Singular Propositions Research Articles

Mathematical structuralism and the Identity of Indiscernibles

context from the antecedent to the consequent which would be required for the utterance to express a falsehood.5 If there were some deep theoretical or intuitive reason to identify propositions with sets of possible worlds, perhaps it would be worth trying to learn to live with such aberrations. But I can see no such reason, even from Lewis's point of view. The impression that sets of possible worlds are 'just right' for a version of the proposition role seems to be due to the thought that, by encapsulating the information about what has to be the case for them to be true, they allow for an especially simple and natural way to analyse modal claims about truth and falsity. Once we realize that these claims will have to be given a counterpart-theoretic treatment in any case (given counterpart theory for individuals), this apparent advantage of sets of possible worlds over 'singular propositions' disappears. I conclude that, for the counterpart theorist, singular propositions outperform sets of possible worlds across the board as candidates to be cast in the proposition role, even on the narrowest conception of what that role might amount to.

Ontology as a Logical System of IS-A Relation

The main aim of this paper is to propose an appropriate logical system that is suitable to describe the notion of IS-A link as well as is-a link. The most important point to be realized is that those relations are not set thoretical ones. They connect two `general names' to construct a proposition, so that what is needed for proper descriptions of the relations in question is a theory of general names. It will be shown that is-a is a logical unit of axiomatically determined behaviour. The axiom concerning is-a relation was established by S. Lesniewski who named his theory of general names ontology. Today `ontology' has also become a common term for AI researchers. I intend to make it clear that there is a close connection between `ontology' used by Lesniewski and by AI researchers, even though they developed quite independently. I wish to stress that ontology created by Lesniewski is a system of syllogistic equipped with singular propositions and the theory of quantification. To make this point clear, I proposed a fragment of syllogism that I called MO(minimal ontology). This paper includes comments and examples articulating the logical power of ontology.

Matemáticas, fiscalidad y crítica de la Escuela Clásica. El pensamiento liberal de José Alonso López

José Alonso López is among the most suggestive figures of the first Spanish liberalism. Some of the most outstanding features in his thought are the object of this article: the links between political and economic liberalism; his criticisms to economic abstractions detached from factual analysis; the use of advanced mathematical methods; and his singular proposition of an income tax with progressive rates.

A Puzzle about Truth and Singular Propositions

It seems that every singular proposition implies that the object it is singular with respect to exists. It also seems that some propositions are true with respect to possible worlds in which they do not exist. The puzzle is that it can be argued that there is contradiction between these two principles. In this paper, I explain the puzzle and consider some of the ways one might attempt to resolve it. The puzzle is important because it has implications concerning the way we think about the relationship between a proposition and the claim that the proposition is true.

Why the tuple theory of structured propositions isn't a theory of structured propositions

Much is at stake. The notion of structured propositions – in particular structured singular propositions – is a cornerstone of the theory of direct reference, yet if the intuitive notion of structured proposition cannot possibly translate into ordered ntuples, as direct reference theory does, then that theory finds itself without a semantics in one of its key areas. This would prove an embarrassment, considering that its founding father, David Kaplan, first put forward the notion a quarter of a century ago. If the objections go through, however, it’s not only direct reference theory that will be seen to have left a central notion dangling. E.g., also Max J. Cresswell’s brand of categorial grammar relies on tuples as propositional structures (see Cresswell, 1985). It’s important to stress that the attack on tuples as propositional structures isn’t an attack on the notions of either singular or structured proposition. Indeed, both have much to be said for them, albeit they would deserve to be developed within a different framework. An historical parallel might be in place. Since Frege never came around to developing a formal theory of Sinne, it at some point became tempting to construe them as intensions a la possible worlds semantics, i.e., as functions (mappings) defined on a set of possible worlds. It’s well-known today that, and why, the construal was an aberration. Similarly, since Russell never got a firm grip on his propositions, it has become tempting to construe them as tuples. This essay tries to show why they shouldn’t be. In setting out why, we’ll see, among other, that the old problem of propositional unity afflicting Russell’s propositions rears its head again (see Jacquette 1992/93, Griffin 1993). But tuples-as-structures are open to an even more fundamental objection (Section IV).

Putting Things in Contexts

Thanks to David Kaplan (1989a, 1989b), we all know how to handle indexicals like 'I'. 'I' doesn't refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, 'I' refers to the agent of C. Since different contexts can have different agents, 'I' can refer to different objects relative to different contexts. For example, relative to a context cwhose agent is Gottlob Frege, 'I' refers to Frege; relative to a context c* whose agent is Alexius Meinong, 'I' refers to Meinong. 'I' is directly referential. This means that the object that 'I' refers to (relative to a context C) is its content (relative to C), where the content of an expression (relative to C) is what it contributes to the propositions that sentences that contain it express (relative to C). As a result, what a sentence that contains 'I' expresses (relative to a context C) is a singular proposition, one that contains the very object that 'I' refers to (relative to C). For example, relative to c, whose agent is Frege, the content of 'I' is Frege himself; and, as a result, relative to c,

Truth Values and the Value of Truth

This paper explores the ways in which truth is better than falsehood, and suggests that, among other things, it depends on the kinds of proposition to which these values are attached. Ordinary singular propositions like “It is raining” seem to fit best the bivalent “scheme” of classical logic, the general proposition “It is always raining” is more appropriately rated according to how often it rains, and a “practically vague” proposition like “The lecture will start at 1” is appropriately rated according to its nearness to exactness. Implications for logic of this “rating system” are commented on.

Justification and Ways of Believing

One of the issues that has been hotly discussed in connection with the direct designation theory is whether or not coreferential names can be substituted salva veritate in epistemic contexts. Some direct designation theorists believe that they can be so substituted. Some direct designation theorists and all Fregeans and neo-Fregeans believe that they cannot be so substituted. Fregeans of various stripes have used their intuition against free substitution to argue against the direct designation theory. Some direct designation theorists have used the same intuitions to argue against the view that belief reports of simple declarative sentences can be accounted for with singular propositions. 1 This paper has two main goals; first, to show that the discussion of the issue has tended to treat all epistemic contexts equally, and second, to argue that we should not treat substitutions in contexts that involve justification (and hence knowledge) in the same way as we treat substitution in simple belief contexts, i.e., contexts that just involve the belief relation. I.

An Invitation to Formal Reasoning. The Logic of Terms

Contents: Reasoning: Introduction The form of an argument A word about the form of statements The form of singular statements Terms and statements Symbolizing compound statements A word about validity How material expressions are meaningful Terms Some terms are 'vacuous' Statement meaning Truth and correspondence to facts Propositions 'States of affairs' The facts and the facts What statements denote Summary and discussion on the meaning of statements Picturing Propositions: State diagrams Representing singular propositions Entailments Negative entailments States and states Positive and negative 'valence' The limitations of state diagrams The statement use of sentences Truth relations Logical syntax.

A puzzle about de rebus beliefs

and he found that their logic cannot be adequately formalized within the first-order predicate calculus. If we try to formalize the sentence by a paraphrase using individual variables that range over critics, or over sets or collections or fusions of critics, we misrepresent its logical structure. To represent plural quantification adequately requires the logical resources of the full second-order predicate calculus.1 The thoughts expressed by plurally quantified statements can be objects of belief, consternation, wonder, puzzlement, and desire, just as other thoughts can, but, when we try to describe the propositions such sentences express, a curious puzzle arises. There is a de dicto reading of ‘Ralph believes there are critics who admire only one another’, according to which Ralph believes the proposition that is expressed by the Geach-Kaplan sentence; that reading is unproblematic. The puzzle comes when we turn to what we may call the de rebus reading, according to which there are some critics of whom Ralph believes that they admire only one another.2 The standard theory of propositions accounts for the distinction between de dicto or notional3 propositional attitude reports and de re or relational propositional attitude reports by proposing that the two kinds of reports describe two kinds of propositions. The de dicto reading of ‘Ralph believes someone is a spy’ attributes to Ralph the belief in an existential proposition that can be symbolized ‘$x x is a spy’. The de re reading avows that Ralph believes one of the de re or singular propositions in the range of the propositional function defined by the English open sentence ‘that he is a spy’; for some individual x, Ralph believes of x that he is a spy. Analogously, we may understand the de rebus reading of ‘Ralph believes there ANALYSIS 60.4 October 2000

A puzzle about de rebus beliefs

and he found that their logic cannot be adequately formalized within the first-order predicate calculus. If we try to formalize the sentence by a paraphrase using individual variables that range over critics, or over sets or collections or fusions of critics, we misrepresent its logical structure. To represent plural quantification adequately requires the logical resources of the full second-order predicate calculus.1 The thoughts expressed by plurally quantified statements can be objects of belief, consternation, wonder, puzzlement, and desire, just as other thoughts can, but, when we try to describe the propositions such sentences express, a curious puzzle arises. There is a de dicto reading of ‘Ralph believes there are critics who admire only one another’, according to which Ralph believes the proposition that is expressed by the Geach-Kaplan sentence; that reading is unproblematic. The puzzle comes when we turn to what we may call the de rebus reading, according to which there are some critics of whom Ralph believes that they admire only one another.2 The standard theory of propositions accounts for the distinction between de dicto or notional3 propositional attitude reports and de re or relational propositional attitude reports by proposing that the two kinds of reports describe two kinds of propositions. The de dicto reading of ‘Ralph believes someone is a spy’ attributes to Ralph the belief in an existential proposition that can be symbolized ‘$x x is a spy’. The de re reading avows that Ralph believes one of the de re or singular propositions in the range of the propositional function defined by the English open sentence ‘that he is a spy’; for some individual x, Ralph believes of x that he is a spy. Analogously, we may understand the de rebus reading of ‘Ralph believes there ANALYSIS 60.4 October 2000

Newton's Propositions on Comets: Steps in Transition, 1681–84

Isaac Newton's closest approach to a system of the world in the critical period 1681–84 is provided in a set of untitled propositions concerning comets. They drastically revise his position maintained against Flamsteed in 1681 and may signal his adoption of a single comet solution for the appearances of 1680/1. Points of agreement and difference with the key pre-Principia texts of 1684–85 are analysed. He shows substantial control of the phenomena of tails which change very little in mechanical detail throughout his subsequent work. An emerging theory of gravitation brings planets, their satellites, and comets under the same laws of motion, yet retains a celestial vortex and includes a singular proposition in lieu of the usual formulation of Keplers area law. The analysis raises questions on a number of issues of recent Newtonian scholarship ranging from his achievement following his correspondence with Robert Hooke in 1679 to his veneration of the wisdom of the ancients.

Singular Propositions and Singular Thoughts

The core of the debate between Fregeans and Russellians in the philosophy of language concerns the content of object-dependent propositions, or how we ought to individuate and semantically represent the content of propositions that are about specific individuals. This essay is an investigation of the contemporary status of this debate. My aim is to show how the causal theorists' picture of reference determination entails the need for both Fregean and Russellian conceptions of propositional content in the study of mind and language, and to investigate some of the consequences of this position.

A Basic Classification of Legal Institutions

The author offers a general definition of legal institutions. A distinction between institutional legal concepts, legal institutions and social institutions makes it possible to define legal institutions as systems of valid presentations of what must occur in social reality in order that the former can be said also to exist as social institutions. Weinberger's idea, that the relation of legal institutions (practical information) to reality is the exact reverse of that between propositions (theoretical information) and reality, is subsequently used in developing a basic classification of legal institutions by analogy with the traditional division of elements of singular propositions in definite descriptions, properties and relations.

Explaining referential/attributive

Kaplan, Stalnaker and Wettstein all urge a two-stage theory of language whereon the propositions expressed by sentences are generated prior to being evaluated. A new ambiguity for sentences emerges, propositional rather than syntactic or semantic. Kaplan and Wettstein then propose to explain Donnellan's referential/attributive ambiguity as simply being two-stage propositional ambiguity. This is tacitly seen as further confinnation for twostage theory. Modal ambiguities are prime motivators for two-stage theory, which distinguishes local from exotic evaluation to explain them. But if sentences can be found which exhibit both modal and referential/attributive ambiguity, an apparent paradox arises for a two-stage account. The theory recognizes both singular and general propositions, in Kaplan's senses. But reflecting one sense of such a doubly ambiguous sentence, two-stage theory would seem to need a proposition both singular and general with respect to a definite description attributively used. Since modal operators will come into rendering the problem sentences, an obvious idea is to let scope distinctions rescue two-stage theory from the apparent paradox. But while a rescue based on multiple renderings is proposed, it is not strictly a scope rescue, though different scopes are involved. Readers are asked to trust the author on missing formalities of an intuitively transparent two-sorted modal language that is employed. Two-stage theorists explicitly oppose scope treatments of modal ambiguities seeing them as rivals. Stalnaker, in particular, argues against them. But his arguments are shown not to count against the proposed rescue, on which the anticipated rivalry proves to be minimal.

Singular Propositions and Modes of Presentation

Singular Propositions and Modes of Presentation

Singular Propositions and the A Priori

Singular Propositions and the A Priori

Os objetos têm história? Encontro de Pasteur com Whitehead num banho de ácido láctico

Did Pasteur discover, construct, invent lactic acid? This Gordian knot in social studies of the sciences is happily cut when the scene played out at Lille in 1857 is peopled with Whiteheadean conceptual characters. The Nature addressed by Pasteur does not speak the language of scientific utterances but neither is it mute; it is imbued with propositions. Insofar as Pasteur plays the character of a scientist, he is 'acted on' by a singular proposition -- "a tale that perhaps might be told," as Whitehead would say, but that will only be true or false if Pasteur manages to make a real world correspond to this proposition, a world capable of providing logical subjects, and thus offering proof to "whomever judges with impartiality." A hybrid-mediator-translator of Pasteurian and microorganismic propositions, the experimental environment "makes the event," in an encounter from which a new Pasteur and a new yeast emerge, partners of a new history.

Ramachandran vs. Russell

Murali Ramachandran [3] has put forward a new objection to Russell's theory of descriptions (RTD). According to RTD, sentences of the form 'the F is G' (let's call them 'description sentences') express quantified propositions expressible as (e.g.) 'there is exactly one F and whatever is F is G' (let's call these 'uniqueness propositions'). If a description sentence expresses a uniqueness proposition rather than a singular, object-dependent proposition, then, as RTD explains, the sentence can be meaningful even if nothing answers to the definite description it contains. Now Ramachandran concedes, without taking up specific Russellian accounts, that RTD can handle Strawson's objection that a description 'the F' can be used to talk about a particular F even when it is mutually known that there is more than one E A 'plausibly-embellished' version of RTD can reckon not only with the fact that definite descriptions are often incomplete, in which case there is no unique F, but with the fact that they can be used to refer to a certain object in particular. Ramachandran grants that the 'context' can complete the description or delimit the domain of quantification, thereby determining the uniqueness proposition being expressed, and also, if the speaker intends to express a singular proposition, aid in the singling-out of the intended object of reference. Ramachandran can concede all this because, he believes, his objection has independent force against RTD. The new objection is based on a difference between description sentences and their Russellian paraphrases. Ramachandran relies on the example of an utterance of (1),

Singular propositions in time

D'apres Russell, dans une phrase, l'objet x dans sa realite est un constituant de la proposition. L'article s'appuie sur une remarque de G. Forbes montrant que cette theorie pose probleme par rapport au temps. En effet, la proposition singuliere fait-elle encore sens lorsque le referent reel disparait ou se modifie?