Supposition theory is a medieval account of the semantics of terms as they function in sentences. The word >supposition= is probably interchangeable with our word >reference=, but I=ll leave it as >supposition= so as to identify the medieval source of the theory I discuss here. Medieval writers had a great deal to say about supposition; this paper focuses on only one part of the theory, the study of what is now generally called the theory of modes of common personal supposition. (...) The word >common= is used here as in >common term=, as opposed to >singular term=, but in fact, the theory focuses on common terms along with the quantifiers that accompany them. The word >personal= is a technical term indicating that the word in question is used in its normal way to refer to the things it is true of, as distinguished from occurrences in which it refers to itself (as in >Giraffe is a noun=) or refers to a particular thing intimately related to the things it is true of (as in >Giraffe is a species=). So we might describe this as a theory of the modes of reference of quantified common terms used normally. There are three such modes, illustrated as follows: DETERMINATE: The term >dingo= has determinate supposition in: Some dingo is a predator. Determinate supposition has something to do with existential quantification. Exactly what it has to do with existential quantification is a question to be discussed. DISTRIBUTIVE: The term >dingo= has distributive supposition in: 1 Every dingo is an animal. Distributive supposition has something to do with universal quantification. MERELY CONFUSED: The term >dingo= has merely confused supposition in: Every predator is a dingo. Merely confused supposition has something to do with existential quantification that occurs within the scope of a universal quantification. (shrink)
Spade 1988 sugges t s tha t t he r e are ac tua l l y two theo r i e s t o address t h i s ques t i o n t o , an ear l y one and a l a t e r one . 2 Most o f the presen t pape r i s a deve l o pmen t o f t h i s i dea . I sugges t (...) tha t ear l y work by Sherwood and o the r s was a s tudy o f quan t i f i e r s : the i r semant i c s and t he e f f e c t s o f con t e x t on i n f e r e n ce s t ha t can be made f r om quan t i f i e d te rms . La te r , i n the hands o f Bur l e y and o the r s , i t changed i n t o a s tudy o f someth i n g e l se , a s tudy o f what I ca l l g loba l quan t i f i c a t i o n a l e f f e c t . In sec t i o n 1 , I exp l a i n what these two op t i o n s are. (shrink)
The Treatise on Univocation is an early work on the fallacy called univocation. This fallacy is a kind of ambiguity due to the shifted reference of words in a sentence when the ambiguity does not fall under the well-known Aristotelian kinds (equivocation, composition and division, . . .). Examples include the shift of reference of common terms due to tense and modality; e.g. the shift whereby the reference of 'giraffe' is extended to past or future giraffes when the tense of (...) the sentence 'A giraffe is spotted' is made past or future, and the shift whereby the reference of 'giraffe' is extended to merely possible giraffes in the sentence 'A giraffe can be spotted'. The translation is by Elizabeth Karger. (shrink)
Methods of representing sentences containing mass terms (e.g. "gold") and amount terms (e.g. "three gallons") within the predicate calculus are given, and the semantics of the resulting sentences is discussed. the appendix sketches a way to systematically translate english sentences into the logical notation, exploiting some results of transformational grammar.
. The truth conditions that Aristotle attributes to the propositions making up the traditional square of opposition have as a consequence that a particular affirmative proposition such as ‘Some A is not B’ is true if there are no Bs. Although a different convention than the modern one, this assumption remained part of centuries of work in logic that was coherent and logically fruitful.
This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)
Peter Geach describes the ?doctrine of distribution? as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...) distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ?taken universally?, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected. (shrink)
Bhartṛhari claims that certain things cannot be signified--for example, the signification relation itself. Hans and Radhika Herzberger assert that Bhartṛhari's claim about signification can be validated by an appeal to twentieth-century results in set theory. This appeal is unpersuasive in establishing this view, but arguments akin to the semantic paradoxes (such as the "liar" paradox) come much closer. Unfortunately, these arguments are equally telling against another of his views: that the thatness of the signification relation can be signified. Bhartṛhari also (...) claims that the relation of inherence cannot be signified--a quite different view that is not borne out by twentieth-century results. Finally, further research is needed to investigate what Bhartṛhari's own reasons might have been for these views. (shrink)
Terence Parsons presents a lively and controversial study of philosophical questions about identity. Because many puzzles about identity remain unsolved, some people believe that they are questions that have no answers and that there is a problem with the language used to formulate them. Parsons explores a different possibility: that such puzzles lack answers because of the way the world is (or because of the way the world is not). He claims that there is genuine indeterminacy of identity in the (...) world. He articulates such a view in detail and defends it from a host of criticisms. (shrink)
I begin by sketching a theory about the semantics of verbs in event sentences, and the evidence on which that theory is based. In the second section, I discuss the evidence for extending that theory to state sentences, including copulative sentences with adjectives and nouns; the evidence for this extension of the theory is not very good. In the third section, I discuss new evidence based on considerations of talk about time travel; that evidence is apparently quite good. I conclude (...) with a problem about formulating default knowledge. (shrink)
We presume a background theory which allows for indeterminacy of states of affairs involving objects, extending even to indeterminacy of identity between objects. A sentence reporting such an indeterminate state of affairs lacks truth-value. We extend this to a theory of sets, similar to ZFU, in which membership in, and identity between, sets may also be indeterminate.
This paper follows up a suggestion by Paul Vincent Spade that there were two Medieval theories of the modes of personal supposition. I suggest that early work by Sherwood and others was a study of quantifiers: their semantics and the effects of context on inferences that can be made from quantified terms. Later, in the hands of Burley and others, it changed into a study of something else, a study of what I call global quantificational effect. For example, although the (...) quantifier in ¬xPx is universal, it can be seen globally as having an existential effect; this is because the formula containing it is equivalent to x¬Px. The notion of global effect can be explained in terms of the modern theory of normal forms. I suggest that early authors were studying quantifiers, and the terminology of the theory of personal supposition is a classification of kinds of quantifiers. In this theory, to say that a term has distributive supposition is to say, roughly, that it is quantified by a universal quantifying sign. Later authors turned this into a theory of global quantificational effect. In the later theory, to say that a term has distributive supposition is to say that the overall effect is as if the term were universally quantified with a quantifier taking (relatively) wide scope. The difference between these two approaches is illustrated by the fact that the term man is classified as having distributive ("universal") supposition in Not every man is running in the earlier theory, whereas in the later theory that term does not have distributive supposition; it has determinate ("existential") supposition. In the paper I explain these options, and I argue from several texts that the earlier and later medieval theories actually worked like this. In an appendix I make further efforts to clarify the obscure early accounts, as well as the nineteenth century "doctrine of distribution". The last section of the paper discusses the "purpose(s)" of supposition theory. (shrink)
It is tempting to think that Meinong overlooked the "specific/nonspecific" distinction. For example, 'I am looking for a grey horse' may either mean that there is a specific horse I am looking for (e.g. one I lost), or just that I am grey-horse-seeking. The former reading, and not the latter, requires for its truth that there be a grey horse. The purpose of this paper is to investigate whether it is defensible to maintain Meinong's theory here: to take nonspecific reading (...) of any verb concerning a possibly non-existent but incomplete object. This requires essential appeal to the distinction between nuclear and extranuclear properties. Included is a discussion of criticisms of Meinong's own theory, and of the Medieval theory of ampliation, according to which psychological discourse can "ampliate" a term such as 'chimera' so as to stand for one or more things that cannot exist, yet are chimeras. The paper concludes inconclusively. (shrink)
This paper arose from an attempt to determine how the very late medieval1 supposition theorists treated anaphoric pronouns, pronouns whose significance is derivative from their antecedents. Modern researches into pronouns were stimulated in part by the problem of "donkey sentences" discussed by Geach 1962 in a section explaining what is wrong with medieval supposition theory. So there is some interest in seeing exactly what the medieval account comes to, especially if it turns out, as I suspect, to work as well (...) as contemporary ones. Besides, finding a good analysis of pronouns has proved to be very difficult, and so we might possibly find some insight in a historically different kind of approach. I discuss a version of supposition theory that aims at producing analyses of sentences containing quantified terms,2 as articulated around 1400 by Paul of Venice, and as further developed by certain logicians such as de Soto and Celaya in the 1400's and early 1500's.3 Much of what I will say also applies indirectly to earlier versions of supposition theory (before 1400). (shrink)
This paper has two goals. The first is to formulate an adequate account of the semantics of the progressive aspect in English: the semantics of Agatha is making a cake, as opposed to Agatha makes a cake. This account presupposes a version of the so-called Aristotelian classification of verbs in English into EVENT, PROCESS and STATE verbs. The second goal of this paper is to refine this classification so as to account for the infamous category switch problem, the problem of (...) how it is that modification of a verb like run by an adverbial like to the store can turn a PROCESS phrase (run) into an EVENT phrase (run to the store). Views discussed include those of Aqvist, Bach, Bennett, Bennett and Partee, Dowry, Montague and Scott, and Vendler. (shrink)
Frege held various views about language and its relation to non-linguistic things. These views led him to the paradoxical-sounding conclusion that "the concept horse is NOT a concept." A key assumption that led him to say this is the assumption that phrases beginning with the definite article "the" denote objects, not concepts. In sections I-III this issue is explained. In sections IV-V Frege's theory is articulated, and it is shown that he was incorrect in thinking that this theory led to (...) the conclusion that "the concept horse is not a concept." Section VI goes on to show that his strict theory about the functioning of ordinary language is inconsistent. Sections VII-VIII investigate Frege's reasons for thinking that "the concept horse" must denote an object; these reasons are not adequate on Frege's own grounds. Section IX sketches a systematic way to allow such phrases to denote concepts (not objects) within the framework of Frege's main views about language. Section X comments briefly on the consequences of this idea for his logistic program. (shrink)
This paper explores the view that there are such things as (nonexistent) fictional objects, and that we refer to such objects when we say things like "Sherlock Holmes is a fictional detective", or "Conan Doyle wrote about Sherlock Holmes". A theory of such objects is developed as a special application of a Meinongian Ontology.
This is a short note indicating how I would revise an earlier paper ("an analysis of mass terms and amount terms," "foundations of language", Volume 6, Number 3, 1970) in the light of criticisms that have been made of it.
This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. slowly in x drives slowly) in a logically perspicuous notation. A proposal of Reichenbach's is given and criticized; then a new theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some problems (...) concerning applications of adjectives to that-clauses and gerundive-clauses are discussed. (shrink)