Questions tagged [logic]

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

Filter by
Sorted by
Tagged with
29
votes
5answers
8k views

Is “I cannot imagine a mechanism for X to happen, so X can never happen” a named logical fallacy?

I have encountered this reasoning quite frequently: Somebody posits the hypothesis that an event X can happpen. A recent example I encountered was "vinegar and salt in the boiling water make eggs ...
11
votes
3answers
472 views

Is the notion in Hume that you cannot deduce an “ought” from “is” related to his assertion that reason must be the servant of the passions?

I hear it asserted that David Hume said one cannot deduce an "ought" from an "is". I also find it asserted that he said reason must be only the servant of the passions. I had long uncritically ...
10
votes
3answers
1k views

Are there rules for dealing with self-reference “paradoxes” in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, ...
9
votes
2answers
162 views

Does fictional discourse pose special difficulties for logic?

Natural language is context-dependent, like the statement “My uncle is a plumber”, which is true or false depending on who asserts it. There has been lots of discussion about fictional entities and ...
8
votes
5answers
347 views

Asymmetries in two opposite arguments from ignorance

Joe claims: "There is no proof that unicorns exist, therefore unicorns do not exist". Alice claims: "There is no proof that unicorns do not exist, therefore unicorns exist". Bob claims: "There is no ...
7
votes
3answers
685 views

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 ...
7
votes
5answers
2k views

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. ...
7
votes
3answers
2k views

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 ...
6
votes
1answer
295 views

Is Belnap's four-valued logic technically a relevance logic?

Belnap, the American Logician, constructed a four-valued logic which is a form of relavance logic; interestingly the truth-values it takes are: true false both true & false neither ...
6
votes
8answers
3k views

Is finding truth possible?

Consider the following argument: If want to know that something is true, I need to first know what is truth. If I need to know what is true, I need to find the truth. (Is there ...
5
votes
3answers
764 views

How could the concept of 'evidence' be defined, and how significant is it?

What is evidence, and how much of it means that a proposition is true? Does a partial / total lack of evidence mean that a proposition should be ignored? Is the concept evidence more important to ...
5
votes
2answers
613 views

Is Gödel's incompleteness theorem still valid if one uses a higher-order logic?

Gödel's incompleteness theorem is wholly formal (in my understanding), and relies on a proof system that I assume is first-order. Does it make any difference to the theorem if higher-order logic is ...
5
votes
3answers
2k views

What is a good first textbook for self-learning logic?

I would like to begin studying logic on my own. The problem: with the quantity of books available, I have no idea on how to distinguish the good ones from the bad ones. Please suggest to me some good ...
5
votes
3answers
147 views

Do limits of human nature suggest that it could be principally understood?

Human nature is limited, so is our thinking. We are limited by our bodies, and power of thoughts is limited by the number of cortical and other neurons, number and speed of their connections, which ...
5
votes
2answers
226 views

What does Wittgenstein mean when he says “there are no numbers in logic”?

From the Tractatus: 5.453 All numbers in logic stand in need of justification. Or rather, it must become evident that there are no numbers in logic. There are no pre-eminent numbers. What does ...
5
votes
5answers
7k views

Why is argument by analogy invalid?

There is a well known fallacy called the "argument by analogy" fallacy. As I understand it, the fallacy occurs in a situation where someone makes a reasonable comparison between two situations and ...
5
votes
1answer
366 views

Can possible-but-non-actual objects have accidental properties?

The modal logic I am considering is the "Simplest Quantified Modal Logic" which combines first-order predicate logic with identity, with S5 in the most straightforward way, described here and slightly ...
5
votes
0answers
318 views

Rigid designators, equality and functions in many-valued logic and (simple) quantified modal logic [closed]

After reading "In Defense of the Simplest Quantified Modal Logic", I wonder how to add functions to the language of the simplest quantified modal logic (QML for short). The simplest model of QML has a ...
5
votes
3answers
405 views

Does one have to become a Platonist to refuse to be a Platonist?

I believe the answer is no, but Scott Aaronson on his blog just gave in interesting argument to the contrary. This is in connection with the now famous paper Undecidability of the Spectral Gap, and ...
4
votes
1answer
116 views

Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...
4
votes
3answers
294 views

Philosophical justifications for the assumption of a non-empty domain in classical first-order logic?

Are there any "canonical" (or at least, quite good) papers that attempt to justify the supposition made in the model theory for classical first-order logic that the domain in non-empty? I know that ...
4
votes
3answers
203 views

Name of fallacy when one says he used to have the same views

I was arguing with a friend (we were at loggerheads with respect to our views) and in the middle of the argument he refuted my claims by saying that even he used to have the same views (as I do now) a ...
4
votes
2answers
367 views

Is there a relationship between implication and supersets?

The "hook" symbol for implication (⊃) is the same symbol for superset. Is this just a coincidence, or is there a relationship between these two ideas?
4
votes
2answers
642 views

An immovable object and an irresistible force [closed]

If an immovable object is an object that cannot be moved no matter what and an irresistible force can move anything, what would happen if an irresistible force is used on the immovable object?
4
votes
1answer
516 views

What is the logic in the Tractatus-Logico Philosophicus in modern terms?

In the SEP entry on Wittgenstein, the description of the logic utilised in the Tractatus Logico-Philosophicus to describe his logical atomism appears to be at least formally classical propositional ...
4
votes
3answers
662 views

What are the “undefinable numbers” in real analysis and philosophy?

What if any important results in real analysis make use of the notion of an "undefinable" real number? (Whatever "important" may mean to the reader.) Or is it used more in the philosophy of ...
4
votes
2answers
175 views

Attacking Factual Detachment in Deontic Logic

Let OB(q/p) represent the conditional ought statement: "If p, we ought q". (Note that depending on your views of deontic conditionals, the statement "If p, we ought q" could be taken to be wide-...
4
votes
4answers
445 views

Is syllogism an inference rule?

I was reading Anthony Andres' article, "ARISTOTLE AND THE CONVENTIONAL LOGICIANS ON THE FOURTH FIGURE". The author explains why according to him the introduction of the fourth figure by his ...
3
votes
8answers
2k views

Can something be true if it does not follow logic?

Can something be true if it is not logical? Can something be true if it does not follow logic? if I can't deduce it logically? or if it contradicts logic? In other words: if someone says statement X ...
3
votes
1answer
192 views

What is the difference between ∃ (existence) and A (actuality)?

The existential quantification can, it seems, be used with modal logic. Now excuse my naivety, but: if so, what is the difference between being actual and existential quantification? I'm just asking ...
3
votes
2answers
1k views

What is Naive Set Theory?

Is naive set theory, simply set theory that has been left unformalised as the entry in Wikipedia suggests? However, the SEP, in its entry on inconsistent mathematics, suggests that: It should also ...
3
votes
2answers
910 views

Does Wittgensteins own solution to Russells Paradox actually work?

In the Tractatus, Wittgenstein attempts a solution of Russells paradox 3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument ...
3
votes
3answers
153 views

What do we mean when we say there's only one type of logic/mathematics and that they can’t change?

Do we want to say that if they changed, they would not be logic/mathematics (as we know) anymore? How can we be sure that there's no other type of logic/mathematics?
3
votes
3answers
391 views

What is the logical form of a question?

A common thread in Analytic philosophy, starting with Frege, and through Russell, Wittgenstein and the Logical Positivists, is that there is an ideal and purely logical language, with which we can ...
2
votes
1answer
222 views

If metaphysical grounding of beliefs is not necessary what is to logically compel one to believe anything?

'Grounding' is the notion that 'because of X, Y', X being the reason one can accept Y beyond pragmatic considerations. In this way, X and Y are analogous to cause and effect respectively. If it is ...
2
votes
0answers
371 views

What is the difference between relational logic and predicate logic?

I am studying the Introduction to logic course from Stanford University and I begin learning about relational logic. However when I search on google for the terms there I end up often with results ...
2
votes
2answers
161 views

(∃x)(∃y)(Jxy v Kxy) ⊃ (∃x)Lx : Why can this not be instantiated?

Source: p 502, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Because line 1 cannot be instantiated, the only strategy is to derive the antecedent of the conditional with ...
2
votes
3answers
3k views

Why is it that when A is false and B is false, we infer that A->B is true?

Why is it that when A is false and B is false, we infer that A->B is true? If A isn't true then we don't know if maybe when it is true then B would be false. could be B would be true, could be it'd ...
2
votes
1answer
175 views

Why is faulty generalization called an informal fallacy?

According to wikipedia faulty generalization belongs to the class of informal fallacies. Also, a fallacy is called informal if it originates in a reasoning error other than a flaw in the logical ...
2
votes
3answers
280 views

Interpretation and symbolic notations of operations in mathematics

As we know a mathematical operation is a function. And a function is a special type of relation. Ultimately a relation is a set of ordered pairs. For example, what is addition of natural numbers? At ...
2
votes
1answer
2k views

How can you derive De Morgan's Law?

Can someone help me prove De Morgan's Law. In my logic class we are using a very basic set of rules for derivations and I can't for the life of me figure out how to prove the law with them. It's not ...
2
votes
1answer
174 views

Does following logic necessarily require one to conclude that they are objective and have no bias?

In social psychology, naïve realism is the human tendency to believe that we see the world around us objectively, and that people who disagree with us must be uninformed, irrational, or biased. It is ...
2
votes
3answers
185 views

Why do we tend towards discretizing things around and within us?

Why do we tend towards discretizing things around and within us? Do our senses (for space and time) fool us into this notion all the way into the need for discretizing abstractions themselves, e.g. An ...
2
votes
2answers
7k views

premise and proposition

I find it difficult to differentiate between premises and propositions. given these statements: "If men evolved from apes then there wouldn't be any ape nowadays" "There are apes nowadays" are ...
2
votes
4answers
163 views

Question about absoluteness

If you say: "Nothing is absolute, everything is relative". Then you make an absolute statement. How can this be?
1
vote
3answers
230 views

Is it possible to prove the invalidity of logic without using logic?

Is it possible to validly invalidate logic without using logic? Mere assertion gives rise to the question, "How do you know?". At that point, you end up having to use logic to justify the thesis ...
1
vote
0answers
156 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
1
vote
2answers
54 views

Are syllogisms independent of humans?

For example, if "All a are b" and "All b are c" then "All a are c". To make this syllogism, does a conscious being need to exist? Or is it inferred from the sentences?
1
vote
1answer
187 views

Is 'strong' omnipotence required to create another omnipotent being

This question is coming out from our conversation with @Conifold: He believes that for creation of another omnipotent being 'strong' omnipotence is required. Can God create a rock that he can not ...
1
vote
3answers
566 views

What kinds of logic or philosophy to improve comprehension of difficult writing?

In this post, the answer uses some logic to simplify a convoluted sentence. What's that kind of logic called? What other branches of logic or philosophy should I self-study in order to help ...