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
-1
votes
4answers
67 views

The truth of statements which do not capture everything about the object [closed]

Logically it could be true to say: "All human beings are mortal (and therefore Peter is mortal because Peter is a human being)." But the above statement could be false in a sense, because mortality ...
0
votes
2answers
38 views

Use-mention distinction

Is it 1+1 or “1+1” that is a formula of addition? To my intuition, it is the former, and the latter seems to be a name of the formula. The reason why I ask this question is that provided my intuition ...
0
votes
3answers
64 views

What is the purpose of logical division for classification?

It's my understanding that we use division to classify things in the world so that we can define them, say, with a genus-species tag. However, in the introductory books I've read, they mention that ...
1
vote
2answers
120 views

Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

Two concepts F,G are equinumerous if there exists a one-to-one correspondence between the objects that fall under F and G. Equinumerosity is one the most fundamental building blocks of Gottlob ...
1
vote
1answer
68 views

Existential Import

How is it that universal propositions (from the Boolean standpoint) don't commit us to the existence of the subject term while particular propositions actually do? Also, why particularly take or focus ...
1
vote
2answers
53 views

Truth Value of Definite Descriptions

I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-...
0
votes
0answers
37 views

why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
1
vote
0answers
183 views

What are the eventual purposes of symbolic logic?

What is the teleology of logic? Every body of knowledge has to have a teleology for which it's designed. The body of knowledge in logic doesn't clearly have any teleology or any purpose to which it ...
-1
votes
2answers
45 views

(p->q) v (q->p) with Natural Deduction

Well, indeed I have the answer to this exercise but I don't understand some steps. From 6 to 17 are OK for me but from 2 to 5 and then when step 5 is again called in step 10 is something I don't get ...
-2
votes
1answer
172 views

Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
1
vote
0answers
24 views

Inductive reasoning and probability: probability of the conclusion versus probability of the supporting relation?

It is often admitted that inductive reasoning has something to do with probability. While in a ( valid) deduction the premises necessarily imply the conclusion, in an inductive reasoning the premises ...
2
votes
1answer
54 views

With or without opposition between A and B, how many ways are there for A not to be B?

I'm looking for references and "loci" regarding the concepts of opposition, distinction, diversity, and negation. I'm not certain if one must distinguish the case in which A and B stand for concepts ...
3
votes
2answers
90 views

Can Hegel's theory of logic be formalized?

In paraconsistent logic, we have dialecticism. So is it possible to formalize the logic of Hegel, like Anton Friedrich Koch in "Hegel's on the logical big bang and the evolution of logical space", and ...
-1
votes
1answer
243 views

Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
2
votes
3answers
76 views

Can the word “probably” be used in a proposition? (logic)

I'm interested in applying logic to day-to-day reasoning. The problem is that formal logic seems really restrictive to limit inductive arguments to be only universal ("all swans are white"). Few ...
0
votes
0answers
22 views

'this statement is true' , 'this statement is not not true' [duplicate]

Given the following self-referential sentences a. this statement is true b. this statement is not not true are (a) and (b) intersubstitutable, given classical logic can one eliminate the double ...
-4
votes
2answers
64 views

how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless
0
votes
1answer
46 views

LPL Predicate Logic Translations Exercise 11.20.7

I have this one question (Part 7) in exercise 11.20 that I can't seem to get the answer from. I tried ∀x∀y ((x ≠ y ∧ Larger(x,y)) → Dodec(x)) and ∀x∀y (Larger(x,y) → Dodec(x)), as well as many other ...
-1
votes
1answer
74 views

Translation to language P

I am taking an intro class in philosophy and I have having trouble with some assignment questions. I need to translate into the language P. Here's the translation keys: Fx: x is a firefighter Dx: x ...
0
votes
4answers
158 views

Liars paradox towards a solution?

This statement is not true 2.This statement is true only if true and not true. (1) and (2) are clearly different sentences, but do they express the same proposition? If yes, then it becomes clear ...
0
votes
1answer
61 views

Proof With No Premise

How would I prove this in Fitch? ((P ->R) ^ (Q->notR)) -> (Q->notP) More generally, what is a strategy I can use to tackle these types of problems in general? I tried working backwards, breaking ...
0
votes
1answer
40 views

Using logic to do metalogical proofs? Is there a circularity problem here?

(1) If modus tollens were not correct, then I could have (P-->Q), ~Q and P. (2) But I cannot have (P--> Q) , ~Q and P. For, in that case, I would have (~P v Q) and ~Q and P; which means I would have ...
3
votes
1answer
171 views

What is the name of the fallacy involving white and black swans?

If one argues: I have seen only white swans, therefore there are no black swans. What would this fallacy be called?
2
votes
1answer
153 views

Is it possible to make decisions without some kind of belief system? [closed]

Normally when we talk about belief, we mean religious beliefs. But even the criticizers of religions have some kind of belief system. They base all their decisions on the premise of logic. Thats why I ...
2
votes
1answer
151 views

Is there a form of set theory involving imperatives and interrogatives?

I finally read the article Is there a Logic of Imperatives? Conifold showed me and it elicited the question, for me, whether imperative programming is a form of imperative logic at all? The essay took ...
-1
votes
1answer
34 views

Existential Elimination in Fitch (Barber of Seville)

To be clear, I'm just struggling to understand why Fitch won't let me use EE. From other examples I've seen, I've set it up correctly for EE. I've also tried using BotE and EE on the desired sentence, ...
12
votes
14answers
6k views

Are we sinners because we sin or do we sin because we are sinners?

This question arose after I read a sentence like this : We are not sinners because we sin We sin because we are sinners. So "because it's carnivore then it eats meat" --vs-- "because it eats meat ...
1
vote
1answer
52 views

Equivalences in Sentence Translation with Quantificational Logic

Consider the sentence "If all the birds in my house are peacocks, then Charlie is a peacock," and let the provided symbols be denoted as B for bird, H for house, P for peacock, and c for Charlie. ...
0
votes
1answer
72 views

What is the fundamental axiom of reasoning?

Is it true that a fundamental axiom of logical reasoning is that reality doesn't contradict? Can someone explain why this assumption is a reasonable starting point if true or what a more accurate ...
2
votes
3answers
117 views

Is this a logical fallacy or simply a bad argument?

In my English class today, we were talking about thesis statements. One of the students said that one of the thesis statements didn't sound right; its syntax sounded odd. However, my teacher said that ...
0
votes
1answer
122 views

How to prove rigorously that “ necessarily ( A OR ~A) ” does not imply “ necessarily A OR necessarily ~A”?

In De Interpretatione , Aristotle criticizes logical fatalism ( a metaphysical doctrine professed in the Megarian School, in particular by Diodorus Cronus). Aristotle reconstructs the reasoning of ...
-1
votes
4answers
147 views

Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
-4
votes
1answer
84 views

do 'p & ~p' , '~p & ~~p' equal 'either p or ~p'? [closed]

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
118 views

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

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
68 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
36 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
187 views

Which fallacy: Thinking everything someone does in a discussion that's wrong is a fallacy?

There are 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 ...
24
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 ...
21
votes
10answers
11k 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'...
0
votes
1answer
59 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 ...
-1
votes
1answer
48 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 ...
0
votes
1answer
97 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
78 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
142 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
86 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
66 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
59 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
59 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 ...
3
votes
2answers
169 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
170 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 ...