Mind, critical thinking, HMRC

I can’t change my mind until I have made up my mind first. The thing is I haven’t made up my mind about anything yet ever, so why would I want to change it?

When everyone is hyping up critical thinking skills, it pays to have another look at uncritical thinking. Not only might it be easier to teach but the mental health benefits to the learner could be substantial.

 

Should I read any significance into the fact that when I type the letters HMRC into any of my phone apps, the default spellchecker corrects them to Hercules?

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 7.7, 3, p. 390

 Prove the logical truth.

1.     P 2.     P v Q 3.     P v P 4.     (P v Q) • (P v P) 5.     [(P v Q) • P] v [(P v Q) • P] 6.     (P v Q) • P 7.     (P • P) v (Q • P) 8.     P v (Q • P) 9.     P ⊃ [P v (Q • P)] 10.  P v (Q • P) 11.  (P v Q) • (P v P) 12.  (P v P) • (P v Q) 13.  P v P 14.  P 15.  [P v (Q • P)] ⊃ P 16.  { P ⊃ [P v (Q • P)]} • {[P v (Q • P)] ⊃ P} 17.  P  ≡ [P v (Q • P)]

/ P  ≡ [P v (Q • P)] ACP 1 Add 1 Add 2,3 Conj 4 Dist 5 Taut 6 Dist 7 Taut 1-8 CP ACP 10 Dist 11 Com 12 Simp 13 Taut 10-14 CP 9,15 Conj 16 Equiv

The humble and the exalted

Whoever exalts himself will be humbled, and whoever humbles himself will be exalted. – Matthew 23:12

Retort 1

 

So now we know: in the afterlife vice is virtue and virtue vice.

 

Retort 2

 

One wonders if the exalted will feel any sympathy for the humbled or just gloat.

 

Retort 3

 

One also wonders if this peculiar symmetry is iterative and continues to replay itself endlessly as one cycles out of one afterlife into another.

 

Retort 4

 

The burning question this prompts is whether the tall will be short and the short tall.

 

Retort 5

 

What’s in store then for someone who follows the middle course?

 

Retort 6

 

Today's exalted had better start purchasing exaltation credit certificates if they want to settle the imbalances when they’ve departed.

 

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 7.7, 2, p. 390

 Prove the logical truth.

 

1.     ~ [(~P ⊃ Q) v (P ⊃ R)] 2.     ~ (~P ⊃ Q) • ~ (P ⊃ R) 3.     ~ (P v Q) • ~ (~ P v R) 4.     ~ P • ~ Q • P • ~ R 5.     ~ P • P • ~ Q • ~ R 6.     ~ P • P 7.     ~ ~ [(~P ⊃ Q) v (P ⊃ R)] 8.     (~P ⊃ Q) v (P ⊃ R)

/ (~P ⊃ Q) v (P ⊃ R) AIP 1 DM 2 Impl 3 DM 4 Com 5 Simp 1-6 IP 7 DN

Fortune telling, Zoom meetings, science

Fortune telling is telling tales about the future. Misfortune telling is telling tales about the past.

When you wonder if you’re in the right meeting, if they can see you and hear you, if anyone is there at all, and if the meeting is still going on, then you are in a Zoom meeting.

 

I enjoy hearing of science set-backs, reversals and dead ends. It reassures me that everything is alright with science. 

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, III, 15 p. 449

Every candidate except Mary was elected. The only candidate who was elected was Ralph. Mary is not Ralph. Therefore, there were exactly two candidates. (Cx: x is a candidate; Ex: x was elected; m: Mary; r: Ralph)

1.     Cm • ~ Em • (x)[(Cx • x ≠ m) ⊃ Ex] 2.     Cr • Er • (x)[(Cx • Ex) ⊃ x = r] 3.     m ≠ r ∴ (∃x)(∃y){Cx • Cy • x  ≠  y • (z)[Cz ⊃ (z = x v z = y)]} 4.     ~ (∃x)(∃y){Cx • Cy • x  ≠  y • (z)[Cz ⊃ (z = x v z = y)]} 5.     (x)(y)~{Cx • Cy • x  ≠  y • (z)[Cz ⊃ (z = x v z = y)]} 6.     (x)(y){~(Cx • Cy • x  ≠  y) v ~(z)[Cz ⊃ (z = x v z = y)]} 7.     (x)(y){~(Cx • Cy • x  ≠  y) v (∃z)~[Cz ⊃ (z = x v z = y)]} 8.     (x)(y){~(Cx • Cy • x  ≠  y) v (∃z)~[~Cz v (z = x v z = y)]} 9.     (x)(y){~(Cx • Cy • x  ≠  y) v (∃z)[Cz • (z = x v z = y)]} 10.  (x)(y)[~(Cx • Cy • x  ≠  y) v (∃z)(Cz • z ≠ x • z ≠ y)] 11.  (y)[~(Cm • Cy • m  ≠  y) v (∃z)(Cz • z ≠ m • z ≠ y)] 12.  ~(Cm • Cr • m  ≠  r) v (∃z)(Cz • z ≠ m • z ≠ r) 13.  Cm 14.  Cr 15.  Cm • Cr • m  ≠  r 16.  (∃z)(Cz • z ≠ m • z ≠ r) 17.  Cq • q ≠ m • q ≠ r 18.  (x)[(Cx • x ≠ m) ⊃ Ex] • Cm • ~ Em 19.  (x)[(Cx • x ≠ m) ⊃ Ex] 20.  (Cq • q ≠ m) ⊃ Eq 21.  Cq • q ≠ m 22.  Eq 23.  (x)[(Cx • Ex) ⊃ x = r] • Cr • Er 24.  (x)[(Cx • Ex) ⊃ x = r] 25.  (Cq • Eq) ⊃ q = r 26.  Cq 27.  Cq • Eq 28.  q = r 29.  q ≠ r • Cq • q ≠ m 30.  q ≠ r 31.  q = r • q ≠ r 32.  ~ ~ (∃x)(∃y){Cx • Cy • x  ≠  y • (z)[Cz ⊃ (z = x v z = y)]} 33.  (∃x)(∃y){Cx • Cy • x  ≠  y • (z)[Cz ⊃ (z = x v z = y)]}

AIP 4 QC 5 DM 6 QC 7 Impl 8 DM 9 DM 10 UI 11 UI 1 Simp 2 Simp 3,13,14 Conj 12,15 DS. 16 EI 1 Com 18 Simp 19 UI 17 Simp 20,21 MP 2 Com 23 Simp 24 UI 21 Simp 22,26 Conj 25,27 MP 17 Com 29 Simp 28,30 Conj 4-31 IP 32 DN

Vaccine, fanaticism, urban cycling

Vaccine – the holy water for atheists, strychnine for the devout

Fanaticism – a conviction that you are right because things are not going your way

 

Urban cycling – wolf races through a flock of sheep, with the sheep nearest the race track most prone to getting their woolly coats caught in the teeth

A Concise Introduction to Logic, Patrick J. Hurley, Wadsworth, 2006, 9th ed,. 8.7, III, 14 p. 449

There are at most two scientists in the laboratory. At least two scientists in the laboratory are Russians.  No Russians are Chinese. Therefore, if Norene is a Chinese scientist, then she is not in the laboratory. (Sx: x is a scientist; Lx: x is in the laboratory; Rx: x is Russian; Cx: x is Chinese; n: Norene) / All accounting is shown below the proof due to blogger formatting constraints.

1.     (x)(y)(z)[(Sx • Lx • Sy • Ly • Sz • Lz) ⊃ (x = y v x = z v y = z)]

2.     (∃x)(∃y)(Sx • Lx • Rx • Sy • Ly • Ry • x ≠ y)

3.     (x)(Rx ⊃ ~ Cx)

∴ (Sn • Cn) ⊃ ~ Ln

4.     Sn • Cn 5.     Rn ⊃ ~ Cn 6.     Cn • Sn 7.     Cn 8.     ~ Rn 9.     (∃y)(Sm • Lm • Rm • Sy • Ly • Ry • m ≠ y) 10.  Sm • Lm • Rm • Sr • Lr • Rr • m ≠ r 11.  (y)(z)[(Sm • Lm • Sy • Ly • Sz • Lz) ⊃ (m = y v m = z v y = z) 12.  (z)[(Sm • Lm • Sr • Lr • Sz • Lz) ⊃ (m = r v m = z v r = z) 13.  (Sm • Lm • Sr • Lr • Sn • Ln) ⊃ (m = r v m = n v r = n) 14.  Rr ⊃ ~ Cr 15.  Rr • Sm • Lm • Rm • Sr • Lr • m ≠ r 16.  Rr 17.  r ≠ n 18.  Rm ⊃ ~ Cm 19.  Rm • Sm • Lm • Sr • Lr • Rr • m ≠ r 20.  Rm 21.  ~ Cm 22.  m ≠ n 23.  m ≠ r • Sm • Lm • Rm • Sr • Lr • Rr  24.  m ≠ r 25.  m ≠ r • m ≠ n • r ≠ n 26.  ~ (m = r v m = n v r = n) 27.  ~ (Sm • Lm • Sr • Lr • Sn • Ln) 28.  ~ (Sm • Lm • Sr • Lr • Sn) v ~ Ln 29.  Sm • Lm • Sr • Lr • Rm • Rr • m ≠ r 30.  Sm • Lm • Sr • Lr 31.  Sn 32.  Sm • Lm • Sr • Lr • Sn 33.  ~ Ln

34.   (Sn • Cn) ⊃ ~ Ln

4. ACP; 5. 3 UI; 6. 1 Com; 7. 6 Simp; 8. 5,7 MT; 9. 2 EI; 10. 9 EI; 11. 1 UI; 12. 11 UI; 13. 12 UI; 14. 3 UI; 15. 10 Com; 16. 15 Simp; 17. 8,16 Id; 18. 3 UI; 19. 10 Com; 20. 19 Simp; 21. 18,20 MP; 22. 7,21 Id; 23. 10 Com; 24. 23 Simp; 25. 17,22,24 Conj; 26. 25 DM; 27. 13,26 MT; 28. 27 DM; 29. 10 Com; 30. 29 Simp; 31. 4 Simp; 32. 30,31 Conj; 33. 28,32 DS; 34. 4-33 CP