Second-Order Modal Logic
01 Jan 2017-
TL;DR: This dissertation develops an inferentialist theory of meaning by developing a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which the authors can reflect on the norms governing the assertion and denial conditions of their language.
Abstract: This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. Second-Order Modal Logic
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213 citations
01 Jan 1979
TL;DR: If the authors are asked what, in general, it is that someone knows when he knows the meaning of a word, it seems natural enough to reply: what that word stands for.
Abstract: If we are asked what, in general, it is that someone knows when he knows the meaning of a word, it seems natural enough to reply: what that word stands for. ‘Stands for’ is of course a metaphor. The phrase suggests a model or picture, of what happens when a language is instituted. The picture it suggests is this. There is an object in the world, and the word serves as a substitute for that object; as, that is, a kind of proxy: something that does duty for, or stands in place of the object.
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Book•
01 Jan 1965
1,157 citations
"Second-Order Modal Logic" refers background in this paper
...2 shows how PHIL solves the above (3)For more on the importance of these features of a calculus see Belnap [4], Prawitz [41], and Humberstone [21]....
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Book•
01 Jan 1991
TL;DR: Michael Dummett's new book is the greatly expanded and recently revised version of his distinguished William James Lectures, delivered in 1976, and shows how the choice between different logics arises at the level of the theory of meaning and depends upon the choice of one or another general form of meaning-theory.
Abstract: Michael Dummett's new book is the greatly expanded and recently revised version of his distinguished William James Lectures, delivered in 1976. Dummett regards the construction of a satisfactory theory of meaning as the most pressing task of contemporary analytical philosophy. He believes that the successful completion of this difficult assignment will lead to a resolution of problems before which philosophy has been stalled, in some instances for centuries. These problems turn on the correctness or incorrectness of a realistic view of one or another realm--the physical world, the mind, the past, mathematical reality, and so forth. Rejection of realism amounts to adoption of a variant semantics, and often of a variant logic, for the statements in a certain sector of our language. Dummett does not assume the correctness of any one logical system but shows how the choice between different logics arises at the level of the theory of meaning and depends upon the choice of one or another general form of meaning-theory. In order to determine the correct shape for a meaning-theory, we must attain a clear conception of what a meaning-theory can be expected to do. Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base camp."
944 citations
"Second-Order Modal Logic" refers background in this paper
...44 As is noted by Dummett [13] ([13, pg.257]), in some cases this may not be problematic....
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...Philosophers such as [13] opt for the former option....
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...Belnap [4], Dummett [13], or Poggiolesi [39], that in order for a set of rules to determine the meaning of an expression the set must meet several constraints....
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...Ultimately, this dissertation takes its cue from Dummett’s The Logical Basis of Metaphysics : it attempts to shed light on difficult metaphysical questions by an examination of a theory of the meaning of the expressions used in discussion of those metaphysical questions....
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...It has been proposed, by e.g. Belnap [4], Dummett [13], or Poggiolesi [39], that in order for a set of rules to determine the meaning of an expression the set must meet several constraints....
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Book•
01 Jun 1937
TL;DR: Carnap's entire theory of language structure appeared in The Logical Syntax of Language (1934) as mentioned in this paper, which led to his famous "Principle of tolerance" by which everyone is free to mix and match the rules of his logic in any way he wishes.
Abstract: Rudolf Carnap's entire theory of Language structure "came to me," he reports, "like a vision during a sleepless night in January 1931, when I was ill." This theory appeared in The Logical Syntax of Language (1934). Carnap argued that many philosophical controversies really depend upon whether a particular language form should be used. This leads him to his famous "Principle of tolerance" by which everyone is free to mix and match the rules of his language and therefore his logic in any way he wishes. In this way, philosophical issues become reduced to a discussion of syntactical properties, plus reasons of practical convenience for preferring one form of language to another. In a tour de force of precise reasoning, Carnap also indicated how two model languages could be constructed. This is one of three books which Open Court is making available in paperback reprint in its Open Court Classics series. The other two are Carnap's The Logical Structure of the World and Schlick's General Theory of Knowledge.
894 citations
Book•
01 Jan 2013
TL;DR: The Barcan Formula and its Converse: Early Developments 3. Possible Worlds Model Theory 4. Predication and Modality 5. From First Order to Higher-Order Modal Logic 6. Intensional Comprehension Principles and Metaphysics 7. Mappings between Contingentist and Necessitist Discourse 8. Consequences of necessitism as discussed by the authors.
Abstract: Preface 1. Contingentism and Necessitism 2. The Barcan Formula and its Converse: Early Developments 3. Possible Worlds Model Theory 4. Predication and Modality 5. From First-Order to Higher-Order Modal Logic 6. Intensional Comprehension Principles and Metaphysics 7. Mappings between Contingentist and Necessitist Discourse 8. Consequences of necessitism Methodological Afterword Bibliography Index
466 citations
"Second-Order Modal Logic" refers background in this paper
...Williamson [74] argues that a contingentist logic must have free first-order quantifiers....
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...Necessitism has been described by Williamson [74] as the view that necessarily everything is necessarily something, or that what does exist exists in every possible world and what exists in any possible world exists in the actual world....
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...Williamson [74] argues that a logic with free first-order quantification ought also to use free second-order quantification....
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...A second problem for contingentists has been raised by Williamson [74]....
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...Prior [43] and Williamson [74] propose problems for a logic that can capture contingentism....
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Book•
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01 Jan 1974
TL;DR: In this paper, the authors define the notion of symbol and idea in the context of metaphysics, and propose a set of symbols and ideas for symbol-and idea-based semantics.
Abstract: of Semantics I.- 1. Goal.- 2. Method.- 1. Designation.- 1. Symbol and Idea.- 1.1. Language.- 1.2. Construct.- 1.3. Predicate.- 1.4. Theory and Language.- 2. Designation.- 2.1. Name.- 2.2. The Designation Function.- 3. Metaphysical Concomitants.- 3.1. Basic Ontology.- 3.2. Beyond Platonism and Nominalism.- 2. Reference.- 1. Motivation.- 2. The Reference Relation.- 2.1. An Unruly Relation.- 2.2. Immediate and Mediate Reference.- 2.3. Reference Class.- 2.4. Factual Reference and Object Variable.- 2.5. Denotation.- 2.6. Reference and Evidence.- 2.7. Misleading Cues in the Search for Referents.- 3. The Reference Functions.- 3.1. Desiderata.- 3.2. Principles and Definitions.- 3.3. Some Consequences.- 3.4. Context and Coreference.- 4. Factual Reference.- 4.1. The Factual Reference Class.- 4.2. The Factual Reference Class of Scientific Theories.- 4.3. Spotting the Factual Referents: Genuine and Spurious.- 4.4. The Strife over Realism in the Philosophy of Contemporary Physics.- 5. Relevance.- 5.1. Kinds of Relevance.- 5.2. The Paradox of Confirmation as a Fallacy of Relevance.- 6. Conclusion.- 3. Representation.- 1. Conceptual Representation.- 2. The Representation Relation.- 2.1. A Characterization.- 2.2. The Multiplicity of Representations.- 2.3. Transformation Formulas and Equivalent Theories.- 3. Modeling.- 3.1. From Schema to Theory.- 3.2. Problems of Modeling.- 4. Semantic Components of a Scientific Theory.- 4.1. Denotation Rules and Semantic Assumptions.- 4.2. Philosophical Commitment of the SA's.- 4.3. Application to Quantum Mechanics.- 5. Conclusion.- 4. Intension.- 1. Form is not Everything.- 1.1. Concepts of Sense.- 1.2. Extension Insufficient.- 1.3. 'Intensional': Neither Pragmatic nor Modal.- 2. A Calculus of Intensions.- 2.1. Desiderata.- 2.2. Principles and Definitions.- 2.3. Main Theorems.- 2.4. Intensional Difference and Family Resemblance.- 3. Some Relatives - Kindred and in Law.- 3.1. Logical Strength.- 3.2. Information.- 3.3. Testability.- 4. Concluding Remarks.- 5. Gist and Content.- 1. Closed Contexts.- 1.1. Closed Contexts and Their Structure.- 1.2. The Logical Ancestry of a Construct.- 2. Sense as Purport or Logical Ancestry.- 2.1. Purport and Gist.- 2.2. The Gist of a Basic Construct.- 2.3. The Gist of a Theory.- 2.4. Changes in Gist.- 3. Sense as Import or Logical Progeny.- 3.1. The Logical Progeny of a Construct.- 3.2. Import.- 3.3. Theory Content.- 3.4. Empirical and Factual Content.- 3.5. Changes in Import and Content.- 4. Full Sense.- 5. Conclusion.- Index of Names.- Index of Subjects.
435 citations
"Second-Order Modal Logic" refers background in this paper
...In principle mathematicians can, as Frege hoped, converse with one another in formal languages....
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...If one held, as philosophers such as Frege [16] and Geach [18] did, that sentences featuring non-denoting names had no truth-value, then option (4) would appear best....
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...It also holds the Fregean thesis that expressions in a v language have both a sense and a reference....
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