9 Is Aristotle the creator of logic? Aristotle was maybe the first to have a logic, a theory of reasoningBut he was not the first person to have a Logic, to reason (not the first logical animal)
10 Before Aristotle, the Greeks introduced a new way of reasoning, a new Logic, based on the reduction to the absurd - IrrationalitySome people consider that this was the birth of MathematicsMathematicians have neverused Aristotle’s theory ofreasoningPythagoras
13 The Paradox of Descartes Descartes was against logicBut he was very logical
14 DESCARTES 4 PRECEPTSClarityNever to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.DivisionTo divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.AscensionTo conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.ExhaustivityTo make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.
15 PASCAL 8 RULES Rules for Definitions Axioms Proofs Not to undertake to define any of the things so well known of themselves that clearer terms cannot be had to explain them.Not to leave any terms that are at all obscure or ambiguous without definition.Not to employ in the definition of terms any words but such as are perfectly known or already explained.AxiomsNot to omit any necessary principle without asking whether it is admitted, however clear and evident it may be.Not to demand, in axioms, any but things that are perfectly evident of themselves.ProofsNot to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it.To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated.To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.
16 TARSKI: Introduction to logic and the methodology of deductive sciences - VI On the Deductive Method 36 Fundamental constituents of a deductive theory—primitive and defined terms, axioms and theorems (Sur la méthode déductive‘, in Travaux du IXe Congrès International de Philosophie, VI, Paris: Hermann, pp )Ideas which are closely related to those presented in this section can be found in earlier literature. See, for instance, the opusculum (posthumously published), De I'esprit geometrique et de I'art de persuader, of the great French philosopher and mathematician B. PASCAL ( ).
17 Logic: the laws of thought KANTBOOLELogic and logicare eternalLogic is eternal,logic is changing
19 Different names for modern logic Formal logicSymbolic logicAlgebra of logicLogisticMetamathematicsMethodology of deductive sciencesMathematical logicLogic
20 Different systems Classical logic Intuitionistic logic Many-valued logicModal logicNon monotonic logicFuzzy logicSubstructural logicLinear logicParaconsistent logic …
21 Universal Logic A general theory of logics, of the different theories of reasoning,of the different logical structuresNot a universal system of LogicNot a Logic, not a system that is the description of the right way of reaoning
22 Languages and Linguistics There are many languagesThey have something in common despite very strong differences, i.e. chinese, english, arabicThis thing in common is not a language itself,the essence of language is not a language,it is the object of linguisticsLinguistics is not a universal languagebut the study of the universal features of languages
23 Ferdinand de Saussure The structure of language The originator of structuralism
43 Special Issue of Logica Universalis Vol4 n2 2010
44 Do all human beings have the same capacity of reasoning Do all human beings have the same capacity of reasoning? Do a man, a woman, a child, a papuan, a yuppie, reason in the same way?Does reasoning evolve? Did human beings reason in the same way two centuries ago? In the future will human beings reason in the same way? Did computers change our way to reason? Is a mathematical proof independent of time and culture ?Do we reason in different ways depending on the situation? Do we use the same logic for everyday life, physics, economy?Do the different systems of logic reflect the diversity of reasonings?Is there any absolute true way of reasoning
45 Logic and logic are relative Nevertheless logic as a sciencecan be universal
46 (1) science is not a private business, it is objective, not subjective, not a question of taste (2) science explains not the idiosyncrasies of a particular phenomenon, but some general patterns of phenomena
47 Science is concerned with a double ALL, ALL minds and ALL objects. Chuaqui and Suppes (1995) have shown that classical physics can be described with a first-order logic theory with only universal quantifiers
48 logic as a science is universal (physics as a science is universal)There is no universal system of logic(there is no universal theory of the universe)
49 Louis Rougier (1889- 1982) The relativity of logic 1941 With the discovery of the conventional and relative character of logic, human spirit has burned his last idol.