Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange
16

In Hartry Field's Saving Truth from Paradox (2009), he splits the resolution of the Liar paradox into two broadly distinct strategies. Either we can accept Classical logic, but need to restrict the class of propositions over which Truth can meaningfully operate, or we can weaken logical inference to block either the deduction of a contradiction from the ...


13

I think it depends a lot on what branch of philosophy you are talking about, but ultimately, the answer is pretty consistently no. In epistemology, the study of knowledge itself, you're much more likely to get into the nitty gritty formal logic. A lot of this branch is studying what we can and can't know, and how different lines of reasoning work; this ...


10

You might try Carnap's famous (but often neglected) Der logische Aufbau der Welt (The Logical Structure of the World). Here is a link to a survey article (unfortunately, behind a paywall). As part of his project he devised a language which he thought could be used to do pretty much what you ask. The project is largely considered a failure, but very ...


10

If philosophy is mathematics and mathematics is computation, can I conclude that philosophy is computation? Yes. So is philosophy merely computation? No because philosophy isn't mathematics and mathematics isn't computation. Can we axiomatize philosophy? If you want. Getting philosophers to agree on a set of axioms should be amusing. Can a ...


8

I think commando has this covered nicely, but I do want to add that strictly speaking Western philosophy and its categories represent (this is contentious) only one culturally distinct view on how to go about philosophy. Other civilizations besides the Anglo-European had/have systems of ethics and ways of knowing that continue to vex Western categorization. ...


6

It has been noted in the preceding answers that attempts at formalization were made in the first part of the 20th century. This isn't really news in philosophy, for centuries philosophers tried to import the rigor found in the mathematics of their time into philosophy by providing a mathematical treatment of philosophical problems. (Think of Spinoza's Ethica ...


5

Formal philosophy is an approach to philosophical questions which attempts to answer them by developing formal systems. Formal systems are those in which ideas (terms, claims, etc) are formalized, meaning symbolized. In such systems, conclusions drawn are typically reached as a function of the form of premises alone, which is to say their logical structure. ...


5

Formalization of philosophy was a primary goal of Russell, the early Wittgenstein and the logical positivists. They applied formal systems of logic to a wide range of philosophical propositions and arguments and on the whole this led them in the direction of logical empiricism, a form of reductionism of sentences to a 'scientific' vocabulary (indeed, the ...


4

Preamble Your fears are regrettably well-founded. Unlike mathematical logic, the philosophy of language is not so clear cut and remains to this day a deeply controversial topic. There are a dozen schools of thought on the philosophy of language, both classical and contemporary. It is a fundamental and unquestionably significant field of philosophical ...


4

Formal philosophy, as others pointed out, is an approach with formalized language. To ease things here, let us assume that the main idea is that by formalization it is possible to infer the thruth value and propositional content directly from grammar and syntax. The ultimate goal is a perfect scientific language where equivocations and misunderstandings are ...


4

Your rephrasings of formulas in words are correct, but in this case moving the quantifier makes no logical difference (classically). You can verify this by converting formulas into equivalent form without implications using A → B = ¬A ∨ B, and then using the fact that quantifiers can be freely moved across conjunction and disjunction as long as the variables ...


3

Firstly, I suggest that you make sure that we're talking about formal philosophy and not 'formal logic', 'formalism' or other areas of philosophy that might use the term in their title, as these likely have much more specific meanings. As far as I know, there is no real definition for what formal philosophy is. In my experience, most people and writers seem ...


3

You're correct that moving from the integers to the rationals does not fit, because the generalisation that inductive reasoning refers to is a generalisation of statements (or predicates) not of the objects themselves. For example, you could generalise from the statement "all the even numbers above 3 we ever tried can be written as the sum of two primes" ...


3

You ask what the implications are for formal modal logic of there being differences among languages in what modal terms they have — or differences with respect to terms we might treat as modal, since it depends on how you define modality. There are no such implications, because the question mixes together two things which logicians keep separate. Terms like ...


3

The way you have chosen to express the rules implies you are assuming a non-monotonic form of reasoning. Rule #1 as stated has no exceptions, while rule #2 expresses an exception to rule #1. In a monotonic system of logic (which includes classical logic) this would lead to a contradiction: if Bob hits Charlie, rule #1 says Charlie may not hit Bob back, but ...


3

The question is, isn't such a doubt contradictory? For if it was possible then one would have accept that nothing is true, and we would have to deny the ensuing cogito argument by default. Not quite. The hyperbolic doubt that Descartes proposes is contradictory, and that's what makes the cogito work, i.e., why we have to accept the cogito. We can doubt ...


2

Classical logic works fine! We assume there is a sentence L such that L = "L is false" 1) L = "L is false" Now we apply Leibniz law: https://en.wikipedia.org/wiki/Identity_of_indiscernibles 2) L is true IFF "L is false" is true Using the definition of truth we get: 3) L is true IFF L is false Our assumption was false! There is no L such that L = "...


2

Is there any formal language such that any problem in the Universe can be described unambiguously using this language? Depending on what you mean with language, one may say that the Universe itself is the language in which every possible problems are "formulated". You may then report your problem to commensurability between "the Universe", and "human ...


2

The arity of a relation R is the number of its "argument places". Thus, the relation "less than" is a binary relation: it has arity 2. We usually write: x < y, but we can write it "more formally" as: <(x,y). An extensional relation of arity n on D is a subset of D^n (i.e. D x D x ... x D: the set of all n-uples). The set of all extensional relations ...


2

The key question here is “Can a computer think for us?” This can be reformulated as “Will strong AI ever be realized?” Or, “Can human understanding be reduced to a program running on a Turing machine?” There are two answers: Yes or No. If Yes, then a program can produce human understanding. Since philosophy is the result of human understanding, ...


2

What you are looking for does not exist. First off, there is no one formal definition for freewill. Not everyone agrees on what free will is beyond generally agreeing that humans have it. There are myriad variants, each with their own little twists. One variant that will give you trouble is the metaphysical freewill approach, which explicitly states that ...


1

The only approach to modality available in any standard First (or Higher-) Order Logic is the approach that attaches an entire theory with a complete axiomatization for every model of every mood. To discuss, for instance Aristotle's famous naval battle argument, we would need to define an entire system of terms that encompass all of the rules and ...


1

If theses can be separated from their antitheses, then yes its 'unlikely'; but Hegel pointed out that this was an assumption that required justifying; and he held that no, it wasn't; theses, contained within themselves their counter-motion (ie negation); and hence to his theory of sublation; see Hegels Logic. It's worth looking at the beginning of paragraph ...


1

I don't have an answer to your first question; but an observation that may help bring forward more helpful answers by focusing on a particular discipline where formal arguments are made as a kind of case study. Take physics, here simplicity is often put forward as a key criteria and thus also a kind of mantra to characterise useful ideas and theories and ...


1

Your first observation sounds like the principle of parsimony, stated cynically, if you are looking for a name. The principle is that the most compact theory is preferred over any more complicated theory that explains the same data. And yours, among other, more aesthetic, considerations is the basic argument supporting the principle. But the connection ...


1

Check out this course on Coursera: https://www.coursera.org/course/mathphil


1

Yes there is. It is the language on which you wrote your question. All other languages including math are subset of your current one. If you look at the history of thought you will see that many thinkers at the end of their life realized the almost infinite power of our language. See Witgenstein for example. People often fly in the clouds of imagination ...


1

I don't see how. If a formal language can do as you suggest, describe anything and everything, then it must be able to describe natural languages. But in natural languages new words are being minted all the time to describe new ideas. For example, Software. This word can be read by someone in Shakespeares time, but would he be able to make any sense of the ...


Only top voted, non community-wiki answers of a minimum length are eligible