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Questions tagged [formalisation]

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18
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7answers
2k views

What formal logical systems “resolve” the Liar Paradox?

Short version of my question. What formal logical systems can represent, and seem robust against, the Liar Paradox? N.B. I would like to avoid reference to truth-values, except inasmuch as they ...
17
votes
4answers
559 views

Is Philosophy formalisable?

This is something that has irked me for quite some time, especially since I come from a mathematically oriented background. Can the field of Philosophy be formalised in the sense that Mathematics is ...
6
votes
6answers
310 views

Is there any formal language such that any problem in the Universe can be described unambiguously using this language?

I asked similar question on the "Theoretical Computer Science" board and theoretical computer scientists advised me ask it here, in "Philosophy". So... Is there any formal language such that any ...
6
votes
2answers
171 views

Rigorous resources on the philosophy of language

I would like to find some introductory resources on the philosophy of language that are also rigorous, as I come from a mathematical background with my interests rooted in mathematical logic. Ideally ...
5
votes
2answers
606 views

How does abstraction/generalization in mathematics fit into inductive reasoning?

I have a question about the nature of generalization and abstraction. Human reasoning is commonly split up into two categories: deductive and inductive reasoning. Are all instances of generalization ...
4
votes
3answers
2k views

What's formal philosophy?

Some great logicians and mathematicians (e.g. Gödel) in the past have pointed (perhaps implicitly) to the possibility of formal philosophy (can be referred to as "exact philosophy" as well). I read it ...
3
votes
3answers
217 views

How is free-will formally defined as distinct from determinism, randomness and determinism-randomness hybrid to support moral responsibility?

Usually free-will is assumed by most faith traditions as a prerequisite for moral responsiblity in order to justify eternal punishment. The argument goes as "you are truly responsible for your immoral ...
3
votes
1answer
251 views

Where should one place quantifiers when translating sentences into predicate logic?

I've been trying to learn formal logic but am somewhat confused. Given the following key, how would I symbolize the sentence "Everyone who trusts Ingmar trusts a vegetarian?" Domain: people Vx: x is ...
3
votes
1answer
108 views

Collecting any formalisations of morality

I'm collecting formalizations of "morality" of any philosophical school. (My special wishes is anything for Kant, which I don't understand and for whom I didn't find anything seriously formal, at ...
2
votes
2answers
96 views

Bayesian Confirmation / Justification

Bradley in his book titled " A critical introduction to Formal Epistemology" mentions the grasshopper example (page 122) where: Hypothesis: Unobserved grasshoppers live south of Canada ...
2
votes
3answers
103 views

Correctness of an argument inversely correlated to length?

How do we label the idea that the likely correctness of an argument or theory decreases with the size of the exposition required to expound it? Let me make a probabilistic analogy. Suppose we have a ...
2
votes
1answer
193 views

Classical logic, symbolic logic, higher-order logic, First-order logic? Learning from scratch

I'd like to ask you a question about logic. I study philosophy in a Spanish Christian university. In the first year, we study logic but it's the classical one, following Aristotle's Organon, the ...
2
votes
1answer
34 views

Need help translating a formal definition into FOL

I need help formally translating the following definition into FOL: "a property F is essential to an object x if and only if x could not have been the object it is without possessing the property F." ...
2
votes
0answers
97 views

What is the difference between Herbrand Logic and Relational Logic or Predicate Logic?

I am learning a course from Stanford University, and it introduces the notion of Herbrand Logic. However in Wikipedia I cannot find a definition specifically for "Herbrand Logic", only for Herbrand ...
1
vote
1answer
93 views

How to infer ¬Q when there seems to be no way to

Rule #1: No man shall hit another man. Rule #2: If someone breaks Rule #1, then Rule #1 does not apply to such a one. My specific question is: How can someone infer that Rule #1 does apply to him? ...
1
vote
1answer
30 views

Putting natural language into sentence logic

I’ve been practicing expressing natural language sentences into sentence logic. However, I need help transcribing these following four sentences into sentence logic (along with an accurate ...
1
vote
2answers
872 views

Can a true statement also imply the opposite of itself?

It's unlikely that there could be a thesis that also is its own antithesis. Similarly, a formula usually isn't the "opposite" of itself if we use well-defined terminology. Somehow I have a notion ...
1
vote
2answers
86 views

Formal philosophy

I heard that there are philosophy classes that teach philosophy in a very rigorous and formal and mathematical manner. Are there books that do this? I would like some recommendations.
1
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0answers
36 views

Trees/tableaux fir K-IF logic

Are there any attempts for tableaux/ tree rules for Hintikkas K-IF logic?
0
votes
3answers
164 views

Is philosophy computation?

If philosophy is mathematics and mathematics is computation, can I conclude that philosophy is computation? Can we axiomatize philosophy? Can a computer think for us, given the current rise of AI? I'...
0
votes
2answers
506 views

Descartes's *Cogito* from a modern, rigorous perspective

In Descartes's Meditations, in order to establish a firm foundation upon which he could build a framework to determine philosophical and material truths, he begins by removing all of his then-current ...
0
votes
1answer
85 views

In what ways are formalisms like modal logic Eurocentric?

I mean this as a linguistic question, not a cultural one. Operators in modal logic, like must and should exist in English, and many other languages -- but not in all of them. I mean: Modality is not ...
0
votes
1answer
42 views

Help understanding possible world formalism

I am a total novice to philosophy trying to make sense of a computer science article which makes reference to possible world theory. I don't really understand the formalization in the last sentence ...
0
votes
2answers
127 views

Is there any formal axiomatized definition of Determinism in First Order Logic (FOL), or any other logical system for that matter?

Is there any formal axiomatized definition of Determinism written in First Order Logic (FOL), with a semantic interpretation maybe rooted in Set Theory, or based on any other logical system and ...
0
votes
1answer
101 views

What is the explanatory power of Possible World Semantics?

What kind of problems is PWS particularly suited that e.g. FOL couldn't address? I'm just wondering when is a good time to use PWS and for what kinds of questions. Thanks!