# Questions tagged [predicate-logic]

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### How do I read predicate logic formulas using proper english not the one used by mathematicans?

Question. How do I reed predicate logic formulas in proper english, not one used by mathematicans? Im interesint in precieving formulas audially not visually. I am interested in simple set of rules ...
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### Are there any known precendents of philosophers using modal logic (or any other theory of math) to formalize works of other philosophers?

Like maybe philosopher Anna wrote a long and complicated treatise on some topic. Then comes philosopher Bob who interprets Anna's treatise in some way and writes down his interpretation of Anna's ...
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### Are sets unary relations, and are unary relations sets?

On page 57 of Axiomatic Set Theory by Patrick Suppes, he defines a binary relation as a set of ordered pairs. Definition 1. A is a binary relation iff ∀x[if x∈A then ∃y∃z[x=(y,z)]] He defines an ...
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### If a predicate doesn't determine a set, does that predicate even exist in the first place?

I thought of asking this in the Math Stack Exchange, but then I thought this stack exchange is better. Certain predicates define sets, such as "x is not equal to x". Other predicates do not, ...
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### Negating the verb and negating the subject 's property

What is the strict and exact relation (implication, equivalence etc.) between these two sentences?: I. Alcibiades is not wise. (Negating the subject 's property) II. Alcibiades is not (=isn 't) wise. (...
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### Did Russell had something like the notion of domain in the sense defined now by mathematics textbooks?

The expression ∀x(ϕx → ψx) is supposed to mean that, in Russell's parlance, ϕx → ψx is true "for all values of x". However, what are those values that Russell is referring to? At some point ...
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### Why not just give up on the idea of truth-functionality?

I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
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### Definite Descriptions VS 'Exactly' Statements

The problem I am facing is why we can’t treat a definite description as a statement about exactly one object having certain properties. For example the statement: “The author of Evangeline is Henry ...
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### Why must we always use different variables with overlapping quantifiers?

The statement "If anything is good and all good things are safe, then it is safe" is expressed logically as: (x){[Gx • (y)(Gy ⊃ Sy)] ⊃ Sx} What are the ambiguities or wrong interpretations ...
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### Existence, Stating/Proving in Logic

Proving dogs exist If x barks then x is a dog: ∀x(Bx → Dx) t: Timmy (a dog) PROOF: ∀x(Bx → Dx) [Premise] Bt [Premise] Bt → Dt [1 UI] Dt [2, 3 MP] ∃x(Dx) [4 EG] QED Proving ghosts don't exist If the ...
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### Predication for Aristotle

According to Aristotle’s predication, in saying “Socrates is a philosopher” would the philosopher be a predication? If so, would referring to a philosopher alone (for example “the philosopher is wise”)...
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### Existence as a Predicate

In Predicate logic if I wanna say, Atoms exist, I don't/*can't (?) use Ex = x exists (make existence a predicate) and state Ea, where a = Atoms. The correct way to express Atoms exist is Ex(Ax), Ax = ...
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### Where do presuppositions fit into Grice's theory of meaning?

To clarify, by "Grice's theory of meaning" I am referring to the view that the informational content or meaning of an utterance is made up of three components: what is said - the actual ...
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### Why is the identity predicate needed?

In Logic: The Laws of Truth the identity predicate is introduced as an extension of general predicate logic (GPL). The following propositions are given as motivating examples: (1) "Mark Twain is ...
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### What does "unqualified notion of truth" mean in this passage?

From pages 252-253 of The Laws of Truth by Nicholas Smith: If we consider bare, uninterpreted closed wffs, we can say that they are true in some models and false in others, but we cannot say that ...
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### Cogito Ergo Sum in Predicate Logic

Descartes' famously declared "cogito ergo sum (I think, thus I exist). How do you translate this into predicate logic? If T = I think and E = I exist, propositional logic has no problems (vide ...
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### General sentence operators

There are lots of operators that act on sentences. Here are a few examples: P and Q not P forall x.P necessarily P eventually P x believes that that P it is obligatory that P etc. The first two ...
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### First order logic and the cosmological argument

The way I see it, the cosmological argument, if one takes into consideration only what has been observed in the universe, goes something like this: For everything in the universe, if it has a ...
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### Is existential quantification in PL exclusive or modally inclusive of other existential quantifications in the same discourse universe?

In "(∃x, ∀x(Px)) ∧ (∃y, ∀y(Qy))", are the sets of x's and y's necessarily exclusive to each other, i.e. does the fact that we are using different variables (x and y) for them imply that NONE ...
1 vote
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### How would a logician define the phrase "all other things being the same"?

Here are some Examples of the Phrase All other things Being the Same All other things being the same, the juice of a Granny Smith Apple is more acidic than a the juice of a Red Delicious Apple. All ...
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### Proof for predicate logic

Prove the following formula in Fitch format: ∃x(∀y(P(y)→y=x)∧P(a)) |= ∀x∀y(¬(x=y)→(¬P(x)∨¬P(y))) I tried to use universal introduction as my main rule but didn't know how to proceed
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### Would a "disagreement operator" break down if iterated too much?

Let D(S) read as, "I disagree that S." It is possible to iterate this, so that DD(S), "I disagree that I disagree that S." Then we can go on to DDD(S), and so on. (For a peer-...
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### What exactly is the relationship between first-order logic and the axioms of ZFC? Which one is more fundamental?

I have never been formally trained in logic and philosophy. I became increasingly interested in the foundation of mathematics after I graduated from university. Recently, I've been self-studying ZFC ...
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### Instantiation of the statement : (x)Px ∨ (x)Qx [closed]

1.(x)Px ∨ (x)Qx I am currently reading a logic book by Patrick J. Hurley, and in the book the author says that we can't universally instantiate a statement like statement 1. Specifically, he says that ...
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### Help needed with predicate interpretations- Wilfrid Hodges logic

I was going through Hodges' Introduction to Elementary Logic and was rather puzzled by a section where one is asked to translate an argument into a predicate interpretation. The entire thing reads: ...
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### Philosophy book written using logic statements

I would like to translate a philosophy text into logic axioms and propositions. Then, I would like to use prolog to check if the text is logically consistent. However, I find it difficult to translate ...
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### Translation of Arguments from Propositional Logic to Predicate Logic

How exactly does this work? What can we assume stays the same, what changes? Take for an example this (valid) argument: A & ~C ~C > ~D ~D > B ∴ B Now let us take rewrite it according to ...
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### At most one relations: using Negation Vs Implication

I am trying to come to terms with expressing using quantifiers using various examples. My question here is about a general approach for expressing at-most one relations in logical language. For ...
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### Natural Deduction Proof with double quantifier (predicate logic) [closed]

Premise: (∃y)(∀x)(Px v Py) Conclusion: ~(∀y)(~Py) I'm starting out assuming the negation, i.e., (∀y)(~Py). But then I'm unsure how to find a contradiction within that subderivation. Here's what I've ...
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### Understanding the syntax of subsitution

I have a question about the meaning and semantics of substitution, I apologise if this is off-topic but I thought here would be the best place as it's more about the semantics and meaning than any ...
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### Nested Quantifiers Proof - Logic

When I prove this: -∃x.P(x) ⊢ ∀x.-P(x) [True] I did it like that: ∀x.-P(x) ⊢ ∀x.-P(x) because (negative ∃) -∃x.P(x) becomes ∀x.-P(x) so that we can say that it's true. However, I didn't ...
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### Proof of the Model Universe Theorem: Proving the invalidity arguments in quantifier logic

I am studying how to prove an argument in quantifier logic is invalid. The textbook I am using by Virginia Klenk claims that you can use a Model Universe that contains a finite number of objects to ...
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### Help me solve this predicate logic proof theory: -(∀z)(∃y)Tzy ⊢ (∃z)(∀y)-Tzy

-(∀z)(∃y)Tzy ⊢ (∃z)(∀y)-Tzy Using Lande, (AI,EI,AE,EE,->E,->I,-I,--E,^I,^E,vI,vE) I cannot figure out the proof on this sequent.
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### What would we gain by allowing quantification over logical constants?

In first-order logic, we quantify over individuals, and in second-order logic, we quantify over properties. However, could we extend this idea to include quantification over logical connectives, ...
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### Is ∀x x = x a first-order validity or simply a logical truth (that is not a first-order validity?

I've been wondering about this. The textbook ''Language, Proof and Logic'' defines a first-order validity as the following: ''A sentence of FOL is a first-order validity if it is a logical truth when ...
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### Is al-Farabi right that predicates must add information and existence is not a predicate?

Al-Farabi claimed that existence is not a predicate, because "exists" as in "Apple is red and exists." doesn't bring any new information, but does a predicate have to bring in a ...
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### Is categorical logic the same as predicate logic

In philosophical logic, categorical logic is the logic that deals with the logical relationship between categorical statements. I wonder if categorical logic is considered the same as predicate logic (...
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### Is the following derivation of predicate logic correct?

I recently discovered https://proofs.openlogicproject.org/, except I'm still figuring out the appropriate rules that are needed for the system to check my proof. I thought it'd be quicker to turn to ...
1 vote
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### Checking translations of predicate logic

Let Dx = "x is a detective", U12 = "1 is the uncle of 2", and appropriate lowercase letters for names. If there are any detectives, John is the only detective. No detective is ...
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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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I think I got it, could you take a look, please.
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### 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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### 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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### 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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### 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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