Content deleted Content added
m Interwiki links to end, link fix |
No edit summary |
||
Line 31:
Formal logic, also called symbolic logic, is concerned primarily with the structure of reasoning. Formal logic deals with the relationships between concepts and provides a way to compose proofs of statements. In formal logic, concepts are rigorously defined, and sentences are translated into a precise, compact, and unambiguous symbolic notation.
There have been three stages in the development of mathematical doctrines: first came propositions with particular numbers, like the one expressed, with signs subsequently invented, by <math>2 + 3 = 5</math>; then came more general laws holding for all numbers and expressed by letters, such as <math>(a + b) c = a c + b c</math>; lastly came the knowledge of more general laws of functions and the formation of the conception and expression "[[function]]". The origin of the symbols for particular whole numbers is very ancient, while the symbols now in use for the operations and relations of arithmetic mostly date from the sixteenth and seventeenth centuries; and these "constant" symbols together with the letters first used systematically by [[Viète]] and [[Descartes]], serve, by themselves, to express many propositions. It is not, then, surprising that [[Descartes]], who was both a mathematician and a philosopher, should have had the idea of keeping the method of algebra while going beyond the material of traditional mathematics and embracing the general science of what thought finds, so that [[philosophy]] should become a kind of [[Universal mathematics]]. This sort of generalization of the use of symbols for analogous theories is a characteristic of mathematics, and seems to be a reason lying deeper than the erroneous idea, arising from a simple confusion of thought, that algebraical symbols necessarily imply something quantitative, for the antagonism there used to be and is on the part of those logicians who were not and are not mathematicians, to symbolic logic. This idea of a universal mathematics was cultivated especially by [[Gottfried Wilhelm Leibniz]]. Though modern logic is really due to [[Boole]] and [[De Morgan]], [[Leibniz]] was the first to have a really distinct plan of a system of mathematical logic. That this is so appears from research---much of which is quite recent---into Leibniz's unpublished work.
Some examples of symbolic notation are:
| |||