Questions tagged [formalisation]

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22
votes
9answers
3k 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
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4answers
588 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
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6answers
319 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 ...
5
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2answers
660 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 ...
5
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2answers
202 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 ...
4
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3answers
3k 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
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3answers
269 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
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1answer
261 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
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1answer
115 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
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2answers
549 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 ...
2
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2answers
98 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
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2answers
197 views

What is the difference between Herbrand Logic, Relational Logic and 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 ...
2
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3answers
104 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
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1answer
210 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
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1answer
54 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." ...
1
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1answer
97 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
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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
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2answers
1k 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
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2answers
107 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
40 views

Trees/tableaux fir K-IF logic

Are there any attempts for tableaux/ tree rules for Hintikkas K-IF logic?
1
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1answer
86 views

What is (∃!e) in Davidson 1967?

Davidson proposes a causal law for singular event causation. Here is one example of a backward-looking part of such a law (changed slightly for clarity and to avoid copyright infringement): (e)(u)((...
0
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1answer
92 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
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1answer
43 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
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2answers
139 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
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1answer
123 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!
0
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0answers
51 views

Life as a formal system

I am curious if there is some existing work on viewing life as a formal system. In formal system we have: axioms and rules of logic (like in math AND, OR) then we derive and prove theorems I see ...
0
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0answers
56 views

Can somehow formalize Quine's argument of the critics on the division between analytic and synthetic or the indeterminacy of translation? [closed]

It seems better if we could formalize Quine's arguments(now they look more like demonstration)-and it could be hard,of course,asthe differ views on Quine's argument even on whether Quine's attack to ...
0
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0answers
44 views

Is there a method for identifying the logical form of everyday speech sentences?

Is there a method for identifying the logical form of everyday speech sentences? Did any logicians attempt to establish such a method? Bertrand Russell gave a few examples of that but nothing ...
0
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0answers
115 views

Bibliography about non-mathematical applications of logic:

I have been recently playing with modal and temporal modal logics in the context of "organisms" (mostly after some study of entelechy in Aristotle and relatedly, some ideas of current biology). I have ...
-1
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3answers
175 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'...