# Questions tagged [predicate-logic]

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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 = ...
39 views

### 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 ...
745 views

### 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 ...
553 views

### 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 ...
77 views

### 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 ...
639 views

### 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 ...
93 views

### 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 ...
25 views

### 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
83 views

### 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 ...
51 views

### 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
66 views

### 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-...
169 views

### ZFC Axioms and First Order Logic

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 ...
37 views

### 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 ...
1 vote
62 views

### 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: ...
159 views

### 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 ...
152 views

### 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 ...
52 views

### 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 ...
54 views

### 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 ...
119 views

### 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 ...
1 vote
113 views

### 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 ...
63 views

### 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 ...
148 views

### 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.
60 views

### Could we supply logics make quantification over logical constants?

In first order logic, we make quantification over individuals, and in second order logic, we make quantification over properties. So could we supply logics make quantification over logical constants, ...
264 views

### 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 ...
142 views

### 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 ...
386 views

### 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 (... 83 views

### 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
75 views

### 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 ...
50 views

### 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 ...
1 vote
135 views

### 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 ...
208 views

### 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 ...
55 views

### 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
97 views

I think I got it, could you take a look, please.
216 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 ...
522 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" ...
800 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 ...
476 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 ...
116 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 ...
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?
103 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 ...
1 vote
36 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 ...
255 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!
1 vote
57 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 ...
118 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 ...
123 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? 104 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) (...
35 views

### 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 ...
284 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 ...