Questions tagged [fitch]
Frederic Brenton Fitch (1908 – 1987) was an American logician who taught at Yale. He invented the Fitch-style for natural deduction. He is also famous for the paradox of knowability. The tag may also refer to natural deduction proof environments in Fitch-style calculus for giving and checking proofs.
83
questions
2
votes
2answers
205 views
Fitch Biconditional Proof Help?
Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
1
vote
4answers
2k views
How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction
Here's another of Tomassi's exercises I can't solve (Logic, page 106):
: (( P → Q ) ∨ ( Q → R ))
I have to use natural deduction and the only rules I know are:
• assumptions,
• modus ponendo ...
1
vote
1answer
66 views
Conditional IFF - Not sure what's wrong
"Not a valid application of the rule".
I don't think 7 - 8 is something that really needs to be proven beyond a reit, but I feel like you should be able to...
I'm quite confused on proving Cube(a) ...
1
vote
2answers
126 views
Symbolic Conditional Help
Premise:
(Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d))
Cube(c) -> Dodec(e)
Goal:
~Tet(a) -> Dodec(e)
Anyone have a clue on where to start with this?
2
votes
2answers
244 views
How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?
I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try.
First attempt:
Second attempt:
0
votes
2answers
529 views
Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?
Wikipedia describes the law of the excluded middle as such:
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
0
votes
2answers
178 views
Why does modal logic need to use ◻◻p?
In Frederic Fitch's Symbolic Logic he proves (11.8, page 66) that "◻p" coimplicates "◻◻p".
In 11.10 (page 66), he writes,
A system almost the same as the system Lewis calls S2 is obtainable by ...
1
vote
0answers
39 views
How did Fitch's opposition to the Russell-Whitehead theory of types turn out since the 1950's?
In a footnote to Appendix C of Frederic Fitch's Symbolic Logic (page 217), Fitch writes about his article, "Self-Reference in Philosophy":
It is reprinted here in order to indicate more fully my ...
3
votes
3answers
779 views
2 simple Formal Fitch Proofs
I'm having difficulty proving these. They seem obvious, but I can't figure how to set up formal proofs for them. Could anyone give me clues on how to start them?
¬(P∧¬Q) from the premise P→Q;
¬Q→(R→P)...
1
vote
2answers
428 views
Prove transitivity in Fitch
How to prove transitivity in Fitch.
Is it Ok?
| 1. a = b
| 2. b = c
| 3. c = c =Intro
| 4. a = c =Elim: 3, 2
| 5. b = c =Elim: 4, 1
3
votes
4answers
995 views
Given p ⇒ q and m ⇒ p ∨ q, use the Fitch System to prove m ⇒ q
I have spent about 6 hours now trying to prove this using the Fitch system and I just keep going in circles! Attached is one of the 500 attempts :) I have a feeling it's done fairly simply and ...
2
votes
3answers
436 views
Prove ¬∃x ∀y (E(x, y) ↔ ¬E(y, y)) given no premises
The only way I could think of to do this problem is reductio, but since the two biconditional terms are not contradictory, I am pretty stuck.
1
vote
1answer
1k views
LPL ( language proof and logic) - FITCH - 14.12
what's wrong with the last line in my proof? i can't understand the error on line 21
i wrote the important line of the proof :
18 - ∀z (Cube(z) → (z = c ∨ z = f))
19 - ∃y (Cube(c) ∧ Cube(y) ∧ c ≠ ...
2
votes
4answers
303 views
In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
1
vote
4answers
349 views
Language Logic Proof Question: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)]
I am wondering if I have completed this proof properly. I don't think I have it right. It's tricky!
Conclusion: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)]
¬¬∃x∀y[E(x,y) ↔ ¬E(y,y)]
∃x∀y[E(x,y) ↔ ¬E(y,y)] ¬E,1
...
2
votes
3answers
795 views
How do I apply existential elimination to the following Fitch proof?
I am trying to prove ∀x.∀y.loves(x,y) from Relational Proofs using the Fitch system from Barwise and Etchemendy.
I can get as far as line 5, but I cannot figure out how to apply Existential ...
-1
votes
1answer
2k views
fitch proof chapter 13 exercise 13.49 [closed]
Does anyone know how to solve
13.49
∃x P(x)
∀x ∀y ((P(x) ∧ P(y)) → x = y)
= ∃x (P(x) ∧ ∀y (P(y) → y = x))
and 13.50
∃x (P(x) ∧ ∀y (P(y) → y = x))
=
∀x ∀y ((P(x) ∧ P(y)) → x = y)
I have big ...
2
votes
1answer
734 views
prove: ∃x ∃y (Cube(x) ∧ Cube(y) ∧ x ≠ y ∧ ∀z (Cube(z) → (z = x ∨ z = y)))
I need a formal (Fitch) first order logic proof for:
∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y ∧ ∀z (P(z) → (z = x ∨ z = y)))
Given
∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y)
∀x ∀y ∀z ((P(x) ∧ P(y) ∧ P(z)) → (x = y ∨ x = z ∨...
2
votes
2answers
232 views
I am stuck on how to prove the contradiction of R(b,a) can anybody help me?
Here are some well-known properties of dyadic (2-place) relations:
∀xR(x, x) (Reflexivity)
∀x¬R(x, x) (Irreflexivity)
∀x∀y(R(x, y) → R(y, x)) (Symmetry)
∀x∀y(R(x, y) → ¬R(y, x)) (Asymmetry)
∀x∀y∀...
6
votes
3answers
1k views
In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?
It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck.
I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
3
votes
2answers
436 views
Formal proof : predicate logic
This is what I need to prove formally:
1.∃x Cube(x) ∧ Small(d)
.
.
.
.
Goal :∃x (Cube(x) ∧ Small(d))
I have already tried different ways, but I still can't prove the goal.
1. ∃x Cube(x) ∧ Small(d)
...
4
votes
2answers
3k views
Fitch Proof - LPL Exercise 8.17
I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise.
I am finding it ...
1
vote
3answers
2k views
Fitch Proof - Logic LPL 13.11
I am currently doing questions for my course from LPL Chapter 13.11.
I have posted the screenshot of what I am trying to do.
I am quite stuck and I can not think of a way to get to ~Tet(a). Any hint ...
2
votes
2answers
201 views
Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B
Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B. (Use Fitch)
I have no idea where to start, can someone help?
5
votes
3answers
631 views
How can I prove a contradiction follows from P <-> Q and P -> ~Q?
I am so close to solving this problem: (Language Logic and Proof 8.36).
http://imgur.com/a/nzYCU
All I need to do to complete the proof is show that P <-> Q and P -> ~Q is a contradiction (the ...
1
vote
4answers
2k views
Fitch Formal Logic Help 6.26
6.26
Premise:
A v (B ^C)
Premise: ~B v ~C v D
Goal:
A v D
Prove it formally without using DeMorgan's Law.
1
vote
1answer
198 views
How would I deduce a≠c from a≠b and b≠c in Fitch?
How would I deduce a≠c from the premises a≠b and b≠c in Fitch?
This is what I've done so far.
b=b (=Intro)
b≠a (Ana Con)
b≠c (Reit)
And then for some reason I get stuck here?
I know this sounds ...
1
vote
1answer
2k views
Logic – Deduction in Tarski's World (Fitch/LPL 13.36)
I am working on proving the following question:
| ∀x [Dodec(x) → LeftOf(x, a)]
| ∀x [Tet(x) → RightOf(x, a)]
|–––
| ∀x [SameCol(x, a) → Cube(x)]
The question has the following rules:
[…] give a ...
3
votes
2answers
1k views
LPL 10.26 - Fitch - How to use ∀ Intro and ∃ Elim?
I am using LPL (Language, Proof, and Logic, commonly known as LPL) and the bundled Fitch program. I am trying to solve problem 10.26:
10.26: ∀x Tet(b) ↔ ∃w Tet(b)
Looks simple enough, as the ...
4
votes
2answers
2k views
Fitch style disjunction elimination
I am having difficulty in formally proving a simple argument. Consider
P(x) v Q(x)
not P(x)
----------
Q(x)
It is easy to see that the argument is indeed valid, but I cannot seem to prove it ...
3
votes
3answers
2k views
Prove A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implication
This is a repeated question: Language Logic and Proof Q. 6.26
Using the natural deduction rules, give a formal proof of
A ∨ D
from the premises
A ∨ (B ∧ C)
(¬ B ∨ ¬ C) ∨ D
...
2
votes
4answers
4k views
Conditional disjunction equivalence proof using FItch
Prove P v Q ⇔ ¬Q → P
So far I have the obvious things...
1. P v Q
_
| 2. ¬Q
| _
| 3.
| 4.
| 5.
| 6.
| 7.
| 8. P
9. ¬Q → P → Intro 2-8
I think the problem here is that I do not ...
4
votes
3answers
2k views
Disjunctive Syllogism in a Fitch Style System
I'm trying to prove an argument of the form:
B
~(C & B)
Therefore: ~C.
I can expand out ~(C & B) into ~C OR ~B, and with the premise B, it is clear that ~C is the case.
...
