Questions tagged [predicate-logic]
The predicate-logic tag has no usage guidance.
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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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