Combining Texts

Ideas for 'Of Liberty and Necessity', 'On 'Insolubilia' and their solution' and 'Goodbye Descartes'

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

display all the ideas for this combination of texts

4 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
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.
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
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'.
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
21563 The 'no classes' theory says the propositions just refer to the members [Russell]
     Full Idea: The contention of the 'no classes' theory is that all significant propositions concerning classes can be regarded as propositions about all or some of their members.
     From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.200)
     A reaction: Apparently this theory has not found favour with later generations of theorists. I see it in terms of Russell trying to get ontology down to the minimum, in the spirit of Goodman and Quine.