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- Christopher Gauker (1997). Universal Instantiation: A Study of the Role of Context in Logic. Erkenntnis 46 (2):185-214.The rule of universal instantiation appears to be subject to counterexamples, although the rule of existential generalization is not subject to the same doubts. This paper is a survey of ways of responding to this problem, both conservative and revisionist. The conclusion drawn is that logical validity should be defined in terms of assertibility in a context rather than in terms of truth on an interpretation. Contexts are here defined, not in terms of the attitudes of the interlocutors, but in terms of the goals of conversation, and assertibility is explained in terms of cooperation.
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The essay undertakes to explore the possibilities of mutually fruitful dialogue between moral philosophy and ontology, in particular, the ontology of relations. The latter copes with the question of how relations relate, whereas moral philosophy often ignores the ontological implications of such crucial relations as love and interpersonality. The paper proceeds as follows. First, the ontology of relations is discussed. Second, various examples are analysed. From this, a conception of relation instantiation emerges, according to which to determine which relation actually obtains, one has to take into account (a) the context, (b) the specific content or meaning of the relation, and (c) some action or decision or mode of existence of the relata. This conception suggests that relation instantiation cannot be explained by a single formula. By the help of this conception, Hume''s thesis of the identity of killing relations between human and nonhuman beings is questioned. Then, the relation of love is analysed. It is shown that love as a moral relation is perfectly explicable in terms of ontology. Moreover, its essence is best captured by the interrelation of the particulars, the relation of love as a universal, and by the relating action of the particulars. Finally, the alleged relation of universal fraternity (interpersonality as such), linking up each human being to all other human beings, is discussed.
For many purposes in pragmatics one needs to appeal to a context of utterance conceived as a set of sentences or propositions. The context of utterance in this sense is often defined as the set of assumptions that the speaker supposes he or she shares with the hearer. I argue by stages that this is a mistake. First, if contexts must be defined in terms of shared assumptions, then it would be preferable to define the context as the set of assumptionsthat the interlocutors really do share. Second, not all shared assumptions belong to the context, because not all are relevant. Third, hearers need not accept every member of the context, because some presuppositions are informative. Finally, presupposition coordination problems show that contexts may have contents that even the speaker does not accept. Contexts, we may conclude, are mind-transcendent. In one sense of the term a "presupposition" is an interlocutor's take on this mind-transcendent context.
The truth-conditional theory of sense holds that a theory of truth for a natural language can serve as a theory of sense: if knowledge of a theory of truth for a language L is sufficient for understanding utterance of L-sentences, the T-sentences of the theory 'show' the sense of the uttered object-language sentences. In this paper I aim to show that indexicals create a serious problem for this prima facie attractive theoretical option. The so-called 'instantiation problem' is that a truth-theory for indexical languages needs to contain universal statements that show how the reference of indexicals depends on features of the utterance context. Now one can deduce from such statements T-sentences that do not show the sense of an indexical sentence on an occasion of use. I survey proposed solutions to the instantiation problem by Evans and Sainsbury and, unfortunately, find them all wanting. Perhaps there is nothing like the sense-giving truth-condition for an indexical sentence.
This paper argues that truth is by nature context-dependent – that no truth can be applied regardless of context. I call this “strong contextualism”. Some objections to this are considered and rejected, principally: that there are universal truths given to us by physics, logic and mathematics; and that claiming “no truths are universal” is self-defeating. Two “models” of truth are suggested to indicate that strong contextualism is coherent. It is suggested that some of the utility of the “universal framework” can be recovered via a more limited “third person viewpoint”. Keywords: philosophy, universality, context, truth, knowledge.
states are to be understood in terms of their functional relationships to other mental states, not in terms of their material instantiation in any particular kind of hardware. But the argument that material instantiation is irrelevant to functional..
"If you turn left at the next corner, you will see a blue house at the end of the street." That sentence -- a conditional -- might be true even though it is possible that you will not see a blue house at the end of the street when you turn left at the next corner. A moving van may block your view; the house may have been painted pink; a crow might swoop down and peck out your eyes. Still, in some contexts, we might ignore these possibilities and correctly assert the conditional. In this book, Christopher Gauker argues that such context-relativity is the key to understanding the semantics of conditionals. Contexts are defined as objective features of the situation in which a conversation takes place, and the semantic properties of sentences -- conditionals included -- are defined in terms of assertibility in a context.
One of the primary goals of a theory of conditionals has to be to distinguish correctly between valid and invalid arguments containing conditionals. According to Gauker, an argument is valid if the conclusion is assertible in every context in which the premises are assertible. This runs counter to what Gauker sees as a systematic misreading of the data by other authors, who judge arguments to be invalid if they can think of a context in which the premises are judged true and some other context in which the conclusion is judged false. Different schools of thought on conditionals reflect fundamentally different approaches to semantics. Gauker offers his theory as a motive and test case for a distinctive kind of semantics that dispenses with reference relations and possible worlds.
Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics.
The co-instantiation thesis is pivotal to a significant solution to the problem of causal exclusion. But this thesis has been subject to some powerful objections. In this paper, I argue that these difficulties arise because the thesis lacks the necessary metaphysical framework in which its claims should be interpreted and understood. Once this framework is in place, we see that the co-instantiation thesis can answer its critics. The result is a rehabilitated co-instantiation solution to the troubling problem of causal exclusion. But questions remain concerning the viability of certain of its applications.
In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, which allows for both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication.
This introduction to rigorous mathematical logic is simple enough in both presentation and context for students of a wide range of ages and abilities. Starting with symbolizing sentences and sentential connectives, it proceeds to the rules of logical inference and sentential derivation, examines the concepts of truth and validity, and presents a series of truth tables. Subsequent topics include terms, predicates, and universal quantifiers; universal specification and laws of identity; axioms for addition; and universal generalization. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. 1964 edition. Index.
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