Friday, March 16, 2018

Some Definitions for Logic Terms

I've compiled a list of definitions for terms commonly employed by logicians since logic is an essential part of academic theology. For without logic, there is no theo-logic:

Logic Definitions

(1) Ostensive Definition: Pointing toward an entity in order to signify a term (e.g., pointing toward a car in order to signify what "car" means).

(2) Extension: The set of individuals, objects, or events to which one can correctly apply a term (e.g., "boat"). Logicians also classify a set of individuals, objects or events as the denotation.

(3) Intension: The set of all and only those properties that a thing must possess in order for a term to have applicability for it (= connotation).

(4) Theory: Refers to a general approach to or belief about some subject matter that is expressed in a set of interrelated statements concerning the nature of the subject.

Secondly, theory may refer to a set of general but precise claims about the nature of society or the physical world.

(5) Epistemology: The branch of philosophy that concerns itself with theories regarding the sources, nature, and limits of knowledge (i.e., theory of knowledge). One writer defines "epistemology" as the critical analysis of cognition.

(6) Validity: If the premises of an argument happen to be true, then the conclusion of the argument has to be true.

(7) Conditional: A statement of the form "If P then Q," asserting that Q is, or will be, the case, so long as P obtains.

(8) Sound: Both the conclusion and premises are true. So the conclusion necessarily follows from the premises: a sound argument has all true premises and is valid.


Duncan said...

Re: validity:-

Edgar Foster said...

Thanks, Duncan. There is helpful information at the link you posted. My work on validity primarily deals with argument forms rather than formulas, but the definitions proposed by Wikipedia are consontant with books I've used over the years to teach logic.

Validity as I've discussed it, is formal validity. Deductive arguments are not true or false: they're valid/invalid or sound/unsound. An argument is formally valid when there's nothing amiss with the form of the argument. So if one uses modus ponens, modus tollens or modus tollendo ponens (etc.), then his/her argument will be formally valid.

This argument is valid:

1) If A, then B
2) If B, then C
3) Therefore, if A, then C.

The following argument is invalid:

1) If my car starts, then it has gas in the tank
2) My car won't start
3) Therefore, it does not have gas in the tank.

Duncan said...

Affirming the Consequent

The rhetoric form of the 9 PM example & its deconstruction is useful.

Edgar Foster said...

Yes,it is useful because those examples like the 9 pm can be tricky for beginners since it's indirect discourse and structured differently. Last time I taught logic, we used a book by Richard T.W. Arthur that contained such examples. People usually have a problem understanding modus tollens too. Thanks again.

Edgar Foster said...

I studied under a logician who did nothing but problem sets in his class. He concentrated on teaching complex symbolic arguments. I teach differently by including history of logic and teaching logical fallacies.