Countering counterpart theory countering counterpart theory sagal, paul t. Lewis interprets modal claims by using a translation from quantified modal logic into the counterpart theory. David kellogg lewis september 28, 1941 october 14, 2001 was an american philosopher. Unquantified logic, modal or not, is much weaker in its expressive power than quantified one.
Handout 15 tree conversion metatheory for quantified modal logic april 10 pages 5960. Counterpart theory still presupposes possible worlds, but differs in certain important respects from the kripkean view. Parts, counterparts, and modal occurrents columbia university. Significant parts of modal discourse involve either implicit or explicit reference to what is actually the case, raising the question of how talk.
Handout 16 expanding substitutional to intensional models april 15. Counterpart theory, quantified modal logic, and extra. In this paper, i shall outline some basic ideas of a semantical theory of modal logic, including quantified modal logic. Logically possible worlds and counterpart semantics for modal logic. Model theory of modal logic 251 over the given frame in e. Basic results about these concepts are stated and some simple. These keywords were added by machine and not by the authors.
Whilst qml adds modal operators the box necessity and diamond possibility to our existing firstorder logic, lewiss counterpart theory simply extends the domain of quantification of firstorder logic, so that it. The survival of my counterpart the survival of my counterpart french, peter a. More precisely, let us call x a worldstage of y iff 1 x is a possible individual. Counterpart theory w t te can conduct formalized discourse about most topics perfectly well bv means of our allpurpose extensional logic, provided with predicates and a domain of quanti fication suited to the subject matter at hand. This approach is described in a very beautiful paper by david lewis of ucla, called counterpart theory and quantified modallogic, which appeared in. It turns out to be a limit case of the categorical semantics. Or what is not the same there is a crossworld individual which is a maximal counterpartinterrelated sum of possible individuals of whom i am one. Ordinary language is notoriously ambiguous and the analysis of ordinary language modal operators is fraught with difficulty. Lewis taught briefly at ucla and then at princeton from 1970 until his. Lewis counterpart theory and quantified modal logic the journal of philosophy, p.
Giving alternative semantics that avoids them is an active project. Basic concepts in modal logic1 stanford university. Unfortunately, this choice does not correspond to an intuitively satisfying semantics. To solve these puzzles, the usual interpretation rules of counterpart theory must be extended beyond the simple language of quantified modal logic. Due to the flexibility of semantics of the counterpart theory, lewiss translation may. It is an open question whether there are appropriate ways to. Counterpart theory and quantified modal logic 41 counterparts. Counterpart theory and quantified modal logic oxford scholarship. Counterpart theory and quantified modal logic andrew m. In order to meet this challenge, lewis modifies his counterpart theory to allow for multiple counterpart relations e. By regimenting our discourse into formal quantified modal logic we can eliminate some of these ambiguities.
By regimenting our discourse into formal quantified modal logic we can eliminate some of. Counterpart theory and quantified modal logic lewis youtube. Counterpart semantics is proposed as the appropriate semantical framework for a foundational investigation of quantified modal logics. In his counterpart theory and quantified modal logic 1968, lewis offers a radical alternative to qml.
Uncontested principles of modal logic while lewis 1968. The logic of counterpart theory with actuality university of michigan. Counterpart theory and the paradox of occasional identity. Xs counterparts in other worlds are all and 3 counterpart theory and quantified modal logic, this journal, lxv, 5. In this tutorial, we give examples of the axioms, consider some rules of inference and in particular, the derived rule of necessitation, and then draw out some consequences.
Lewis, counterpart theory and quantified modal logic. Many philosophers, following david lewis, believe that we should look to counterpart theory, not quantified modal logic, as a means of understanding modal discourse. Counterpart theory and quantified modal logic authors. Or what is not the same there is a crossworld individual which is a maximal counterpart interrelated sum of possible individuals of whom i am one. In philosophy, specifically in the area of modal metaphysics, counterpart theory is an alternative to standard possibleworlds semantics for interpreting quantified modal logic. Handout 14 trees for quantified modal logic april 8 pages 5658. On the translation from quantified modal logic into the. Foundations of modal metaphysics columbia university. These notes are meant to present the basic facts about modal logic and so to provide a common. This means that the classic theory of quantification is not valid on the class of all kripke frames.
Over the past few years, different interpretations and developments of the view have been proposed. Combinations and completeness transfer for quantified. The simplest quantified modal logic sqml defines a class of firstorder modal languages, a semantic theory for those languages, and a complete system of axioms and rules of inference for the semantics. In light of the various ways the world could be arranged, it is plausible thatthere is a nearby possible world, which would be almost identical to the actual world, if it were actualized, where you and your modal counterpart disagree over modal belief p. Among the positions lewis defends are modal realism, materialism, socially contextualized formal semantics, and functionalism of the mind. A semantic perspective 3 chapters in this handbook. Yet there remain residual quinean worries in the epistemic case. The other is to give a detailed survey of the large variety of modal logic systems found in the literature, with an eye to both their formal properties consistency, completeness and their philosophi. The eight postulates constitutive of lewiss counterpart theory are expressed in an extensional first. The counterpart theory which was introduced by david lewis is an alternative semantics to the possible worlds semantics for quantified modal logic. Philosophical papers volume i oi oxford index journals.
Since a fuller treatment is easy to carry out on the basis of this outline. Counterpart theory has at least three advantages over quantified modal logic as a vehicle for formalized discourse about modality. Pdf counterpart semantics for quantified modal logic. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. Fragmentalism is a nonstandard version of atheory originally presented by kit fine. The eight postulates constitutive of lewiss counterpart theory are expressed in an. Lecture notes lecture notes will be made available in blackboard. To read them, youll need to have either adobe acrobat or adobe acrobat reader installed. Counterpart theory, quantified modal logic, and extra argument places. There is a difference, however, between quantified modal logic and its semantics in terms of possible worlds.
I is the relation of being a part of a world, c is the counterpart relation. That is plausible enough, for the counterpart relation is a relation of similarity. Counterpart semantics a foundational study on quantified. The survival of my counterpart, the southern journal of. In this tutorial, we give examples of the axioms, consider some rules of inference and in particular, the derived rule. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states an abstraction through implicit universal. On the translation from quantified modal logic into the counterpart. I in gar05 garson considers completeness for kripke structures with domains of intensional objects. Counterpart semantics for quantified modal logic department of. One is to explain what modal logic is, and how it is done. This process is experimental and the keywords may be updated as the learning algorithm improves. The possibility of a person switching bodies presents a challenge to lewiss conviction that necessarily, a person occupies a body at a time if and only if that person is identical with that body at that time.
This approach is described in a very beautiful paper by david lewis of ucla, called counterpart theory and quantified modal logic, which appeared in the march 1968 issue of the journal of philosophy. A modala word that expresses a modalityqualifies a statement. In this landmark paper, lewis outlines his theory of modality and counterparts. Transworld identity stanford encyclopedia of philosophy. Modal fragmentalism the philosophical quarterly oxford. Modal logic nest domain kripke frame counterpart theory rigid designator.
I in cor02 corsi tries to provide a completeness proof for qml systems based on classical and free logic, and kripkes theory of quanti. Buehler based on first order modal logic by fitting and mendelsohn january 5, 2015. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. Objections 1 a system of modal propositional logic is a bona fide logic only if it has a quantificational extension. Whilst qml adds modal operators the box necessity and diamond possibility to our existing firstorder logic, lewiss counterpart theory simply extends. The predicate logic is a free logic, permitting the empty domain, and nonreferring singular terms. I present a more comprehensive semantics that allows talking about pecific times and worlds, that takes into account the multiplicity and sortaldependence of counterpart relations, and that does. The six philosophers youll read in college college humor parody philosophy tube duration. You might be tempted to think that your modal belief is true. The reason we want to utilize modal logic is to precisify ordinary language. Counterpart theory and quantified modal logic oxford.
Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Modal logic and its applications encyclopedia of life. Examples for convenience, we reproduce the item logicmodal logic of principia metaphysica in which the modal logic is defined. Counterparts of persons and their bodies oxford scholarship. For example, the statement john is happy might be qualified by saying that john is usually happy, in which. For example, the statement john is happy might be qualified by saying that john is usually happy, in which case the term usually is functioning as a modal. In the next paragraph we highlight the unsatisfactory features of.
The novice may wonder why quantified modal logic qml is considered difficult. Kripkes objectual interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these quinean worries. Actualism the simplest quantified modal logic sqml. Or we can proceed more directly, speaking explicitly of possible worlds from the start. Indexicality glossary bibliography biographical sketch summary modal logic is a broad and rapidly expanding area of logic with applications to such. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. The quantified modal logic that lewis employs for this purpose has two salient features. Standardly counterpart theorists will need the two primitive symbols. David lewiss classic counterparttheoretic treatment of quantified modal logic fails to validate three of the least controversial principles of the propositional logic of metaphysical modality. Feb 20, 2014 the six philosophers youll read in college college humor parody philosophy tube duration. Topics discussed include possible worlds, counterpart theory, modality, personal identity, radical interpretation, language, propositional attitudes, the mind, and intensional semantics.
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