. (shrink)

Truth and Meaning is a classic collection of original essays on fundamental questions in the philosophy of language.

A Logical Form (LF) is a syntactic structure that is interpreted by the semantic component. For a particular structure to be a possible LF it has to be possible for syntax to generate it and for semantics to interpret it. The study of LF must therefore take into account both assumptions about syntax and about semantics, and since there is much disagreement in both areas, disagreements on LF have been plentiful. This makes the task of writing a survey article in (...) the field fairly difficult, a difficulty that is amplified by the amount of material that needs to be covered if the result is going to be in any way representative. My response to this difficulty is to limit my objectives. As a start, I will confine myself to issues relating to the syntactic positions of Quantificational Noun Phrases (QNPs) at LF and to various interpretive consequences. But even within these relatively narrow confines, I will not attempt anything close to a comprehensive survey. Instead my goal will be restricted to the presentation of one leading idea and to the discussion of some evidence that might bear on it.1 Much research on the nature of LF has consisted in attempts to account for the meaning of sentences containing QNPs. (shrink)

It is widely believed that existential quantifiers can bring about the semantic effects of a scope which is wider than their actual syntactic scope (See Fodor & Sag (1982), Cresti (1995), Kratzer (1995), Reinhart (1995) and Winter (1995), among many others.) On the other hand, it is assumed that the syntactic scope of universal quantifiers can be determined unequivocally by the semantics. This paper shows that this second assumption is wrong; universal quantifiers can also bring about scope illusions, though in (...) a very specific environment. In particular, we argue that in the environment of generic tense, universal quantifiers can show the semantic effects of a scope which is wider than the one that is actually realized at LF. Our argument has four steps. First, we show that in generic contexts, universal quantifiers escape standard “scope-islands” (Section 1). Second, we show how the effects of wide scope in generic contexts can be achieved without syntactic wide scope (Section 2.1). Third, we show that this result is actually forced on us, once we take seriously certain independent issues concerning the interpretation of generic tense (Sections 2.2 - 2.4). Finally, the semantics of generic tense and, in particular, its interaction with focus, will yield some intricate new predictions, which, as we show, are borne out (Sections 3 - 5). (shrink)

In "Abstracts from Logical Form I/II," it was stated in the abstract that it remained necessary to put the pilot experiments into a "comprehensive theory." It is suggested here that the comprehensive theory is nothing other than classical logic modestly extended to include higher-order predicates, functions, and epistemic predicates, as well as a quantitative quantifier to deal with cases other than "all" (taken literally) or "some" in the sense of at least one. It is further suggested that up to a (...) point the theory should generalize across languages, and that logical form is very powerful. (shrink)

See the abstract for the "Abstracts from Logical Form II".

This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then selected (...) the top propositions—by a priori falsity—and strung them together to form ad hoc abstracts and compared these abstracts with the published summary. The results were startling: translation to logical form, followed by application of the Asimovian idea and Bar-Hillel/Carnap mathematics as elaborated into an AI/NLP proposal in Fulda (1986, 1988), produced excellent abstracts, thereby providing a proof-of-concept that merely by knowing the logical form of long text passages, one can produce reasonable abstracts of them—without actually understanding the text. We here report on a second experiment analyzing, in the exact same manner, the correspondence that followed the published text of the first experiment. While the results of this confirming experiment are less startling, they nevertheless provide additional confidence in the promise of the technique. In other words, were the results of these two experiments to generalize, that would show that logical form captures much more semantics than has heretofore been considered likely. Far from (as is commonly supposed) being merely the syntactical rewrite of text into formal notation, translation to logical form, even when undertaken with almost no knowledge about the particular predicates, individual constants, or other objects referred to in that form, might capture the core of the meaning in some important sense. -/- Note: There is a key difference in the /style/ of the texts analyzed in I and II in this long paper, divided into two only for practical reasons—space; the first text analyzed is written in a tight mathematical style, while the second is written in the discursive style of philosophy. -/- Finally, the unusual (for me) length of this two-part paper is justified by its being data-driven. (shrink)

This has been made available gratis by the publisher. -/- This piece gives the raison d'etre for the development of the converters mentioned in the title. Three reasons are given, one linguistic, one philosophical, and one practical. It is suggested that at least /two/ independent converters are needed. -/- This piece ties together the extended paper "Abstracts from Logical Form I/II," and the short piece providing the comprehensive theory alluded to in the abstract of that extended paper in "Pragmatics, Montague, (...) and 'Abstracts from Logical Form'" by motivating the entire project from beginning to end. (shrink)

Gives a general method as well as some results (inspired by Asimov, 1951; since discovered to be in Bar-Hillel and Carnap [several versions; Charles Parsons referred me to /Language and Information/]) to recover meaning (eventually automatically) from logical form/logical probability, which are mirror images. (Sets are taken as extensions of predicates, and knowledge of the sizes is needed; to that extent the method is a posteriori).

A theory of reference may be either an analysis of reference or merely an account of the correct use of the verb "refer". If we define the validity of arguments in the standard way, in terms of assignments of individuals and sets to the nonlogical vocabulary of the language, then we will be committed to seeking an analysis of reference. Those who prefer a metalinguistic account, therefore, will desire an alternative to standard semantics. One alternative is the Quinean conception of (...) logical validity as essentially a matter of logical form. Another alternative is Leblanc's truth-value semantics. But these prove to be either inadequate for purposes of metatheory or philosophically unsatisfactory. This paper shows how validity (i.e., semantic consequence) may be defined in a way that avoid the problems facing these other alternatives to standard semantics and also permits a metalinguistic account of reference. The validity of arguments is treated as a matter of logical form, but validity for forms is defined on analogy with the definition of semantic consequence in truth-value semantics. (A more radical kind of semantics without reference is the context logical approach represented in several of my other publications.). (shrink)

We discuss Hintikka’s Thesis [Hintikka 1973] that there exist natural language sentences which require non–linear quantification to express their logical form.

This paper claims that there is a plausible sense in which validity is a matter of truth preservation relative to interpretations of the sentences that occur in an argument, although it is not the sense one might have in mind. §1 outlines three independent problems: the first is the paradox of the sorites, the second concerns the fallacy of equivocation, and the third arises in connection with the standard treatment of indexicals. §2 elucidates the claim about validity, while §§3-5 show (...) how the three problems outlined can be handled in accordance with it. §6 explains how the claim squares with the traditional idea that validity is related to formality, and in particular with a broadly accepted definition based on that idea, the model-theoretic definition of logical consequence. Unlike other works on the subject, this paper does not focus on necessity. It is not its intention to provide a characterization of necessity that conforms to some ideal of rigour or to some pre-theoretical understanding of validity. What follows can be taken as conditional on the assumption that such a characterization can be provided. (shrink)

Semantic Structures is a large-scale study of conceptual structure and its lexical and syntactic expression in English that builds on the theory of Conceptual...

My interest in semantic categories arises out of consideration of what is often called structural entailment. Consider the following: 1. Lisa quickly left; so Lisa left. The first of the two sentences in (1) entails the second; necessarily, if the first is true then so is the second. Moreover, (1) is an instance of a more general pattern whose validity doesn’t seem to depend on the specific meanings of the words in (1). The adverb ‘quickly’, for example, can be replaced (...) with any of a wide range of adverbs without loss of validity; analogous remarks hold for the verb ‘leave’. Here are a few more paradigm examples of structural entailment. (shrink)

Notice that each of (1)–(4) is an instance of a more general pattern. For example, we could replace ‘black’ in (1) with any of a wide range of other adjectives such as ‘furry’ or ‘hungry’ or ‘three-legged’, without rendering the entailment invalid or any less obvious. Similarly, there are a number of verbs that occur in entailments parallel to (3): ‘Moe boiled the water; so the water boiled’; ‘Bart blew up the school; so the school blew up’; ‘Homer sank the (...) boat; so the boat sank’ and so on. (shrink)

The term ‘logical form’ has been called on to serve a wide range of purposes in philosophy, and it would be too ambitious to try to survey all of them in a single essay. Instead, I will focus on just one conception of logical form that has occupied a central place in the philosophy of language, and in particular in the philosophical study of linguistic meaning. This is what I will call the classical conception of logical form. The classical conception, (...) as I will present it in section 1, has (either explicitly or implicitly) shaped a great deal of important philosophical work in semantic theory. But it has come under fire in recent decades, and in sections 2 and 3 I will discuss two of the recent challenges that I take to be most interesting and significant. (shrink)

In his essay ‘“Conceptual Truth”’, Timothy Williamson (2006) argues that there are no truths or entailments that are constitutive of understanding the sentences involved. In this reply I provide several examples of entailment patterns that are intuitively constitutive of understanding in just the way that Williamson rejects, and I argue that Williamson’s argument does nothing to show otherwise. Williamson bolsters his conclusion by appeal to a certain theory about the nature of understanding. I argue that his theory fails to consider (...) the role that the structure of a sentence plays in determining its meaning. The cases I present suggest that this role imposes greater cognitive requirements on understanding than Williamson can acknowledge. (shrink)

... and new questions in philosophical logic arose, when Russell introduced his ... whether Scott is the author of Waverley without wishing to know whether ..

Everyday reasoning is replete with arguments which, though not logically valid, nonetheless harbor a measure of credibility in their own right. Here the claim that such arguments force us to acknowledge material validity, in addition to logical validity, is advanced, and criteria that attempt to unpack this concept are examined in detail. Of special concern is the effort to model these criteria on explications of logical validity that rely on notions of substitutivity and logical form. It is argued, however, that (...) such a parallel is not easily located and that it is uncertain that a construal of material validity can be fashioned after traditional accounts of logical validity. Attention is also given to the topics of enthymemes and to the proper domain of logic. (shrink)

In the opening sections of this paper, we defined ambiguity in terms of distinct sentences (for a single sentence-string) with, in particular, distinct sets of truth conditions for the corresponding negative sentence-string. Lexical vagueness was defined as equivalent to disjunction, for under conditions of the negation of a sentence-string containing such an expression, all the relevant more specific interpretations of the string had also to be negated. Yet in the case of mixed quantification sentences, the strengthened, more specific, interpretations of (...) some such positive string are not all of them necessarily implied to be false if the corresponding negative sentence-string is asserted. On the contrary, as we saw in section 6, a negative sentence-string can be used to deny one of the more specific interpretations of the corresponding positive string without also denying other weaker interpretations of that same string. One might therefore argue that the only empirical evidence availble for assessing quantified sentences suggests clearly that these sentence-strings are ambiguous. Indeed logicians, many of whom restrict their attention to propositions, MUST recognise logical ambiguity at this point. For the contextualisation of the negative sentences in section 6 showed that it was possible to assert the falsity of some proposition P expressed by the sentence S while asserting a further proposition which was compatible with the truth of S. However the corresponding conclusion that such sentence-strings are sententially ambiguous is not a necessary conclusion for the linguist: for the alternative account of postulating a single semantic representation plus a set of semantic procedures is also compatible with the negation evidence. Moreover we have seen independent reasons for thinking that if sentential ambiguity is assumed to be in one-to-one correspondence with what we should now call logical ambiguity, a considerable body of generalisations is lost. For the maximal ambiguity account, it should be recalled, is committed to assigning at least thirteen distinct propositions and hence thirteen distinct sentence outputs for every sentence-string containing no more than two quantifiers, for three out of the four interpretations originally outlined in this paper can be understood with each numeral taken either in an ’exactly’ sense or in an ’at least’ sense. Moreover there is no explanation of why just these interpretations are available-they are merely an arbitrary list, no more connected than are the two interpretations of John saw her duck, with no reason to predict that the ambiguity would carry over from language to language. If then it is granted that an ambiguity account fails to capture appropriate generalisations, only two alternative accounts of mixed quantification sentence-strings remain viable-an analysis proposing an initial co-ordinate logical form like the logical form III, which is the strongest form compatible with each of the propositional interpretations of sentence-string Two examiners marked six scripts, and the radically weak form in which only existential quantification (both over sets and over members of those sets) is invoked. Since there are strong arguments to suggest that the procedures which both analyses require are semantic, there seems no reason not to adopt the radical vagueness account, with its considerably greater simplicity. (shrink)

In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

In this paper I propose a novel treatment of generic sentences, which proceeds by means of different levels of analysis. According to this account, all generic sentences (I-generics and D-generics alike) are initially treated in a uniform manner, as involving higher-order predication (following the work of George Boolos, James Higginbotham and Barry Schein on plurals). Their non-uniform character, however, re-emerges at subsequent levels of analysis, when the higher-order predications of the first level are cashed out in terms of quantification over (...) individuals: this last step, I suggest, involves knowledge concerning the lexical meaning of the predicates in question. (shrink)

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a natural logic, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made (...) in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed. (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)

This paper offers an expressivist account of logical form, arguing that in order to fully understand it one must examine what valid arguments make us do (or: what Achilles does and the Tortoise doesn’t, in Carroll’s famed fable). It introduces Charles Peirce’s distinction between symbols, indices and icons as three different kinds of signification whereby the sign picks out its object by learned convention, by unmediated indication, and by resemblance respectively. It is then argued that logical form is represented by (...) the third, iconic, kind of sign. It is noted that icons uniquely enjoy partial identity between sign and object, and argued that this holds the key to Carroll’s puzzle. Finally, from this examination of sign-types metaphysical morals are drawn: that the traditional foes metaphysical realism and conventionalism constitute a false dichotomy, and that reality contains intriguingly inference-binding structures. (shrink)

Charles Peirce famously divided all signs into icons, indices and symbols. The past few decades have seen mainstream analytic philosophy broaden its traditional focus on symbols to recognise the so-called essential indexical. Can the moral now be extended to icons? Is there an “essential icon”? And if so, what exactly would be essential about it? It is argued that there is and it consists in logical form. Danielle Macbeth’s radical new “expressivist” interpretation of Frege’s logic and Charles Peirce’s existential graphs (...) are mobilized in support of this claim. (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 proposes and defends an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence is semantically associated with a canonical procedure for determining its truth value (cf. Dummett 1973, Horty 2007); and while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from (...) a psycholinguistic experiment examining adult judgments concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves many issues unsettled—e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|Dot(x) & ~Blue(x)|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|Dot(x)| - |Dot(x) & Blue(x)|’; etc. We obtained evidence in favor of the second hypothesis. Participants saw displays of between 2 and 5 colors of dots for 150ms, with between 5 and 17 dots per color. Ratios of blue to non-blue dots ranged between 1:2 and 7:8, with half the trials containing more blue dots and half containing more nonblues. Results indicated use of the Approximate Number System (Dehaene 1997) in verification, with accuracy unaffected by the number of colors. It is independently known that for dots of up to 3 colors, the size of the total array is automatically computed. Given this fact and our result, we argue that the number of nonblue dots was specified via subtraction, and that sentences of the form ‘Most !s are "’ have corresponding meanings, with truth conditions canonically specified along the following lines: |!(x) & "(x)| > |!(x)| - |!(x) & "(x)|.. (shrink)

This work contains Peter Long's important essay, Logic, Form and Grammar , which resolves many difficulties for the logical form of an argument where the reasoning is hypothetical. Also included are two essays on classical problems in philosophical logic, relating to logical form and formal relations.

On this conception, the semantic types of its primitive terms and their mode of combination determine the logical form of a sentence as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is revealed by a (canonical) proof of its T-sentence in an interpretive truth theory for L. We give a precise characterization of sameness of (...) logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that of identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well grounded. (shrink)

Davidson made a strikingly distinctive and valuable contribution to the practice of ontology. It was a species of argument for the existence of things of one kind or another. It was inspired by Quine’s doctrine that “To be is to be the value of a bound variable,” but it combined that with Davidson’s own apparently antiQuinean views on semantics and logical form in natural language. Roughly: Suppose truth-conditional analysis of certain English sentences assigns them logical forms containing characteristic quantifiers, and (...) the quantifiers’ domains include entities of a certain sort. Then, assuming that some of the relevant sentences are true, it follows that there exist entities of that sort. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)