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.
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language proof and logic chapter 13 question 49 Help
Premises:
∃xP(x)
∀x∀y((P(x)∧P(y)) → x = y)
Prove:
∃x(P(x)∧∀y(P(y) → y = x))
I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
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1answer
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language logic and proof chapter 12 question 49 and question 50
I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
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2answers
264 views
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
I can't figure out how to prove that formally. Please, help!!
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4answers
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’
What would a formal Fitch proof for this look like?
I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it.
I started with this, but I don't know if I am doing the right thing, and where to go ...
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4answers
142 views
Symbolic Logic - Quantifier Proof (w/ Conditionals)
I'm not sure if lines 6 - 7 & 8 - 11 are being done correctly. I feel like it's necessary to prove 12 which proves the rest of the problem.
I'm a bit stuck on lines 8 - 11. I initially tried to ...
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2answers
650 views
Fitch Proof by Contradiction help
Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question.
I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
2
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2answers
249 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 ...
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4answers
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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
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1answer
67 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) ...
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2answers
131 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
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2answers
277 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:
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2answers
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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 ...
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2answers
180 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 ...
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0answers
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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 ...
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3answers
984 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)...
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2answers
570 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
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4answers
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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 ...
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3answers
501 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.
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1answer
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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 ≠ ...
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4answers
317 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 ...
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4answers
377 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
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3answers
906 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 ...
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1answer
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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
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1answer
766 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
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2answers
247 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∀...
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3answers
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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
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2answers
473 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)
...
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2answers
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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 ...
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3answers
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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 ...
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2answers
207 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?
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3answers
672 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
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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
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1answer
220 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 ...
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2answers
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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 ...
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2answers
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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
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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
...
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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 ...
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3answers
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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.
...
