Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'Logical Pluralism' and 'The Extended Mind'

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 / A. Overview of Logic / 1. Overview of Logic

13235	Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
	Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all.
	From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
	A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic.

13238	Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
	Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms.
	From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
	A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence!

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

13234	The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
	Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly.
	From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
	A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all.

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

13232	Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
	Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted.
	From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
	A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view.

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics

13241	The model theory of classical predicate logic is mathematics [Beall/Restall]
	Full Idea: The model theory of classical predicate logic is mathematics if anything is.
	From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1)
	A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics.