Questions tagged [philosophy-of-logic]
Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.
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Does the plurality of type-theoretic foundations disprove logical monism?
There is apparently controversy around accepting logical pluralism - the view that there is more than one "correct" logic, which is surprising to me as a mathematicians.
Logical pluralism ...
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Taxonomy of Reason
How many types of reasoning are there? It seems to me that there are only three that spoken of frequently. Is it only deductive, inductive, and abductive, and rest can be derived from them or should ...
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What is the nature of proof in type-theoretic models of linguistic infelicity?
In computer programing languages, some compilers and interpreters are capable of dynamically assigning types at run-time. Types, which are specified by the grammar that describes the compiler and its ...
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On the Notion of an Underlying Logic [closed]
Context: I have recently been developing the idea of an 'underlying logic' behind reality, in particular how it is understood through the lens of the Tarskian framework and so wish to present my ideas ...
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Question about Hilbert ε-calculus
Why is Hilbert’s ε-calculus used?
I am reading a paper(Schiemer& Gratzl [2016]) in which a mathematical structuralist attempts to provide a semantics for arbitrary reference. The process goes as ...
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Is there consensus whether function or predicate/relation is the more basic notion, particularly in the philosophy of mathematics?
So, usually in logics and mathematics in general, both concepts are introduced.
In set theory a function can be defined as a triple of two sets and a relation (which itself is defined as a pair of ...
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Natural language as a metalanguage for formal logics?
I have recently been researching the relation between formal and natural languages as well as Tarskian hierarchies and so would like to present an idea has been on my mind. I am not aware if anything ...
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On Trivial Systems
Context: I have been thinking about the idea of trivial theories for some quite some time now and would like to express some ideas about trivial systems of logic that I haven't really seen anywhere ...
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Is the statement, “The existing golden mountain doesn’t exist” a contradiction?
Is the statement, “The existing golden mountain doesn’t exist” a contradiction? I ask because it seems it isn’t, especially if you equivocate on the meaning of the word “exist”. To illustrate what I ...
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Is the structure of logical cognition due to a mathematical inevitability?
When you apply formal logic to real-world domains, it becomes evident how central some of the essential notions of logic are in how we reason about the world: negation, disjunction, and implication ...
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Confusion in regards to a passage in "Introduction to Logic" by Alfred Tarski
PASSAGE OF THE BOOK IN QUESTION:
When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be ...
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If a mathematical theorem is true, what it is true of?
Do mathematicians believe that a theorem provides knowledge?
If a theorem is true, it is true of what, according to mathematicians?
Thank you for any scholarly reference.
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What sort of fallacy is it when the reasoner argues from within too narrow a context of an issue?
Sometimes, people reason unacceptably when a critique or command given within a certain context is assumed to be valid only within that context. This is obviously an example of poor judgement in the ...
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Is there a middle ground between demonstrative and probabilistic reasoning?
There are certain things that I feel confident of, things that I feel confident of almost in a demonstrative sense, and yet I find it troubling to articulate it in that matter. It is hard to come up ...
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Would Robert Nozick's "principle of plenitude/fecundity" include worlds based in different logics?
Robert Nozick's proposed his "principle of plenitude" or "principle of fecundity" where he proposed that all possible worlds would exist (a very similar position to that from David ...
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