Every new generation, in this century, comes in shouting that has something new to do and goes out saying it only has something new to regret.

Let's check in on Illinois:

According to court records, Will County Judge Derek Ewanic informed Rodriguez on Thursday that she would not be kept in the jail because her criminal charges related to accusations of spitting on multiple police officers are not detainable crimes under the SAFE-T-Act.

hell yeah

People gonna be talking about this one for years

Why aren't you in a book club?

parenting be like

Using these six rules and natural deduction, prove that [C > (C > C] entails C > C

Here's another one. Use any rule system you like:

1. (W ∨ X) ∨ (Y ∨ Z)
2. X → Y
3. ¬Z
∴ W v Y

A solution using a Frege-Hilbert system:

01. (W ∨ X) ∨ (Y ∨ Z)
02. X → Y
03. ¬Z
04. | ~(W v Y) - Assume
05. | ~W & ~Y - 4 DeMorgan's Theorem
06. | ~Y & ~W - 5 Commutation
07. | ~Y - 6 Simplification
08. | ~X - 2,7 Modus Tollens
09. | ~W - 5 Simplification
10. | ~W & ~ X - 8,9 Conjunction
11. | ~(W v X) - 10 DeMorgan's Theorem
12. | Y v Z - 1,11 Disjunctive Syllogism
13. | Z - 7,12 Disjunctive Syllogism
14. | Z & ~Z - 3,13 Conjunction
15. ~~(W v Y) - 4-14 Reductio ad Absurdhum/Indirect Proof
16. - W v Y - 15 Double Negation

A solution using a Fitch system:

01. (W v X) v (Y v Z)
02. X → Y
03. ¬Z
04. | ~(W v Y) - Assume
05. | | W - Assume
06. | | W v Y - 5 vI
07. | | ⊥ - 4,6 ⊥I
08. | ~W - 5-7 ~I
09. | | Y - Assume
10. | | W v Y - 9 vI
11. | | ⊥ - 4,10 ⊥I
12. | ~Y - 9-11 ~I
13. | | W v X - Assume
14. | | | W - Assume
15. | | | ⊥ - 8,14 ⊥I
16. | | | X - Assume
17. | | | Y - 2,16 →E
18. | | | ⊥ - 12,17 ⊥I
19. | | ⊥ - 13,14-15,16-18 vE
20. | | Y v Z - Assume
21. | | | Y - Assume
22. | | | ⊥ - 12,21 ⊥I
23. | | | Z - Assume
24. | | | ⊥ - 3,23 ⊥I
25. | | ⊥ - 20,21-22,23-24 vE
26. | ⊥ - 1,13-19,20-25 vE
27. ~~(W v Y) - 4-26 ~I
28. W v Y - 27 ~E

Tomorrow maybe we do FOL problems

Here's an easy set for y'all niggas:

Problem #1: ∀x(Fx → Gx), ∃xFx ⊢ ∃xGx
Problem #2: ⊢ ∀xFx v ~∀xFx
Problem #3: ∀x∀yGxy ⊢ ∃xGxx

Good morning.

Concentrate.

Problem 1: ∀x(Fx → Gx), ∃xFx ⊢ ∃xGx

Frege system:
01. ∀x(Fx → Gx)
02. ∃xFx
03. Fa - 2 Existential Instantiation
04. Fa →Ga - 1 Universal Instantiation
05. Ga - 3,4 Modus Ponens
06. ∃xGx - 5 Existential Generalization

Fitch system:
01. ∀x(Fx → Gx)
02. ∃xFx
03. | Fa - Assumption
04. | Fa →Ga - 1 ∀E
05. | Ga - 3,4 →E
06. | ∃x(Gx) - 5 ∃I
07. ∃x(Gx) - 2,3-6 ∃E

Problem #2: ⊢ ∀xFx v ~∀xFx

Frege system:
01. | ~(∀xFx v ~∀xFx) - Assume
02. | ~∀xFx & ~~∀xFx - 1, DeMorgan's Theorem
03. ~~(∀xFx v ~∀xFx) - 1-2 Indirect Proof
04. ∀xFx v ~∀xFx - Double Negation

Fitch system:
01. | ~(∀xFx ∨ ~∀xFx) - Assume
02. | | ∀xFx - Assume
03. | | ∀xFx ∨ ~∀xFx - 2 vI
04. | | ⊥ - 1,3 ⊥I
05. | ~∀xFx - 2-4 ~I
06. | ∀xFx ∨ ~∀xFx - 5 vI
07. | ⊥ - 1,6 ⊥I
08. ~~(∀xFx ∨ ~∀xFx) - 1-7 ~I
09. (∀xFx ∨ ~∀xFx) - 8 ~E

Problem #3: ∀x∀yGxy ⊢ ∃xGxx

Frege system:
01. ∀x∀yGxy
02. ∀yGay - 1 Universal Instantiation
03. Gaa - 2 Universal Instantiation
04. ∃xGxx - 3 Existential Generalization

Fitch system:
01. ∀x∀yGxy
02. ∀yGay - 1 ∀E
03. Gaa - 2 ∀E
04. ∃xGxx - 3 ∃I

Now that we've studied Frege's logic, let us move on to his social theories