Combining Texts

Ideas for 'fragments/reports', 'Reasoning and the Logic of Things' and 'Spreading the Word'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

5 ideas

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
19237 Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce]
     Full Idea: The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds.
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078 Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
     Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics.
     From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
     A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true.
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
19256 Our research always hopes that reality embodies the logic we are employing [Peirce]
     Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII)
     A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
6023 Every proposition is either true or false [Chrysippus, by Cicero]
     Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false.
     From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38
     A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
19238 The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce]
     Full Idea: In the place of the class ...the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: Peirce's logic of relations might support the purely structural view of reality defended by Ladyman and Ross. Modern logic standardly expresses its semantics in terms of set theory. Peirce pioneered relations in logic.