Questions tagged [formal-system]
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23 questions
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What is it to write something "formally"?
Note: this question seems apt for flagging as a duplicate, but I haven't found a duplicate of it yet. Apologies in advance if I haven't done my full due diligence regarding this matter.
Now, I was ...
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How can one determine the ontological statuses of variable and constants in this type theory?
I am reading the book "Type theory and formal proof" by Rob Nederpelt, Herman Geuvers.
Chapter 2 "Simply typed lambda calculus"
Section 2.2 "Simple types" says "We ...
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Analytic vs. continental approaches to knowledge and Gödel's Incompleteness Theorem
My main question relates to what is unknowable and unprovable, although I'm not sure proof is even the right word to use in philosophy. I am not educated in philosophy in any way so in advance sorry ...
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Can we define a formal language as a set generated by at least one recursive function? [closed]
If we think about different formal languages like first-order logic and various variations thereof, propositional logic, etc., is it true that they all amount to the fact that the "language" ...
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Would an ontological pluralist view existence as a relation between an object and its mode?
Would an ontological pluralist view existence as a relation or two-place predicate between an object and its mode? To give an example of what I mean consider the following sentence: Pegasus exists in ...
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Can a cone represent Gödel's 1st incompleteness theorem? [closed]
I want to understand if a cone represents visually Gödel's result. Firstly I am summarizing key points of Gödel. We have one grid, with rows representing predicates S[1, ], S[2, ], etc. and column (...
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Did Wittgenstein think that non-numeric entities can exist in numeric systems? [duplicate]
I once watched a lecture on YouTube about Wittgenstein’s philosophy of mathematics.
The speaker said something very interesting: Wittgenstein did not simply dismiss Gödel’s incompleteness theorems as ...
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What is the technical difference between an algebra and a logic?
TLDR
What is the difference between a generic algebra and a generic logic, and by what way can we articulate by definition that they have the same metatheoretical structure in the case they are ...
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What are the most relevant investigations into the complete formalization of philosophy, at the level of rigor and precision found in mathematics?
I'm referring to attempts to translate or structure all philosophical reasoning within formal systems (such as mathematical logic). Are there any schools of thought or authors who have seriously ...
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Making first-order logic perspectival
How do linguists and computer scientists typically make propositions in first-order logic "perspectival", in the way that natural language gives us pronouns like "I", relative ...
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Does logic "come before" mathematics?
I always thought of mathematics as being founded on logic. After all, even the most basic mathematical definition is based on logic. When we enunciate ZFC axioms, we're relying on the concepts of &...
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Philosophical system
I want to build a philosophical system and describe a certain process. The system has x number of axioms. I can translate the axioms into predicates and quantifiers or into Boolean form. My question ...
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Why does existential quantification appear to be predicative?
When one uses the universal quantifier '∀', it is ungrammatical to not include both a variable it binds, and a formula it scopes over: ∀ x, Φ. Likewise, in natural language, "For all x, Φ is true&...
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Does Gödel’s incompleteness theorems imply the necessity of an infinite recursive hierarchy of “proofs”, and that any “proof” is relative?
My understanding is that Gödel’s incompleteness theorems state that the consistency of any axiomatic system cannot be proven within that axiomatic system, and requires a stronger axiomatic system in ...
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What is the proof of that self-application in the λ-calculus is not inconsistent?
The SEP entry on lambda calculus discusses its consistency, surmising:
Early formulations of the idea of λ-calculus by A. Church were indeed inconsistent. The Church-Rosser theorem gives us, among ...
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