By Carlo Cellucci
This quantity examines the constraints of mathematical good judgment and proposes a brand new method of common sense meant to beat them. To this finish, the publication compares mathematical good judgment with previous perspectives of common sense, either within the historical and within the sleek age, together with these of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparability it really is obvious simple problem of mathematical good judgment is that it narrows down the scope of good judgment confining it to the learn of deduction, with out delivering instruments for locating whatever new. accordingly, mathematical common sense has had little influence on clinical perform.
Therefore, this quantity proposes a view of good judgment in accordance with which common sense is meant, firstly, to supply ideas of discovery, that's, non-deductive principles for locating hypotheses to resolve difficulties. this can be crucial if good judgment is to play any appropriate position in arithmetic, technology or even philosophy. to conform with this view of common sense, this quantity formulates a number of ideas of discovery, equivalent to induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A common sense in response to such ideas is largely a good judgment of discovery, and comprises a brand new view of the relation of good judgment to evolution, language, cause, procedure and data, quite mathematical wisdom. It additionally includes a brand new view of the relation of philosophy to wisdom. This ebook places ahead such new perspectives, attempting to open back many doorways that the founding fathers of mathematical good judgment had closed traditionally.
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Additional resources for Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method
Example text
3–4). 6. 43–45. 1–2. 1. 2 C. ”7 Rather than relying on the senses, you must judge by reasoning, because only in this way you may avoid being deceived. For example, the senses may lead you to believe that the moon increases and wanes during the course of time. Judging by reasoning, you will realize that this is an illusion, that the moon is a globe which is always the same size and shape. ”9 As another example, the senses incline you to believe that what is is generated. Judging by reasoning, and specifically by reduction to the impossible, you will realize that this is not the case; see Chapter 5.
46 Plato, Timaeus, 52 d 3–4. , 52 e 1–5. , 30 a 3–5. , 30 b 3–5. , 30 b 7–c 1. 44 32 2 The Origin of Logic The claim that the universe is an eunomia has great political significance. The birth of Greek science and philosophy was by and large coeval with an important change in Greek society: the transition from the arbitrary powers of the aristocratic magistrates to a written or customary law which limited their powers and regulated social conflict. This transition was a step towards a lawful order, or eunomia.
7 Logic, Intuitive Thinking and Discursive Thinking (6) Logic is discursive thinking but, in order to acquire knowledge of the universe, the human mind also needs intuitive thinking, which is the highest faculty. ”32 This does not mean that what is exists only insofar as it is intuited. ”33 Rather, it means that intuiting is an act of mind by which the content of that act and what is are the same thing. 8 An Articulated View of the Origin of Logic On the basis of claims (1)–(6), it is possible to give an answer to the question: What is the origin of logic and its relation to method?