Monday, March 28, 2016

Bound/bounded/binded and Bound vs. Free Variables

I guess "binded" is restricted to contexts in which "binders" are in play:

And "bounded" has a different meaning altogether:

But here's a tidy description of the distinction between bound and free variables:

Saturday, February 27, 2016

Wednesday, February 24, 2016

(Logic II) "Paradoxes" of material implication

Peter Suber, again, on the obvious failure of material implication to capture fully the meaning of many "if...then" or "implies" claims:

Friday, February 19, 2016

(Logic II) Translation of "unless"

Nice tip from Peter Suber:

Unless. Sometimes "unless" should be translated as inclusive disjunction, and sometimes as exclusive disjunction. For example, "I'll go to the party unless I get another offer" means that I'll go if nothing else comes along. In many contexts it also means that I might go anyway; the second offer might be worse. So I'll go or I'll get another offer or both (inclusive disjunction). Consider by contrast, "I'll go to the party unless Rufus is there". In many contexts this means that if I learn Rufus is going, then I'll change my mind and not go. So I'll go or Rufus will go but not both (exclusive disjunction). For symbolizing exclusive disjunction, see Tip 2, above. Because there is no hard and fast rule, paraphrase the English before translating. (I thank Susanna S. Epp for helpful correspondence on the subtlety of "unless".

Also, as mentioned in class (and in line with several of Suber's paraphrases above), we can usually symbolize unless claims in the form of conditional (material implication) claims.

So I think Hurley's answer was both wrong and incomplete.


Wednesday, February 10, 2016

(Logic II) Existential Import of Categorical Propositions

And, in more detail:

So, in sum:

Since particular propositions assume existence ("at least one..."), subalternation does not produce valid results with universal (A or E) propositions where the subject denotes an empty set, (eg., All unicorns are pink, therefore some unicorns are pink),  Arguments of this form are (on the modern, Boolean approach) only conditionally valid (i.e., on the condition that the subject term denotes an existing thing).