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Ideas for 'fragments/reports', 'Events' and 'Goodbye Descartes'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

8091	Situation theory is logic that takes account of context [Devlin]
	Full Idea: In many respects, situation theory is an extension of classical logic that takes account of context.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 8)
	A reaction: John Barwise is cited as the parent of this movement. Many examples show that logical form is very hard to pin down, because word-meaning depends on context (e.g. 'several crumbs' differs from 'several mountains').

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

8087	Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin]
	Full Idea: The period from 1900 to about 1960 could be described as the golden age of 'pure' logic, and 1950 to 1985 the golden age of 'applied' logic (e.g. applied to everyday reasoning, and to theories of language).
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 4)
	A reaction: Why do we always find that we have just missed the Golden Age? However this supports the uneasy feeling that the golden age for all advances in human knowledge is just coming to an end. Biology, including the brain, is the last frontier.

8089	Montague's intensional logic incorporated the notion of meaning [Devlin]
	Full Idea: Montague's intensional logic was the first really successful attempt to develop a mathematical framework that incorporates the notion of meaning.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 8)
	A reaction: Previous logics, led by Tarski, had flourished by sharply dividing meaning from syntax, and concentrating on the latter.

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 / B. Logical Consequence / 7. Strict Implication

8082	Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin]
	Full Idea: Implication involves some form of link or causality between the antecedent and the consequent of an if-then; normally it says that the conclusion is a consequence of the premise (where conditionals are just defined by 'true' and 'false').
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 2)
	A reaction: This distinction is a key one when discussing 'If-then' sentences. Some are merely formal conditionals, but others make real claims about where you can get to from where you are.

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 / 1. Logical Form

8072	Sentences of apparent identical form can have different contextual meanings [Devlin]
	Full Idea: "Safety goggles must be worn in the building" is clear enough, but "dogs must always be carried on the escalator" doesn't require us to head off in search of a dog.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 1)
	A reaction: A nice illustration of how the requirements of logical form will often take us beyond the strict and literal meaning of a sentence, into context, tone, allusion and subjective aspects.

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox

8075	Space and time are atomic in the arrow, and divisible in the tortoise [Devlin]
	Full Idea: The arrow paradox starts with the assumption that space and time are atomic; the tortoise starts with the opposite assumption that space and time are infinitely divisible.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 2)
	A reaction: Aquinas similarly covers all options (the cosmos has a beginning, or no beginning). The nature of movement in a space which involves quantum leaps remains metaphysically puzzling. Where is a particle at half of the Planck time?