Questions tagged [predicate-logic]

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Translation into predicate

How would these statements be translated in predicate? No toddlers drink juice. Someone is Sasha and drinks juice. Therefore, Someone is Sasha and is not a toddler.
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Are ontic predicates similarly (or even well) defined across philosophers? Do they differ from logic predicates?

I've seen the term "ontic predicate" bandied around in some works. Whenever it has a clear definition it seem no different than how one would define it in (first-order) logic, i.e. it being ...
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ontological commitments to properties

Quine's famous thesis about ontological commitment is roughly the following: there exist only entities which fall under the domain of quantification of our theory and that can be the values of ...
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How to prove ∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy) using natural deduction? [closed]

∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy) I tried to use reductio ad absurdum by assuming ¬∃y∀x(Fx→Gy) and then using quantifier negation to simplify it further, but it got very messy when I had to use ∃-elimination ...
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Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)

Does ∃x(Nx & ~Nx) contradiction itself? Is there an error in my proof? Thank you
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2answers
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Fitch Proof help please

I think I got it, could you take a look, please.
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2answers
96 views

Can 'All S is P' ever be false if S is empty?

I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"? In the boolean interpretation 'All S ...
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5answers
249 views

Why is first-order logic interesting to philosophers?

This site had a question: Is First Order Logic (FOL) the only fundamental logic? Let me ask the opposite: Why is FOL still interesting or useful to philosophers? For example, the "ancestor" ...
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4answers
232 views

Why is the notion of domain of discourse at all necessary in predicate logic?

The notion of domain of discourse (also: domain of discourse, universe of discourse, universal set, or universe) is a fixture of mathematical logic which is sometimes claimed to be necessary to the ...
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1answer
252 views

What are the advantages of Aristotle's term logic over predicate logic?

I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic: "I come to semantic ...
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1answer
60 views

What are some of the struggles that come with teaching formal logic? [closed]

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
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1answer
2k views

How do you differentiate between At least one X and Exactly one X in predicate logic?

Here are the following two sentences. At least one person speaks English. ∃𝑥E(x) Exactly one person speaks English. Instead of ∃𝑥E(x), what do I write?
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60 views

What is the difference between p ∧ (p → q) and p → q?

I understand why with a truth table p ∧ (p → q) and p → q are different but from a semantic point they look exactly the same to me. At a glance from a semantics point they look like they should have ...
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0answers
35 views

Can you universally specify using a proper name that is already present in the premise?

i was working on one of the problems in Patrick Suppes' An Introduction to logic, and it asks to show whether "Ptah is an egyptian god. Ptah is the father of all egytpian gods. Therefore Ptah is the ...
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3answers
187 views

Is ¬(a = b) the same as (a ≠ b) in logic

Are these the same in predicate logic with identity: ¬ (a = b) a ≠ b I'm not quite sure whether they can be used interchangeably in proofs. Any help would be great!
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1answer
38 views

How does identity work in modal predicate logic?

Namely how can we can have a correspondence between objects in different possible worlds if they are different? If we have two worlds in S5 aw0(P(x)) = 1 and aw1(P(x)) = 0 How can we 'identify' x ...
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2answers
104 views

Predicate Logic

How do I derive this? Pr 1 ∀x(Fx -> ∀xGx) ∴ ∀x(Fx -> ∀x(Gx \ / Hx)) My attempt: However I cannot used universal derivation due to the free x. I think using ass id and qn would be better ...
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1answer
70 views

Predicate Logic Proof Help! ∃xAx ∨ ∃yFy , ∀x(Ax → Fx) |= ∃xFx [closed]

I am unable to prove it :( I think I need to assume - ∃xFx but what follows later on?
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1answer
78 views

Predicate Logic - Are these two sentences equivalent?

Could you tell me if these two sentences are equivalent? If they aren't, what would be the correct sentence that is equivalent to (1)? Please explain. Thank you! (1) (∀x)[Ax→(∃y)(By & Txy)] (2) (...
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1answer
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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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1answer
117 views

Question about v-variants of variable assignments

In Full Predicate Calculus, some variable assignment q satisfies a disjunction under interpretation U if q satisfies one or both disjuncts under U, it satisfies a conjunction under interpretation U if ...
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1answer
29 views

Having trouble translating english to FOL

Having trouble with this phrase: Any column that contains a cube contains a tetrahedron, and vice versa. I tried this: ∀x ∀y ((Cube(x) ∧ Tet(y)) → SameCol(x, y)) which is incorrect because this says ...
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2answers
82 views

Truth Value of Definite Descriptions

I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-...
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1answer
68 views

SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC

Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.): (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula ...
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1answer
347 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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1answer
73 views

What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
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2answers
85 views

How does one tell if logical expressions are equivalent?

How do I check if these expressions are equivalent? ∀a,b [P(a) ∧ ¬R(a) ∧ S(b)] → G(a,b) ∀a [(P(a) ∧ ¬R(a)) → (∀b [S(b) → G(a,b)])]
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2answers
205 views

Is it possible to construct infinitely many non-equivalent formulas in predicate logic?

In the language of predicate logic with only identity and no predicates, function symbols, or constants, is it possible to construct infinitely many non-equivalent formulas?
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Are there paradoxes involved in allowing for an unrestricted domain in predicate logic?

I've put some thought into this, and just want to make sure I'm on track, or if I need to be corrected. Basically, my answer is this: Yes, you need to always specify a domain when formalizing into ...