display all the ideas for this combination of texts
4 ideas
8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
Full Idea: Most people find it hard to find any conclusion that fits the following premises: 'No councillors are bankers', and 'All bankers are athletes'. There is a valid conclusion ('Some athletes are not councillors') but it takes quite an effort to find it. | |
From: Keith Devlin (Goodbye Descartes [1997], Ch. 2) | |
A reaction: A nice illustration of the fact that syllogistic logic is by no means automatic and straightforward. There is a mechanical procedure, but a lot of intuition and common sense is also needed. |
8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
Full Idea: Where Aristotle had 19 different inference rules (his valid syllogisms), modern propositional logic carries out deductions using just one rule of inference: modus ponens. | |
From: Keith Devlin (Goodbye Descartes [1997], Ch. 4) | |
A reaction: At first glance it sounds as if Aristotle's guidelines might be more useful than the modern one, since he tells you something definite and what implies what, where modus ponens just seems to define the word 'implies'. |
8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
Full Idea: Since predicate logic merely extends propositional logic, all the axioms of propositional logic are axioms of predicate logic. | |
From: Keith Devlin (Goodbye Descartes [1997], Ch. 4) | |
A reaction: See Idea 7798 for the axioms. |
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |