Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

Questions tagged [quantification]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
0answers
61 views

Is there a quantitative model of Bentham's Hedonic Calculus?

Jeremy Bentham, in Chapter 4 of his 1781 An Introduction to the Principles of Morals and Legislation, defines what has become known as the Hedonic Calculus. He states, Pleasures then, and the ...
6
votes
4answers
1k views

In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?

I am having a discussion whether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation. Discussion ...
3
votes
1answer
332 views

How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me ...
1
vote
2answers
88 views

When are Accessibility Relations satisfied?

We can only "measure" (quantify) counterfactuals by an accessibility relation to our own world. Therefore how can we assert something as necessarily true in all possible world's if quantification of ...
1
vote
1answer
34 views

Translation from English to FOL

This is what it looks like in English: There is a large sphere, and all large things are to the right of b. Therefore, there is a sphere to the right of b. Which I translated as: [Premise 1] ∃x(...
3
votes
4answers
2k views

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 ...
2
votes
1answer
197 views

Why is faulty generalization called an informal fallacy?

According to wikipedia faulty generalization belongs to the class of informal fallacies. Also, a fallacy is called informal if it originates in a reasoning error other than a flaw in the logical ...
2
votes
4answers
284 views

Any solution to prove (∀x)(∃y)(Fx & Gy) ⊢ (∃y)(∀x)(Fx & Gy) with natural deduction?

(∀x)(∃y)(Fx & Gy) ⊢ (∃y)(∀x)(Fx & Gy) I cannot figure out a way to prove this. I am not even certain that it is provable.
1
vote
3answers
133 views

How can I prove ⊢(∀x)(Fx V ~Fx) with natural deduction?

⊢(∀x)(Fx V ~Fx) How can I prove this with natural deduction?
5
votes
1answer
137 views

Square of Opposition with percentages?

What happens if you replace the statements of the Traditional Square of Opposition with "percentages of the subject term"? Do all the relationships from the Traditional Square of Opposition still ...
2
votes
0answers
40 views

Contact and Separation

If we say for argument that two objects are in contact withstanding physical properties of atoms that prohibit actual contact at that level of observation. From classical observation of the world if ...
1
vote
1answer
88 views

Quantificational Logic Question (Determining Truth-Values)

I was working through these questions and I just wanted to verify my answers since I don't have access to any solutions and I wanted to make sure I was on the right track: Let the following be the ...
3
votes
1answer
101 views

fallacious proof

This is a homework question, but I just have no clue how to approach it. I'm trying to find the step in the following "derivation" which violates the allowed rules of inference. Sorry if the ...
3
votes
1answer
253 views

Where should one place quantifiers when translating sentences into predicate logic?

I've been trying to learn formal logic but am somewhat confused. Given the following key, how would I symbolize the sentence "Everyone who trusts Ingmar trusts a vegetarian?" Domain: people Vx: x is ...
1
vote
2answers
170 views

If it can't be measured, how can we know it's not a delusion?

I'm not talking about solipsism, or the evil demon/genius of Descartes. I'm talking about the McNamara fallacy, which is obviously a fallacy. Can we say that everything that exists is measurable, ...
4
votes
1answer
915 views

General vs Universal

Source: p. 44 Bottom. Ethics ; A Beginner's Guide (2015) by Peter Cave.   The universal and the general are distinct; the general is a matter of degree. Kant sought laws that are universal, ...
2
votes
2answers
1k views

What does the order of nested quantifiers in predicate logic express?

I was looking at this short and helpful slideshow But it's early: in general, what does the ordering of quantifiers translate to?
2
votes
1answer
152 views

How would you go on proving Law of Excluded Middle with Quantifiers?

The following obviously follows true from no premises, but I can't seem to find a formal proof to it unfortunately. ∃x ∀y (¬P (y) ∨ P (x))
1
vote
3answers
160 views

Deduce a new quantifier that negates “there are at least two objects with property P.”

Source: p 195. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I replaced the author's, 2 rotated by 180º with ❷, and 2 horizontally flipped by 180º ✌; because I ...
5
votes
3answers
268 views

What does the term “mathematical logic” mean?

What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical? Also, is "quantificational logic" a particular type of "...
4
votes
1answer
129 views

Prove ∀w(∀v((v=w∧φ(v))⇔φ(w)))

In this math question of mine, an answer pointed me to this theorem: ∀w(∀v((v=w∧φ(v))⇔φ(w))) which in turn, the answerer stated, implies another theorem: ∃v(v=t∧φ(v))⇔φ(t) which was the fact I ...
5
votes
2answers
121 views

Multiple universal quantifiers in an argument

Consider the argument ∀x∀y((S(x,a)∧ S(a,y))→S(x,y)), ∀x¬S(x,x) ├ ∀x(S(x,a)→¬S(a,x)) My approach to formally proving this was to first eliminate ∀x and use x0 as the free variable. Then afterwards ...
4
votes
3answers
567 views

Proving the negation of universal quantification

Consider the following argument ∀x(R(x) ∨ S(x)), ∃x(¬R(x)) ⊦ ¬∀x(¬S(x)) My strategy is to try to prove that ∀x(¬S(x)) is a contradiction, and therefore ¬∀x(¬S(x)) must be true. My solution so far ∀...
1
vote
1answer
65 views

'There aren't any R that aren't B' vs 'There are R and all of them are B'

Source: 14 minutes 40 seconds juncture, Lecture 6-1 (transcription, ... How to Reason and Argue, by Prof Ram Neta PhD in Philosophy So the way we've been using the quantifier all, if you say:   [...
4
votes
1answer
249 views

Universal instantiation and substitution

I've recently read some of the article on first order logic from http://mathworld.wolfram.com/First-OrderLogic.html and I'm puzzled by the explanation of universal instantiation that the author gives. ...
3
votes
5answers
152 views

Can you infer a house exists from the proposition “food cannot be found in any house”?

Give this statement "Food cannot be found in any house (in this area)" Can you correctly infer that "There is AT LEAST a house (in this area)"
1
vote
2answers
56 views

Can someone clear up this semantic proof of quantification logic?

The idea is to proof validity of ∃x(Fx ^ Gx) / ∃xFx To do this I understand you assume invalid and get a contradiction. I have the answer but I don't understand the wording ∃x(Fx ^ Gx) is true-in-...
4
votes
4answers
170 views

Do some things not exist? [closed]

Quod sic: The Statue of Zeus no longer exists (it was destroyed by fire in the 5th century A.D.) Therefore, there is something (the Statue of Zeus) that does not exist. Contra: How can there be ...