I. Hacking. What is logic? Journal of Philosophy, LXXVI(6):285-319, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....taken to defining a logic is to specify its set of theorems, or valid formulas. This was, for example, the original approach taken to defining various modal logics [LL59] However, logic originally started as the study of sound arguments. In fact, Hacking defines logic as a science of deduction [Hac79]. We would argue that in order to study the reasoning patterns appropriate to a logic, it is not sufficient to specify just the valid formulas. Indeed, there are well known relevance logics [AB75, Dun86] which were specifically designed to capture legitimate patterns of reasoning about ....

I. Hacking. What is logic? Journal of Philosophy, 76(6):285--319, 1979.

....first order entailment and consistency are used to model the notions of diagnostic of covering and consistency. However, a large number of other entailment relations is available in the literature. There is no clear notion of what properties an entailment entailment should minimally satisfy, but [Hacking, 1994] suggests reflexivity, A A) transitivity (if A B and B C then A C) are suggested as minimal. Other properties which might be considered (but which do not hold for many non classical deduction relations) are monotonicity (if A B then AC B) and dilution (if A B then A BC) or ....

I. Hacking. What is logic? In D. Gabbay, editor, What is a logical system? Oxford Science Publications, 1994.

....semantic point of view, in contrast, is based on the intuitive meaning of a given connective. In the case of negation this is simply the intuition that the negation of a proposition A is true if A is not, and not true if A is true. 1 Like in most modern treatments of logics (see, e.g. Sc74] [Ha79], Ga81] Ur84] Wo88] Ep90] Av91a] Cl91] FHV92] our study of negation will 1 We have avoided here the term false , since we do not want to commit ourselves to the view that A is false precisely when it is not true. Our formulation of the intuition is therefore obviously circular, ....

Hacking I. What is logic? The journal of philosophy, vol. 76 (1979), pp. 285-318. Reprinted in [Ga94].

....order entailment and consistency are used to model the notions of diagnostic of covering and consistency. However, a large number of other entailment relations is available in the literature. There is no clear notion of what properties an entailment entailment should minimally satisfy, but [Hacking, 1994] suggests reflexivity, A A) transitivity (if A B and B C then A C) are suggested as minimal. Other properties which might be considered (but which do not hold for many non classical deduction relations) are monotonicity (if A B then AC B) and dilution (if A B then A B C) or ....

I. Hacking. What is logic? In D. Gabbay, editor, What is a logical system? Oxford Science Publications, 1994.

....truth definition for first order arithmetic can be obtained by using quantification over first order definable relations (i.e. the lowest level 112 In particular, we have the propositional types ( for all 0. 113 Among the promoters of ramified higher order logic are Hacking and Hazen [ Hacking, 1979; Hazen, 1983; Hazen, 1985 ] The following observation is due to Sundholm [ 1981 ] it follows from the fact that ramified higher order logic satisfies the conditions of Lindstr om s Theorem (Section 5.2) namely compactness and Downward Skolem L owenheim, by work of Leblanc [1976] and is ....

I. Hacking. What is logic? Journal of Philosophy, 76:285-- 319, 1979.

....to the view that A is false precisely when it is not true. Our formulation of the intuition is therefore obviously circular, but this is unavoidable in intuitive informal characterizations of basic connectives and quantifiers. Like in most modern treatments of logics (see, e.g. Sc74a,b] [Ha79], Ga81] Ur84] Wo88] Ep95] Av91a] Cl91] FHV92] our study of negation will be in the framework of Consequence Relations (CRs) Following [Av91a] we use the following rather general meaning of this term: Definition. 1) A Consequence Relation (CR) on a set of formulas is a binary ....

Hacking I. What is logic? The journal of philosophy, vol. 76 (1979), pp. 285-318. Reprinted in [Ga94].

....uniformly replaces variable terms in a sequent by meta variables. Here (as in [34] we assume that the basic symbols of our language are partitioned in two disjoint sets: the set of variable terms and the set of fixed terms or logical constants. Following Tarski (and differently from [13]) we make no attempt at defining these concepts, assuming the sets as input parameters for our algorithm. Definition 9 Universal Generalization of a sequent S = Def a metasequent obtained from S by replacing each variable term with a meta variable of the same type, assuring that all occurrences ....

Ian Hacking. What is logic? The Journal of Philosophy, LXXVI(6), 1979.

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I. Hacking. What is logic? Journal of Philosophy, LXXVI(6):285-319, 1979.

No context found.

Ian Hacking. What is logic? The Journal of Philosophy, 76(6):285-319, June 1979.

No context found.

Ian Hacking. What is logic? The Journal of Philosophy, 76(6):285-319, June 1979.

No context found.

Ian Hacking. What is logic? The Journal of Philosophy, 76(6):285-319, June 1979.

No context found.

Hacking I. What is logic, The journal of philosophy, vol. 76 (1979), pp. 285-318. Reprinted in [Ga94].

No context found.

Ian Hacking. What is logic? The Journal of Philosophy, 76(6):285--319, June 1979.

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