In this paper we offer a formallogical analysis of the famous reversibility objection against the second law of thermodynamics. This is part i of a twopart essay introducing case intensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. Relevant alternatives and subjunctivism epistemic closure and epistemic logic i. After pointing out shortcomings of standard systems of quantified modal logic, we introduce cifol, case intensional first order logic, as a newly established formal framework that helps to elucidate the notion of tracing. Accordingly, the journal invites papers in all of the traditional areas of philosophical logic, including but not limited to. This dissertation provides a new semantics for firstorder modal logic. Stepanov propositional logic of reflexive sentences or truth without contradiction d. In part i we introduced cifol, a caseintensional firstorder logic, as a general purpose quantified modal logic derived from bressan.
This volume seeks to further the use of formal methods in clarifying one of the central problems of. Such an intensional first order logic, or quantified modal logic. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things. This dissertation provides a new semantics for first order modal logic. The identity of individuals in a strict functional. The reversibility objection against the second law of thermodynamics viewed, and avoided, from a logical point of view. The identity of individuals in a strict functional calculus. Synonymy a binary relation between two equivalent but not identical expressions. This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of firstorder logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. This is part i of a twopart essay introducing caseintensional firstorder logic cifol, an easytouse, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressans general interpreted modal calculus yale university press 1972. The reversibility objection against the second law of. Aug 25, 20 this paper follows part i of our essay on caseintensional firstorder logic cifol. We introduce a framework of branching histories to take account of indeterminism. Caseintensional first order logic i toward a theory of sorts nuel belnap thomas muller.
Caseintensional logic as a framework for tracing things from case to case. The reader is asked to make the following changes in the enumeration of the axioms and theorems. Mar 22, 2014 cifol is defined in belnap and muller 20 j phil logic 20 as the firstorder fragment of aldo bressans higherorder modal typed calculus \mc u \. Apr 21, 2014 we illustrate the importance of tracing via a discussion of possible experiments in science and in everyday life. Case 2 uses the extensionof operator, converting a term of intensional. Caseintensional first order logic by nuel belnap and thomas muller download pdf 702 kb. We are still exploring what firstorder modal semantics should be.
Belnap department of philosophy, university of pittsburgh, 1001 cathedral of learning, pittsburgh, pa 15260, usa this paper follows part i of our essay on caseintensional firstorder logic cifol. Full text of nuel belnap on indeterminism and free action. Strong completeness defined contrasting the case of modal logic with the case of the standard propositional calculus, the first difference we come across is that. Deduction rules for caseintensional higherorder logic matthew dickau 4 of 11 the brackets in these expressions are optional. Backward chaining 31 start with query check if it can be derived by given rules and facts.
The perfect being argument in case intensional logic matthew dickau 2 of 9 this corresponds to a kind of preliminary premise of the perfect being argument. Classical firstorder logic can be extended in two different ways to serve. Here we refine and enrich cifol to take account of indeterminism, relying for that purpose on a branching structure that we call branching histories. The journal of philosophical logic provides a forum for work at the crossroads of philosophy and logic, old and new, with contributions ranging from conceptual to technical. The logical problem of the trinity and the strong theory of relative identity the logical problem of the trinity and the. The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modallogic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many. Cifol is a recent research focus of belnaps, as reflected in his own contribution to this volume. We show that in that framework we can account for the role of sortals in. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e.
But first we need to sketch the alternative framework. Caseintensional first order logic i toward a theory. Nuel belnap on indeterminism and free action thomas. To submit an update or takedown request for this paper, please submit an updatecorrectionremoval request. The perfect being argument in caseintensional logic matthew dickau 1 of 9 the perfect being argument in caseintensional logic the perfect being argument for gods existence is the following deduction.
It is philosophicallymotivated by the epistemic reading of modal operators and, in particular, three desiderata in the analysis of epistemic modalities. Arndt comparing sequent calculus and natural deduction in the light of linear logic units v. Universal logic iii estoril 2010 tutorial on truth values. In this introduction to the outstanding contributions to logic volume devoted to nuel belnaps work on indeterminism and free action, we provide a brief overview of some of the formal frameworks and methods involved in belnaps work on these topics. Journal of philosophical logic, volume 43, issue 5 springer. We start with the flexible notion of possible cases rather than possible worlds, and we apply carnaps method of extension and intension for terms and sentences uniformly, to arrive at the system of caseintensional first order logic, cifol. Muller department of philosophy, utrecht university, janskerkhof a, 3512 bl utrecht, the netherlands 1 n. David toman and damian niwinski, firstorder queries over temporal databases inexpressible in temporal logic, advances in database technology edbt 96, 10. The complexity of the dependence operator pdf paperity. Solving a special case of the intensional vs extensional. Agents can make inferences and report them to other agents to whom they are linked, but communication is restricted to the common vocabulary of the reporter and recipient.
This paper follows part i of our essay on caseintensional firstorder logic cifol. The perfect being argument in caseintensional logic. In cifol, truth is relative to cases, where cases play the formal role of worlds but with less pretension. The volume also contains an extended biographical interview with nuel belnap. Nuel belnap on indeterminism and free action som ebog. In caseintensional first oder logic, which derives from bressans work, a predication. Branching histories 0 1 nuel belnap 0 1 thomas m uller 0 1 0 t. From highest priority to lowest, the order of operations for the truthfunctional connectives is. In the first case, extensional synonymy is being considered, for example, a. We introduce a framework of branching histories to. Our system bhcifol adds structure to the cases, which in part i formed just a set. The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modal logic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many logicians and. This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful. Belnap department of philosophy, university of pittsburgh, 1001 cathedral of learning, pittsburgh, pa 15260, usa this paper follows part i of our essay on case intensional first order logic cifol.
In the rst of these they do an especially nice job of explaining the virtues of ml, and their own caseintensional first order logic cifol, in. Nuel belnap on indeterminism and free action electronic. We present cifol, an 1 easytouse, 2 uniform, 3 powerful, and 4 useful combination of first order logic with modal logic resulting from philosophical and technical modifications of bressan 1972. Tutorial on truth values fabien schang and heinrich wansing lectures 1 and 2, references heinrich wansing. After pointing out shortcomings of standard systems of quantified modal logic, we introduce cifol, caseintensional first order logic, as a newly established formal framework that helps to elucidate the notion of tracing. It also introduces caseintensional first order logic cifol, a general intensional logic offering resources for a firstorder extension of the mentioned frameworks and a recent research focus of belnaps. Full text of nuel belnap on indeterminism and free action electronic resource see other formats. Solving the caesar problem without categorical sortals solving the caesar problem without categorical sortals. We reconstruct the objection as a deductive argument leading to a contradiction, employing resources of standard quantified modal logic and thereby highlighting explicit and implicit assumptions with respect to possibility, identity, and their interaction. This is part i of a twopart essay introducing caseintensional first order logic cifol, an easytouse, uniform, powerful, and useful combination of firstorder. In this section we describe a logical framework that offers the resources for properly representing what is right about the reversibility objection without leading to inconsistency. Our system bhcifol adds structure to the cases, which in part i formed just. Nuel belnap on indeterminism and free action uni konstanz.
Bressan based his calculus on carnaps method of extension and intension. Nuel belnap on indeterminism and free action thomas muller. Deduction rules for caseintensional higherorder logic. The volume also contains an extended biographical interview. To the memory of arthur prior formal properties of now. This paper follows part i of our essay on caseintensional. Alscher arithmetization of geometry as interpretation between firstorder theories break. Inference in firstorder logic department of computer. This paper follows part i of our essay on caseintensional first order logic cifol. Caseintensional first order logic ii branching histories. We illustrate the importance of tracing via a discussion of possible experiments in science and in everyday life. I toward a theory of sorts article pdf available in journal of philosophical logic 4323 june 20 with 80 reads.
253 1342 1002 1128 221 785 1418 59 1233 496 1062 1316 841 1409 49 1230 1003 1184 902 149 1477 183 1352 198 927 511 1252 1102 1086