Questions tagged [quantification]

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Homework Question on Quantified Logic Falsehood

For one of my homework challenge questions, I have a true or false type question. The question is as follows: True or False: I'm not particularly sure how to solve this. I have no information about ...
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Can/Do there exist any quantifiers other than “there exists” and “for all”?

I'm curious about why there are only the two logical quantifiers there exists and for all. Intuition and human language support the idea that these quantifiers make sense, but otherwise it seems ...
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Trouble translating English to FOL with Quantifiers

The sentence is: Of all the students, only Claire was angry at 3:00 Here is what I think it is: ∀x [(Student(x) ∧ Angry(x, 3:00)) → x=claire] The textbook (LPL) uses these names and predicates for ...
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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 ...
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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 ...
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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 ...
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2answers
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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 ...
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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(...
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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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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 ...
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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.
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How can I prove ⊢(∀x)(Fx V ~Fx) with natural deduction?

⊢(∀x)(Fx V ~Fx) How can I prove this with natural deduction?
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1answer
153 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 ...
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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 ...
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1answer
92 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 ...
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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 ...
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1answer
256 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 ...
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2answers
174 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, ...
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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, ...
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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?
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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))
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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 ...
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280 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 "...
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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 ...
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2answers
126 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 ...
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635 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 ∀...
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'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:   [...
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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. ...
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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)"
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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-...
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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 ...