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
-3
votes
1answer
31 views

do 'p & ~p' , '~p & ~~p' equal 'either p or ~p'?

In classical logic, (1) p & ~p is equivalent to (2) ~p & ~~p; if we read 'p & ~p' as p, ~p are both true/the case, and if we read '~p & ~~p' as p, ~p are both false/not the case (...
-2
votes
6answers
92 views

If false imples true then you can't make statements about real life? Confused [on hold]

I might have rushed into this and have insufficient knowledge about logic, however i have yet to see anything online go against this. Though i am not foolish enough to believe I have 'broken' logic, I ...
0
votes
2answers
51 views

When does a fallacy fallacy apply?

I'm confused on how the 'fallacy fallacy' is applied in an argument. Let's say a person, let's call them X, proposes an argument to another person, let's call them Y. X proposes an argument to Y ...
0
votes
1answer
32 views

How pardoxes relate to a theory's decidability and completeness

Would "this sentence is false" make a theory containing it both undecidable & incomplete, while "this sentence is unprovable" make a theory containing it incomplete(syntatically) but not ...
5
votes
3answers
108 views

Which fallacy: Thinking everything someone does in a discussion thats wrong is a fallacy?

There a lot of questions about which fallacy something is on this site. Many times, the argument in the question is not actually a fallacy, but something that the questioner doesn't like/agree with ...
23
votes
7answers
5k views

What type of rhetorical device is the offering of a source which is really long and not specifying what part of the source is relevant?

I'm encountering a frequent recurrence of a rhetorical device that seems to me fallacious but I can't figure out what it's called. When making an argument, the person does the following: Makes a ...
-4
votes
0answers
59 views

Prove “Everything is what it is, and not another thing” is a tautology [closed]

"Everything is what it is, and not another thing" Find a tautologous form for this sentence, and draw a tree to check it is tautologous, making sure to keep the number of branches as small as ...
-3
votes
0answers
71 views

Prove “God is three” is a contradiction [closed]

"God is three" Find a contradictory form for this sentence, and draw a tree to show that it is contradictory, making sure to keep the number of names as small as possible. The number of names on the ...
21
votes
7answers
10k views

Which fallacy: “If white privilege exists, why did Elizabeth Warren pretend to be an Indian?”

I recently came across this meme. It's clearly a logical fallacy (the existence of one use of a socioeconomic tool other than white privilege does not preclude the existence of white privilege), but I'...
-1
votes
0answers
21 views

What should you do in view of the first principle of practical reasoning? [closed]

You've been on a cruise for two days when there's an accident that forces everyone on board to abandon ship. During the evacuation, one of the boats is damaged, leaving it with a hole that fills it ...
-3
votes
0answers
21 views

Derive: ~Av~B from the premises: ~AvA , ~(A&B) [duplicate]

Derive: ~Av~B from the premises: ~AvA , ~(A&B) I am very stuck!
0
votes
1answer
54 views

SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC

Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.): (9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula ...
0
votes
1answer
34 views

How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
-1
votes
0answers
135 views

Is there an existing, published philosophy of mathematics that was designed to avow or declare all of the following four points of view?

Just as medicine is about human health, and astronomy is about the universe beyond the Earth's atmosphere, with the defining nature of medicine not white coats or stethoscopes, and the defining nature ...
0
votes
1answer
90 views

Trying to formalize a certain sentence in predicate modal logic

I have the following sentence which I want to formalize in predicate modal logic. Let me know if it's correct or not. The sentence is:" What is good for you is not necessarily good for others". My ...
0
votes
3answers
72 views

Help understanding deductive arguments

I am currently finding it hard to understand deductive arguments. I am taking a module called 'Effective Reasoning'. I've been finding it so hard to understand some things (as simple as this). I ...
-1
votes
1answer
137 views

Why should a system of set theory represent the following property of x: ((x = h) or (x = k))) using the set that Frege used?

I have been considering the possibility of an approach to set theory that represents the following property of the free variable x, in the terms of parameters h and k: ((x = h) or (x = k))) by means ...
2
votes
1answer
78 views

Does everybody have a bias? [closed]

I was in a heated debate with a housemate, and they mentioned that 'Everyone has a bias'. At the time I disagreed, and these were my reasons: To say 'all have a bias' is to then say that I have a ...
0
votes
0answers
64 views

What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and elementhood?

An excerpt from a question at Math SE (Bounty of 100 available for an answer): What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and ...
1
vote
0answers
55 views

Thoughts on Open Logic Project?

I'm currently thinking about starting to expand my knowledge of logic beyond what I retain from my previous study of logic by making use of the materials available through: OpenLogicProject (https://...
1
vote
1answer
37 views

On the Donald Davidson Discourse of Contradictory Beliefs

The following excerpt is taken from Donald Davidson, Problems of Rationality, Chapter 14, Who is Fooled (1997), page 217: We should not agree that believing the contradictory or the contrary of a ...
-1
votes
0answers
37 views

Is this logic correct?

I just can’t work out if the logic is correct. Please completely and absolutely ignore the content, it is just the logic and the form of the argument I am trying to validate. P1. Unless we are ...
2
votes
2answers
158 views

Can knowledge exist without structure?

For reference: https://en.wikipedia.org/wiki/Knowledge https://plato.stanford.edu/entries/knowledge-analysis/ https://plato.stanford.edu/entries/knowledge-how/ https://plato.stanford.edu/...
2
votes
4answers
126 views

What Is Critical Thinking, and How Does One Go About Learning It?

I am a freshmen taking an 'Effective/Logical Reasoning' course as an elective. Admittedly, I thought it would be something I could understand easily, but I soon found that this is not something I can ...
2
votes
0answers
17 views

The name for an anticipatory counter-argument?

There's the argument ad absurdum along with several other kind of reasoning. What is the name for a forestalling counter-argument - an argument put forward pre-emptively in anticipation of an ...
-2
votes
0answers
57 views

Does a logician need to memorize all binary logical connectives truth tables, equivalences, and properties?

Pretty much what is contained in these pages: https://en.wikipedia.org/wiki/Logical_connective https://en.wikipedia.org/wiki/Truth_function I feel like having all this info burned into my head and ...
0
votes
1answer
87 views

What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
3
votes
1answer
104 views

In logic, which came first: the semantic approach or the syntactic approach?

Logic is today developing in many, very different directions. But the basic distinction between the semantic approach (truth, "⊨") and the syntactic one (provability, "⊢") is still important and ...
-1
votes
1answer
57 views

Formalisation of an Argument [on hold]

I just came across the following passage in the Appendix B of "Why Race Matters" by Michael Levine: Let $G$ be a genotype expressed by phenotypic variable $P$, and lets $G$'s home organism $O$ ...
1
vote
1answer
34 views

Aristotelian vs Boolean, trying to determine the exact difference [duplicate]

Good afternoon, I've looked at some other answers and I feel those don't quite answer what I'm trying to ask, so I'll just ask it here. I'm in a logic course and I'm either misunderstanding ...
0
votes
0answers
47 views

Logic Philosophy question

I am looking for help in answering the full question with a full conditional proof (cp). This will help me understand this question and others that I am trying to understand. Thank you. Would ...
-2
votes
1answer
47 views

Help with a Predicate Logic homework proof

I have a Predicate Logic argument I need to translate into the symbolism of predicate logic first and then I need to construct a proof in CP. The argument is "Some wars are just. No war of ...
-2
votes
2answers
59 views

Rhetoric: How to frame redundancy in an argument as deficiency?

How can we categorize redundancy in an argument as deficiency? That is, weaken the argument because of its redundancy? Suppose X is an argument that boasts coherence and clarity, but it has various ...
4
votes
1answer
87 views

Did William of Soissons prove the law of explosion in the 12th century?

In the 12th century, William of Soissons attempted to prove that any proposition can be inferred from a contradiction. I've adapted his proof into a logical system I'm more familiar with: Let E ...
1
vote
1answer
63 views

Does a pattern constitute evidence, logic or something else? [closed]

Powerful groups (e.g. tribes and states) often exploit or attack weaker groups. That's a historical pattern suggesting that people will continue to prey on each other. Many wars have begun with ...
0
votes
1answer
46 views

What counts as a logically necessarily true statement and what is not?

"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death." Is this statement considered logically necessarily true? I personally ...
1
vote
2answers
63 views

Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
-1
votes
0answers
18 views

How do I show that using NOR one can express NOT and OR?

The answer given in the texbook is as follows: ¬A: (A↓A)≡¬(A∨A)≡¬A A∨B: (A↓B)↓(A↓B)≡¬(¬(A∨B)∨¬(A∨B))≡¬¬(A∨B)∧¬¬(A∨B)≡A∨B However, its not clear to me how to go about finding this solution.
4
votes
3answers
156 views

Could philosophers via Logic prove the validity of some holy books, then use them as a source of trustful knowledge?

Could philosophy or philosophers or some philosophers prove the validity of the text of a holy book, e.g: Qur'an or the Bible, or some holy books, using logic and philosophical means, then use these ...
0
votes
0answers
42 views

Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
1
vote
1answer
62 views

Tableaux for normal modal logics [closed]

Does ⊢ ◻p ⊃ ◻◻p hold in Kρ? Check with tableaux and if the tableau does not close, define and draw a counter-model.
-1
votes
1answer
62 views

How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
3
votes
3answers
93 views

What is the justification for the claim that observing something that is both a raven and black increases the likelihood that all ravens are black?

Suppose that I have access to a machine that allows me to input a positive integer (perhaps up to ten decimal digits) and the machine will -- depending only on the input -- output a statement. If the ...
0
votes
0answers
29 views

How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
0
votes
2answers
123 views

Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
0
votes
1answer
41 views

How can a undecidable theory be complete?

I don't understand how a theory can be undecidable (there is no effective procedure for determining if a sentence of the language is a theorem) and also be complete. How do we know all sentences are ...
4
votes
0answers
67 views

Is Herbrand semantics a kind of term formalism?

Michael Genesereth and Eric Kao describe Herbrand semantics as follows: Herbrand semantics is an alternative semantics for First Order Logic based on truth assignments for ground sentences rather ...
2
votes
1answer
42 views

Why doesn't one assert in metamathematics that a sentence S is a logical consequence of the conjunction of a set of sentences?

In other words, why isn't there -- at least in standard textbook presentations of things like the deduction theorem and the compactness theorem -- a conjunction connective that is applied to sets of ...
2
votes
1answer
42 views

Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
1
vote
2answers
148 views

To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...