A Little Logic Challenge

Here's a small challenge:

Demonstrate the following without using conditional or indirect proof.
(Conditional proof makes it way too easy!)

1. (A ⊃ B)
2. (A ⊃ (B ⊃ C))
/ ∴ (A ⊃ C)


Rules you can use (see full post):


MP (p ⊃ q), p, / ∴ q
MT (p ⊃ q), ~q, / ∴ ~p
DS (p ∨ q), ~p, / ∴ q
HS (p ⊃ q), (q ⊃ r), / ∴ (p ⊃ r)
CD (p ⊃ q), (r ⊃ s), (p ∨ r), / ∴ (q ∨ s)
Add p, / ∴ (p ∨ q)
Simp (p · q), / ∴ p
Conj p, q, / ∴ (p · q)

Com (p · q) ⇔ (q · p), (p ∨ q) ⇔ (q ∨ p)
DM ~(p · q) ⇔ (~p ∨ ~q), ~(p ∨ q) ⇔ (~p · ~q)
DN p ⇔ ~~p
Assoc (p ∨ (q ∨ r)) ⇔ ((p ∨ q) ∨ r), (p · (q · r)) ⇔ ((p · q) · r)
Dist (p ∨ (q · r)) ⇔ ((p ∨ q) · (p ∨ r)), (p · (q ∨ r)) ⇔ ((p · q) ∨ (p · r))
Impl (p ⊃ q) ⇔ (~p ∨ q)
Contra (p ⊃ q) ⇔ (~q ∨ ~p)
Exp (p ⊃ (q ⊃ r)) ⇔ ((p · q) ⊃ r)
Taut (p ∨ p) ⇔ p, (p · p) ⇔ p
Equiv (p ≡ q) ⇔ ((p ⊃ q) · (q ⊃ p)), (p ≡ q) ⇔ ((p · q) ∨ (~p · ~q))


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"Make me a channel of your peace."
- St. Francis

Read the full post.

Required Beliefs in Philosophy Classes

I heard this from my sister:

There is a report among some politically active fundamentalists that a philosophy professor threatened to reduce a student's grade or prevent her from passing a required gen ed course if she did not personally accept that the existence of God cannot be proven...see link below.
http://www.aclj.org/TrialNotebook/Read.aspx?id=605


A semester or two ago, on a Logic assignment, I gave students a list of propositions, including

C = Chicago is the capital of Illinois
G = God exists

and asked them to give English translations of ~C and ~G. Two or three of my students refused to write the corresponding proposition for ~G; one wrote instead something like "But God *does* exist!"; the other one or two left it blank.

I wrote an explanation on their papers that my point was that G and ~G are meaningful propositions. Maybe I should have made a class announcement-but I didn't want to embarass anyone.
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"Make me a channel of your peace."

--St. Francis

Read the full post.

I've been enjoying grading the world religions papers for the most part.
But lately I've been having trouble staying awake.
I didn't sleep enough last night or the night before (in neither case because I was staying up grading, unfortunately).
And some papers seem easier to grade than others--big surprise!

Aside from that issue, one paper compares and contrasts Mormonism (that is, LDS) and Christianity, and asks whether Mormonism should be regarded as Christian. The student (who is not LDS) answers that question in the affirmative.

I had been under the impression that Mormonism was non-monotheistic (let alone non-Trinitarian), and so have had deep misgivings regarding the appropriateness of labeling Mormonism a kind of Christianity. The student's paper doesn't bring up that issue, but I was thinking of mentioning it to the student in a comment.

However, I wanted to make sure I knew what I was talking about first (and not basing my statements of Mormonism on Kingdom of the Cults!). I found that this question is rather more complicated than I thought.

I'm trying to make sense of this article:
http://farms.byu.edu/display.php?table=review&id=474

But as I said, I've been having trouble staying mentally awake.
I think I should go back to grading papers.

I emailed a Taylor prof who was researching Mormonism not that long ago to ask for help. (This is someone I never actually had for class myself, unless you count the interview lecture he gave to my summer Greek class on the problem of evil with administration and faculty sitting in the back of the classroom.)

In general I've been swamped with school-related busy-ness. It will be awhile before I resume my Martyr's Mirror series, but I plan to eventually....


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"He Himself is our Peace." (Eph 2)

Read the full post.