Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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How do I check if two logical expressions are equivalent?

For example: Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as (A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C &...
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The difference between soundness and completeness

Is anyone able to articulate the difference between the properties of soundness and completeness insofar as they relate to the validity of the tree test?
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Are there any books which reduce famous Philosophical Arguments to Logical Notation?

I have just started studying logic and wish to find some example arguments by famous philosophers broken down very plainly into their premises and conclusions, along with the logical notation to the ...
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Desirable features in an introductory logic textbook?

I have been very unsatisfied with the quality of the free, open-source textbooks in logic I have found so far. Some, like P. D. Magnus's forall x and the wikibooks Formal Logic text seem overly ...
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Which ontological commitments are embedded in a straightforward Turing machine model?

Let's assume that in response to a question or problem, a certain type of idealized finite Turing machine can be presented as an answer as if it would really (=physically) exist. Is the corresponding ...
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In Gödels Incompleteness theorem what is the notion of truth?

The entry on Gödels Incompletenss theorem in Wikipedia says: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for ...
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What is Wittgenstein claiming when he says that “each thing can be the case or not the case while everything else remains the same”?

In Tractatus 1.21 Wittgenstein writes  Each item can be the case or not the case while everything else remains the same. [1] I'm looking for commentary on this point, since it seems out of place ...
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Does a philosopher need much knowledge of mathematical/formal logic?

I am not a philosopher but I would like to ask this question. I know that there are philosophers like Hobbes, Locke or Foucault, who excel in the areas of ethics, political philosophy and aesthetics. ...
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Are there different levels/categories of falsehood?

Consider the following sentences: The current president of the United States has 2 daughters. The current president of the United States has 5 sons. The current emperor of the United States has 12 ...
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248 views

Does Fodor present any argument for his use of computable methods in his view of the mind?

In defense of his Language of Thought Hypothesis (SEP article), Jerry Fodor argues that Thought is recursively compositional in just the same way that Language is. When we understand a sentence, we ...
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Why would this not resolve the Sorites paradox?

Bear with me here, I know nothing about philosophy that I haven't read on Wikipedia. I don't understand why the Sorites paradox is considered an unsolved problem in philosophy (according to Wikipedia)...
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Are all non self-referential statements true or false?

It is well known that there exists self-referential statements which are neither true or false, such as "I am lying". Is it possible to have statements neither true or false which are not self-...
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What's the big deal with Gödel's second incompleteness theorem?

Edit: My question is specifically about Gödel's second incompleteness theorem. I get the significance of his first incompleteness theorem, which is of course completely amazing. According to the ...
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How to justify Occam's Razor?

I'm aware of a few justifications for Occam's (or Ockham) Razor, as it's usually understood that extra factors/complexities should not be added unnecessarily. The only truly compelling justification I ...
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Logical consequence and material conditional - Are they the same?

I'm taking basic discrete math course which includes basic intuitive introduction to logic (only things like statements, tautology truth tables, etc.). During the learning, I've wondered what is the ...
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Why does the material conditional have the truth table it does?

Can someone provide me with the simplest possible argument for why the material conditional has the truth table it does? Googling doesn't help at all, providing only flimsy and clumsy arguments. I ...
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What is the difference between logic and reasoning?

What is the difference between logic and reasoning? I can makes sense of what logic is about. But when it comes to reasoning what does it do more than logic does? Can you give an example which shows ...
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Does the imperfection of man imply the imperfection of God?

I'll begin by laying out some some ideas that are considered true for the sake of argument: 1. Given: God Exists 2. Given: God is Perfect 3. Given: Everything God does is good 4. Given: Everything ...
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Can an argument be formally valid with sound premises and still be informally fallacious?

Consider the following two assumptions: Validity Assumption: Assume an argument is valid. It follows all the formal logical rules of inference. The inference contains no formal logical fallacy. ...
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In predicate logic, do we necessarily have to restrict the domain of discourse?

Can we combine formalized statements in predicate logic from widely different domains of discourse (say, one regarding integers, one regarding the fruits in one's garden) by using logical rules/...
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Is it true that (P∧Q≡P)⇔(Q≡⊤)?

Consider the statement (P∧Q≡P)⇔(Q≡⊤) Where P and Q are statements, and ⊤ denotes the tautology (true) statement. It seems intuitively true that the above biconditional statement is true. But I ...
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What is the meaning of “predicate” in this definition?

I have trouble understanding the article on existence in this Philosophy dictionary. Instantiation in reality, or actual being. Kant pointed out that existence is not a predicate. What is the ...
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541 views

What are the arguments for and against “one true arithmetic”?

This question was born out of a discussion Is the real number structure unique? on Math SE, but since it is more philosophical than mathematical I decided to ask here. From Gödel completeness and ...
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What is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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Why is the darapti syllogism invalid?

I found the following exposition of darapti on wikipedia: All squares are rectangles. (MaP) All squares are rhombuses. (MaS) ∴ Some rhombuses are rectangles. (SiP) As far as I can see, this is ...
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Is philosophical naturalism circular reasoning?

I'm a steadfast proponent of science and logic, but it's been occurring to me lately that this belief in the veracity of science may be just that, a belief---no different than a theist's beliefs in ...
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Where is a good place to start reading about logic?

I would like to learn logic as an introductory subject. I am an undergraduate student and would appreciate any suggestions for books/articles where I can start from, also any books/articles about ...
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Why are sentences expressing one's opinion statements?

I'm in a class on critical thinking and we are discussing statements and arguments. Here is an example the instructor gave which is supposed to be a statement, but I don't see why. I do not want ...
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Why is Tarski's notion of logical validity preferred to deductive one?

Its flaws are well-known and serious. To recall, an inference from A to B is valid iff all interpretations of "non-logical constants" that make A true also make B true. What are interpretations, a.k.a....
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On the Validity of Modus Tollens

One of the valid forms of argument is Modus Tollens (ie If P, then Q. Not Q, therefore, not P). An example is "If Putnam is guilty, she is lying now. She is not lying now. Therefore Putnam is not ...
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Modal Logic: a question concerning accessibility

I’m reading a lot about modal logic lately, right now Lewis “On the Plurality of Worlds” and Priests “Introduction to Non-classical Logics”. It is postulated that the different worlds have nothing to ...
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342 views

Are there any interesting examples of a formal system that can prove its own consistency?

Because of Godels 1st incompleteness theorem it will need to be weaker than PA (Peano Arithmatic), (or perhaps uncomparable to it?). In fact it needs to be weaker than Robinsons Arithmatic which is ...
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What is fallacious about an argument that “I know X well, so she is right”?

I often hear from media personalities that they are right about a theory or assertion merely by associating themselves with someone or something. For example: "I know Mr. X very well (for years) and ...
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Why don't we have consensus in more complicated areas of logic?

When I once realised I don't really understand how and why proof by contradiction works, I started reading about it. And apparently I wasn't the only one who felt there's something wrong about it - ...
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Is it possible to generate logically valid sentences made up of “atomic contradictions”?

Is it possible to generate sentences that are made up of "atomic contradictions", but which remain logically valid as a whole? By "atomic contradictions", I mean atomic propositions that are not ...
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What is a “straw man” argument? [closed]

What is a "straw man" argument? Assuming an interlocutor is utilizing such an argument against you, what are some techniques for countering it? What motivations might lie behind a disputant using a ...
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes But do you know whether his hypothesis also allows/accept universes described by other types ...
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Is there such a thing as a 'necessary truth'?

Wikipedia (note the redirect) defines 'necessary truth' as statements which "could not be untrue", and I assume that this is how the term is usually used. A search through the SEP shows that while ...
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Can an eternal god destroy himself? [duplicate]

Possible Duplicate: Is the definition of God consistent? (primary) also: An immovable object and an irresistible force God's paradoxes and their implications To many, at first sight, ...
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Are there any potential flaws in the definition of validity as “provable or falsifiable”?

I have made an argument in another thread that a proposition must be provable or falsifiable to be valid. Are there any flaws in this definition of validity? What might be a potential counter-argument ...
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Is Ross' paradox really a paradox?

Consider the following disjunction introduction: Your room is clean. Therefore, your room is clean or your house is burnt down. Ross' paradox allegedly arises when applying this inference to ...
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How do Kripke's rigid designators and the necessity of identity relate to the Duhem-Quine thesis?

The Duhem-Quine thesis refers to the underdetermination of scientific theories and the fact that it is impossible to test scientific theories in isolation, we always need to make background ...
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Logic as a (bad) model language

Can someone name the most well known philosophers to explicitly put forward an idea along the lines that formal systems can only be used descriptively, not prescriptively - that they're just a model, ...
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A (possible) puzzle regarding John Lane Bell's “Abstract Sets”

John Lane Bell, is his paper "Abstract and Variable Sets in Category Theory" (go to Bell's Homepage to download it), defines an abstract set as follows: "An abstract set is then an image of pure ...
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Is it possible to deny that affirming a logical contradiction implies every possible proposition?

I find myself aligned with the motivation behind paraconsistent logic, they seem to me reason enough to warrant an attempt to structure logical systems which deny logical explosion. It does seem very ...
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What is the logical structure of this argument by a Hindu philosopher about causation?

The Khandana Khanda Khadya is a work by the 12th century Hindu philosopher Sri Harsha which in some sense sets out to disprove epistemology - it seeks to show that all putative means of knowledge, ...
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Is there modal logic without possible worlds?

Would it be desirable to carry out a deflationary research programme in modal logic? In other words, would it be desirable to re-think modal logic without the possible worlds semantics? The original ...
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How to express Kant's notion of existence on first-order logic according to Ayer?

In Language, Truth, and Logic, Ayer writes: [As] Kant pointed out, existence is not an attribute. For, when we ascribe an attribute to a thing, we covertly assert that it exists. However, I can't ...
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Are there any known deficits of “relevant logic”?

The principle of explosion is the law of classical logic and similar systems of logic, according to which any statement can be proven from a contradiction. Some early formal systems like Frege's ...
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Why substitutivity doesn't work in an intensional context?

I was trying to grasp some more insights on the difference between intensional and extensional. I started reading this article by Melvin Fitting on intensional logic. It seems interesting but I ...