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...A \Rightarrow A,</math> whose type, read as a proposition, is a theorem of intuitionistic propositional calculus. ...titutes a hint or clue to the proof of <math>A \Rightarrow A</math> in the intuitionistic propositional calculus. Although guesswork may succeed in easy cases such

...">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. Peirce's law holds in classical propositional calculus, but not in intuitionistic propositional calculus. The precise axiom system that one chooses for clas

==Differential Logic== ===[[Zeroth Order Logic]]===

===Differential Logic=== * Project Page : [[Differential Logic]]

...ular conception of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion tha ...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale

...ular conception of [[truth]], such as those used in [[art]], [[ethics]], [[logic]], [[mathematics]], [[philosophy]], the [[science]]s, or any discussion tha ...een truth and ''[[logical validity]]'', "because the fundamental notion of logic is validity and this is definable in terms of truth and falsehood" (Kneale

...ans call ''[[logica docens]]'', logic as taught, and ''[[logica utens]]'', logic as used. [[C.S. Peirce]], as a logician, mathematician, and philosopher wh ...The answers that suggest themselves naturally depend on the definitions of logic and mathematics that are taken to be in force at the moment in question, or

...ans call ''[[logica docens]]'', logic as taught, and ''[[logica utens]]'', logic as used. [[C.S. Peirce]], as a logician, mathematician, and philosopher wh | expressive power to limited subsets of logic.

...al Notes#HOC. Higher Order Categorical Logic|HOC. Higher Order Categorical Logic]] in Lambek & Scott's 'Higher Order Categorical Logic', and there are links

...an, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fact becomes a standing premise of Peirci ...th previous editors. It purpose was to place some of Peirce's projects in logic within the context of his times, partly by comparing one of his important s

...easoning built into it, and this disposition to a particular conception of logic may be lodged in such a way that it makes it nearly impossible to reflect o ...bly more advanced forms of analysis and synthesis that are involved in the logic of relations.