Understanding Symbolic Logic, Virginia Klenk, Pearson Prentice Hall, 5th ed., Unit 8: 7(a), p. 173

 

1.     (~ A v ~ B) ⊃ ~ C 2.     A ⊃ F 3.     [~ F ≡ (D • ~ E)] 4.     ~ (D ⊃ H) 5.     E ⊃ H ∴ ~ C 6.     ~ (~ D v H) 7.     D • ~ H 8.     ~ H 9.     ~ E 10. D 11. D • ~ E 12. [~ F ⊃ (D • ~ E)] • [(D • ~ E) ⊃ ~ F] 13. (D • ~ E) ⊃ ~ F 14. ~ F 15. ~ A 16. ~ A v ~ B 17. ~ C

4 Impl 6 DM 7 Simp 5,8 MT 7 Simp 9,10 Conj 3 Equiv 12 Simp 11,13 MP 2,14 MT 15 Add 1,16 MP

Solutions to problems

The solution to long-term problems is short-term problems. When a long-term problem finally catches up with you, it becomes a short-term problem.

 

The solution to long-term problems is short-term problems, while the solutions to short-term problems are many and varied: wait-and-see, stoical disregard, practiced indifference, calculated transcendence. 

 

The solution to long-term problems is short-term problems, while the solution to short-term problems is putting them in perspective.

 

Epigramology: essence, luminescence, incandescence

I like one-liners, bon mots, witticisms, epigrams, maxims, quips, by whatever name such distillations of life’s wisdom are known, from the acerbic pens of Ambrose Bierce, Oscar Wilde, Mark Twain, G.K. Chesterton, Winston Churchill, Woody Allen, et al. Who doesn’t?

Regrettably and realistically in equal measure, my sources rarely include the original texts. Life is too short. So, I often look to secondary sources for my daily dose of humour – collectors such as Ambrose Bierce (who belongs in both groups), Aubrey Dillon-Malone, Mardy Grothe, Nigel Reese, Des Machale, to name a few.

 

But none of the above are found in these pages, except inadvertently through inspiration, negligence or ignorance. What follows is my own attempts at distilling life in epigrammatic form. 

 

Since it is hard to draw clear lines between a quip and a crack or a retort and a riposte, since modesty dictates that such elegant labels are better suited to other people’s thoughts than my own intellectual flatulence, and, finally, since I want to be original, naturally, I have grouped my thoughts under: ESSENCE, LUMINESCENCE, and INCANDESCENCE. 

 

Essence is just definitions, luminescence (emission of light from an unheated source) is my musings and reflections on life when I am on top form, and incandescence (emission of light from a heated source) is what I would like to say when someone else lands a blow on me with a clinching quote. The retort seldom comes at the right moment, leaving me stewing in resentment until I can think of a comeback. Incandescent!

 

I follow three criteria in my essence and luminescence categories. They are borrowed from Des Machale’s Wittipedia: the thoughts must be short, funny, and context-free. I fall short on all three, but I keep trying. The point of the whole exercise: to have better arguments.

 

The inevitable flaw as much as the avowed aim of deploying such pre-packaged wisdom is of course the dubious value of settling arguments by adage. Truth by adage is a recognised logical fallacy. No one likes having arguments shot down by a borrowed one-liner, but if it’s your own wisdom? 

Some essence to start with:

Builders – opportunists who never knowingly undercharge for the corners they never fail to cut.

 

Builders – the rock on which your dreams crumble as your bills soar to magnificent heights.

 

Builders – just like dentists only without the anaesthetic.

How to think of the truth functionality of the material implication p ⊃ q

The “If p then q” implication is true when both p and q are true. So, if this implication is true, when is it false? It is false when the same true p implies the opposite of the same true q (the law of excluded middle). After all, the same true p cannot imply the false q while at the same time implying the true q, can it?

What about the other two implications where p is false, that is “If the false p, then the true q”, and “If the false p, then the false q”? And the answer is: why should we even bother? They are not relevant to our original implication “If the true p, then the true q”. They are different statements. There is nothing in our original statement about q being false. 

Our conditional is a kind of minimal conditional. It captures only those scenarios that are strictly relevant, leaving others out of consideration - “leaving others out of consideration” but not jumping the gun and consigning them to falsehood. But if we choose to probe, it might be instructive to think of the “If p then q” implication like this:  truth can imply only truth, falsehood can imply anything.

So, suppose someone says:

You can roll a seven on a single roll of a dice.

You roll out your eyes and think: “Aha, we are not on the same planet,” or “One of us excluding me is away with the fairies.” But to humour them, you say:

Sure, if a coin has three sides, then you can roll a seven on a single roll of a dice.

You have just shown them under what sort of circumstances (a world of three-sided coins) their sentence is true!

The sentence:

You can roll a six on a single roll of a dice.

is certainly true. If it is true in the demanding world of two-sided coins, it must be even more true in the less demanding world of three-sided coins. So, the sentence:

If a coin has three sides, then you can roll a six on a single roll of a dice.

is true too.

Logic and Philosophy, A. Hausman, H. Kahane, P. Tidman, Wadsworth, 11th ed., 2010, 13-1(7)

Prove valid, as usual:

1. (∃x)[Px • (y)(Py ⊃ y=x) • Qx]
2. (∃x) ¬ ( ¬ Px ∨ ¬ Ex]
3. ∴ ( ∃x)(Ex • Qx)
4. (∃x) (¬ ¬ Px • ¬ ¬ Ex] ......... 2 DeM
5. (∃x) (Px • Ex] ........ 4 DN
6. Pa • (y)(Py ⊃ y=a) • Qa ......... 1 EI x/a
7. Pm • Em ......... 5 EI x/m
8. (y)(Py ⊃ y=a) ......... 6 Simp.
9. Pm ⊃ m=a ......... 8 UI y/m
10. Pm ......... 7 Simp.
11. m=a ...... 9,10 MP
12. Em ......... 7 Simp.
13. Ea ......... 11,12 Id
14. Qa ......... 6 Simp.
15. Ea • Qa ......... 13,14 Conj.
16. (∃x)(Ex • Qx) ......... 15 EG