Editing History of logic (section)

====Plato====
{{blockquote|Let no one ignorant of geometry enter here.|Inscribed over the entrance to Plato's Academy.}}
[[File:MANNapoli 124545 plato's academy mosaic.jpg|alt=Mosaic: seven men standing under a tree|thumb|200px|[[Plato's Academy mosaic]]]]
None of the surviving works of the great fourth-century philosopher [[Plato]] (428–347 BC) include any formal logic,<ref>Kneale p. 17</ref> but they include important contributions to the field of [[philosophical logic]]. Plato raises three questions:

* What is it that can properly be called true or false?
* What is the nature of the connection between the assumptions of a valid argument and its conclusion?
* What is the nature of definition?

The first question arises in the dialogue ''[[Theaetetus (dialogue)|Theaetetus]]'', where Plato identifies thought or opinion with talk or discourse (''logos'').<ref>"forming an opinion is talking, and opinion is speech that is held not with someone else or aloud but in silence with oneself" ''Theaetetus'' 189E–190A</ref> The second question is a result of Plato's [[theory of Forms]]. Forms are not things in the ordinary sense, nor strictly ideas in the mind, but they correspond to what philosophers later called [[universals]], namely an abstract entity common to each set of things that have the same name. In both the ''[[The Republic (Plato)|Republic]]'' and the ''[[Sophist (dialogue)|Sophist]]'', Plato suggests that the necessary connection between the assumptions of a valid argument and its conclusion corresponds to a necessary connection between "forms".<ref>Kneale p. 20.  For example, the proof given in the ''Meno'' that the square on the diagonal is double the area of the original square presumably involves the forms of the square and the triangle, and the necessary relation between them</ref> The third question is about [[definition]]. Many of Plato's dialogues concern the search for a definition of some important concept (justice, truth, the Good), and it is likely that Plato was impressed by the importance of definition in mathematics.<ref>Kneale p. 21</ref> What underlies every definition is a Platonic Form, the common nature present in different particular things. Thus, a definition reflects the ultimate object of understanding, and is the foundation of all valid inference. This had a great influence on Plato's student [[Aristotle]], in particular Aristotle's notion of the [[essence]] of a thing.<ref>Zalta, Edward N. "[http://plato.stanford.edu/entries/aristotle-logic/#Def Aristotle's Logic]". [[Stanford University]], 18 March 2000. Retrieved 13 March 2010.</ref>