All Questions
Tagged with symbolic-logic logic
252
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Was Tarski the first to discuss the logically of the truth predicate?
Tarski famously discussed, formally, the logically of the truth predicate, in The Concept of Truth in Formalised Languages (1935).
Was he the first to do so?
Thank you for any scholarly reference.
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What is a definition, written in symbolic logic, for a person living nearby?
Students often need some axioms and/or definitions to play with in order to learn formal logic.
What is a definition of a neighbor written in the style of symbolic logic?
By neighbor, we mean a person ...
2
votes
1
answer
75
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Importance of Logical Notation
Does better notation lead to ease of abstraction and shorter proofs? I ask because I tried translating the following from Euclid’s Elements into my own idiosyncratic notation: Prime numbers are more ...
4
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1
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Can assumption in Hilbert style proof system be contradictory?
⊢（¬A→A）→A
I don't know how to solve this proof with the Axiom, Theorem and Inference rule in Hilbert-style proof system so I ask my classmate and he show me his answer. After viewing his proof, I was ...
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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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3
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stuck! first order logic - identities (specifically "only")
Please correct me on why these may be wrong(identities). I've tried many times but it seems I'm missing something.
for they key: M(x) = is a moon, O(x,y) = x orbits y, and m = mars, e = earth
Only ...
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6
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What does Tarski mean when he says "variables do not posses any meaning by themselves"?
This is an excerpt from Alfred Tarski's Introduction to Logic and the Methodology of Deductive Sciences:
As variables we employ, as a rule, selected letters, e.g. in arithmetic the small letters of ...
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How is this logic valid?
An excerpt from Logic 2010:
In particular, what is confusing is that it permits assuming the conditional but then reaching a contradiction to prove the conditional. In my experience, that is not a ...
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1
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2
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Is it possible to stick to one of these viewpoints of variables?
It has been a struggle to find a precise account of the concept of variables. There are however two viewpoints that I've seen authors convey in several logic textbooks.
Variables as placeholders for ...
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A question on contrapositives and predicates
So I am a freshman taking an intro class to logic. And the question started off from a class exercise we've got which asked us to identify the covering generalization for the following conditional ...
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What did Bertrand Russell mean exactly when he said that *such that*, while fundamental both to formal logic and to mathematics, is "undefinable"?
Bertrand Russell in Principles of mathematics (1903) presents the notion of such that as fundamental to logic and mathematics, and states that it is “undefinable”:
The Indefinables of Mathematics
...
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Treating truth as a predicate
It is interesting to me that in some conventions of logic I have seen (generally, common ones), the form of logical language is designed to make “truth” implicit. For example, merely to write:
P(x)
is ...
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formalization: definite description (narrow reading)
I am not sure which formalization is right [1] or [2]:
'The teacher of Plato does not exist.'
[1] ∃x(Tx,p ∧ ∀y[Ty,p → y=x] ∧ ¬∃y[y = x])
[2] ∃x(Tx,p ∧ ∀y[Ty,p → y=x] ∧ ¬∃z[z = x])
Is it possible to ...
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3
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What's the difference between "iff" and "=df"?
Just a quick question I stumbled upon from my readings.
When some philosophers write A ↔ B and others write A =df B, is there supposed to be a difference?
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Is symbolic logic just a non scientific way when it comes to interpret human natural language?
Let me ask you a thing it is about implication: when I say, if I go to London, I will talk to Paul, I mean an implication, or S=>P. Well, implication means it is necessary that S belongs to P, ...
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