Truth functional 'if'

If the number of infections is in the high twenty thousands for five consecutive days, tough restrictions on personal freedoms will be introduced.

The statement (or a very similar one) by the Polish prime minister has been seized upon by the opposition as a lie because tough restrictions have been introduced while the number of cases, at the time of writing, is in the low ten thousands. Politics aside, in terms of first-order logic, the facts do not actually make the statement false. The sentence is not the best candidate for truth-functional analysis because it is phrased as a hypothesis rather than an observation, but it will do to show the ‘weak’ force of a logical conditional. Thus:

 

If the government does as it says, the statement will be true. No problem there.

 

If the number of cases is in the high twenty thousands for five consecutive days, and the government does not introduce tougher restrictions, the statement will be false. No problem there either.

 

If the number of cases is in the low ten thousands, and the government introduces tougher restrictions, the statement will be true too. Why? Because in saying what it says, the original statement does not rule out this scenario, it merely doesn’t mention it.

 

If the number of cases is in the low ten thousands, and the government has not introduced tougher restrictions, the original statement is true as well. Why? The reason is the same as in the preceding scenario. This scenario also appeases the critics – low number of cases, therefore no restrictions – but logically it is immaterial. 

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 12, p. 447

 

1.     (x)[Rx ⊃ (Hx • x = m)] ∴ Rc ⊃ Hm 2.     Rc 3.     Rc ⊃ (Hc • c = m) 4.     Hc • c = m 5.     Hc 6.     c = m • Hc 7.     c = m 8.     Hm 9.     Rc ⊃ Hm

ACP 1 UI 2,3 MP 4 Simp 4 Com 6 Simp 5,7 Id 2-8 CP

Indefinite pronouns, conservative, liberal

English indefinite pronouns in 2020: everybody, nobody, anybody, somebody, antibody

Conservatism – a hereditary condition but can be faked at any age; liberalism – an acquired communicable disease that is always genuine

 

Conservative – someone who has done everything right in life but who cannot understand why he is not happy; liberal – someone who has done everything wrong in life but who is happy nonetheless

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 11, p. 447

 

1.     (x)(y)(Txy ⊃ x = e) 2.     (∃x)Txi ∴ Tei 3.     Tmi 4.     (y)(Tmy ⊃ m = e) 5.     Tmi ⊃ m = e 6.     m = e 7.     Tei

2 EI 1 UI 4 UI 3,5 MP 3,6 Id

Foxholes, atheists, God

No one is an atheist in a foxhole. – Anon

Retort 1

 

Thus putting God in a difficult position whereby He has to save a believer in a foxhole on one side of the line and allow a believer on the other side of the line to die.

 

Retort 2

 

Foxholes – therein hangs God’s secret. And in takeoffs and landings.

 

Retort 3

 

If you spend your whole life preparing for the foxhole moment, your whole life will be a foxhole.

 

Retort 4

 

It’s certainly impossible to understand ballistics away from God’s plans.

 

Retort 5

 

If there is a God, why are there foxholes?

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 9, p. 447

 

1.     (x)(Lx ⊃ x = e) 2.     (x)(Sx ⊃ x = i) 3.     (∃x)(Lx • Sx) ∴ i = e 4.     Lm • Sm 5.     Lm ⊃ m = e 6.     Sm ⊃ m = i 7.     Lm 8.     m = e 9.     Sm • Lm 10. Sm 11. m = i 12. i = m 13. i = e

3 EI 1 UI 2 UI 4 Simp 5,7 MP 4 Com 9 Simp 6,10 MP 11 Com 8,12 Id

e-books, ties and turtlenecks, souls and muscles

Fans of e-readers and e-books are a point down in the print v digital reading debate. E-books make a poor background in Zoom meetings.

Wearing a tie with a turtleneck will get you the looks, but you can just about get away with it if you complement the outfit with a pair sandals and lederhosen shorts.

 

That the priests fight for your soul and the gym fights for your body is par for the course, but the game has moved on when the priests muscle in on sports and the gym fights for your soul.

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 8, p. 447

1.     (x)(x = r) 2.     Hr • Kn ∴ Hn • Kr 3.     n = r 4.     Hr 5.     Hn 6.     Kn • Hr 7.     Kn 8.     Kr 9.     Hn • Kr

1 UI 2 Simp 3,4 Id 2 Com 6 Simp 3,7 Id 5,8 Conj

The mole

The way things are going it is looking increasingly likely they will award the Nobel Prize not to the guy who builds the first fail-safe mole trap but to whoever finds a way of turning contemplation of a churned up lawn from exasperation to mole hill therapy.

I’ve got the mole sussed ... I think. Too often now I have brought the hoe down too soon. Next time I will feint on the zig and whack on the zag.

 

The good folk of my town have declared it a mole-free zone. They have an instinctive fear of slick, pink-faced things sneaking up dark, subterranean passages. Tensions are high as the town braces itself for the mole’s response.

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 6, p. 447

 

1.     (x)(Ax ⊃ Bx) 2.     Ac • ~ Bi ∴ c ≠ i 3.     c = i 4.     Ai ⊃ Bi 5.     Ac 6.     Ai 7.     Bi 8.     ~ Bi • Ac 9.     ~ Bi 10. Bi • ~ Bi 11. c ≠ i

AIP 1 UI 2 Simp 3,5 Id 4,6 MP 2 Com 8 Simp 7,9 Conj 3-10 IP

Small talk about Kant, larks and owls, words

None of my EFL students has pointed out yet that, whenever I start a lesson with a warm-up that involves small talk about Kant, Nietzsche or Hegel, the lesson proper invariably turns out to be very thin. I wonder if they’ve noticed the connection.

All larks I know would be quite happy for mornings to last forever, yet no owls I know could contemplate nights without mornings, from which I take being a lark to be a genuine desire, and being an owl – only an affectation.

 

Words are mightier than the sword, and in English, one-syllable words cut deeper and with more savagery than multi-syllable ones.

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, II, 5, p. 447

 

1.     (x)(Gx ⊃ x = a) 2.     (∃x)(Gx • Hx) ∴ Ha 3.     Gm • Hm 4.     Gm ⊃ m = a 5.     Gm 6.     m = a 7.     Hm • Gm 8.     Hm 9.     Ha

2 EI 1 UI 3 Simp 4,5 MP 3 Com 7 Simp 6,8 Id