Questions tagged [symbolic-logic]
For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.
352 questions
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Is addition a ternary predicate or a predicate with an arity greater than three? [closed]
Is addition a ternary predicate or a predicate with an arity greater than three?
I ask because of the following: Addition is a mathematical operation.
A mathematical operation is a function.
A ...
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Does math admit (care about) the existence of an entity?
Philosophers always concern about the existence of entities. For example, they discuss the propositions like "The bird exists." or "Unicorn does not exist". But in math, ...
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How would you formalise the sentence "I am a liar" in first order logic?
How would you formalise the sentence "I am a liar" in first order logic?
ChatGPT can't do that, what seems to be the problem?
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Does a vacuous quantifier have to be interpreted vacuously?
Does a vacuous quantifier have to be interpreted vacuously? I would say no because of the following:
Let multiplication be interpreted as conjunction
Let addition be interpreted as disjunction
Let N ...
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3
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Relation between the truth of P→Q when P is false and the principle of explosion
According to the truth table, P→Q is true when P is false.
On the other hand, the principle of explosion (ex falso quodlibet) states that from a contradiction, such as P∧¬P , any statement Q can ...
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Can existence be treated of as an n-ary predicate? [closed]
Can existence be treated of as an n-ary predicate?
I ask because it seems it can be treated as an n-ary predicate due to the following examples:
A. Infinity exists in divisibility as a mode.
A1. ∀X1∀...
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Can the definitions of quantifiers be formalized inside first-order logic?
Can the definitions of the universal and existential quantifiers be formalized inside of first-order logic?
Consider the following:
There exist X1 and X2, such that X1 is a quantifier, and X2 is a ...
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Has a closed set of rules of inference, sans conditional/indirect proof, for a textbook system of natural deduction ever been crafted/discovered?
By "textbook system", I mean like the commonplace 18-or-so-rule kind of systems of natural deduction that prevalently appear in logic textbooks, such as those of, say, Patrick Hurley or Stan ...
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4
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Truth Tables vs Metalanguage
I've seen in the book "Logic for everyone" by Jason Decker that he writes the Propositions on the header of the tables as meta-Propositions.
E.g. for the formula
A→C
𝒜
𝒞
𝒜→𝒞
T
T
T
T
F
F
...
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Do variables belong to metalanguage
I'm learning the nuance between using and mentioning. Maybe what I'm going to write is a result of misunderstanding.
The object language (OL) contains names of objects from a domain, a assumed real ...
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Is there a theory which is the true theory of logical reasoning?
Is there any theory of which any logician would be prepared to say that it is the true theory of logical reasoning?
If there is one, which is it, and who says that it is the true theory of logical ...
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How to prove ¬(A ∧ B) → (¬(C → D) ∧ ¬C) ⊢ A? Fitch-style for TFL proof
I'm really confused how to solve this and how to correct it? If anyone could help I would greatly appreciate it!
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How to prove this argument? I'm thinking it's an invalid argument, but it was presented on an exam as valid & provable
The argument is as follows:
~D ∨ F
F ⊃ ~D /~D
with lines 1 and 2 being premises, and ~D being the conclusion. Apologies if that is not the most standard notation; that's how it was ...
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Chemistry & Peirce’s Existential Graphs
Do Peirce’s Existential Graphs remind one of the orbital and molecular diagrams used in General Chemistry & Organic Chemistry?
For reference, check the following links:
https://plato.stanford.edu/...
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Why are we allowed to use inference rules instead of truth tables in order to prove an argument's validity?
According to Copi's Symbolic Logic
A more convenient method of establishing the validity of some
arguments is to deduce their conclusions from their premisses by a
sequence of shorter, more ...
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