Axiomatic Set Theory by James E. Baumgartner (ed.)

By James E. Baumgartner (ed.)

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In the present day logic is generally divorced from natural philosophy or psychology and thought of as a formal system that can be used independently of the knowledge content to which it is applied. Not infrequently it is spoken of as a formal logic, or alternatively as a symbolic logic, since content can be replaced by symbols, or again as a mathematical logic, since symbols can be manipulated in much the same way as the numbers and figures of mathematics. While this way of viewing logic has elements in common with that implicit in Galileo's MS 27, it leaves out of consideration much of what would be important for understanding the logical teaching contained in the lecture notes on which that manuscript is now known to be based.

He first makes a distinction between natural logic (logica naturali~l), the innate capacity of the human mind to define, to distinguish, and to reason correctly, and artificial logic (logica artificialis), contained in various treatises on the subject. The first obviously existed before the second, and yet no one denies that the second exists also; even those who reject all the sciences and deny the necessity of logic, such as Sextus Empiricus, admit its existence. Vallius lists the early treatises in which artificial logics were first proposed, pointing out that they were developed, though in imperfect form, before Plato and Aristotle.

These powers include the intellect and the will, the various senses and the appetites or emotions associated with them, motive powers, and so on. Each power is known and characterized through the operations it initiates, and thus one can speak of the operations of the mind, of the will, of the senses, of the appetites, etc. In this context the operations of the intellect take on a dual character and thus fall under two disciplines, psychology and logic. They fall under psychology insofar as they themselves are real activities of a thinking human being, and they fall under logic insofar as they involve a type of reflective activity associated with the beings of reason described above.

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