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
vote
2answers
28 views

How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
4
votes
2answers
265 views

Prerequisites for Michael Dummett texts

I want to read Michael Dummett's The Logical Basis of Metaphysics. Is it hard to read ? I would like an answer for the same question regarding his other texts. Do I need a prior exposition to other ...
2
votes
1answer
95 views

Which philosophers proposed theories containing a performative contradiction?

Socrates was blamed of this by being wrongly interpreted of saying: "I know that I don't Know." or other variants. What he really said was: "I neither know nor think that I know." Source: https://en....
0
votes
0answers
44 views

What is the name of the fallacy where acknowledging an issue is confused with actually addressing the issue?

A few days ago an artist came to present his work to our class. At the beginning of his presentation he said "I know cultural appropriation is a very loaded topic, and it occupies my mind often" as ...
0
votes
2answers
246 views

Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
1
vote
1answer
136 views

I don't understand Parmenides's argument for why we can't think about what doesn't exist

I have been learning about Parmenides, and I don't think I am correctly understanding his argument for why we can't think/speak about things that don't exist. I tried to apply his logic to a ...
0
votes
2answers
61 views

Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
-1
votes
1answer
62 views

Honestly have no Idea how to prove A v ¬¬B from A v B (LPL Q. 6.18)

Premise A v B Goal A v ¬¬B Please help. It seems so self evident but I don't know how to get there.
2
votes
1answer
291 views

What logical fallacy considers a personal experience to be common place

While my wife and I were discussing the news a few days ago I stated that an argument expressed (in a news article, not by my wife) was a fallacy -- but I've been unable to put a name to it. ...
34
votes
17answers
12k views

Why doesn't philosophy have higher standards for its arguments?

Mathematical systems are an excellent model for organizing and conducting thought: In the mathematics community, any argument in support of a conjecture, that deviates from "sound argument" never ...
1
vote
2answers
72 views

What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
6
votes
5answers
3k views

Is it nonsense to say B -> [A -> B]?

Is it nonsense to say B → [A → B]? I would have thought so, it seems to say that every fact deductively follows from every other. But I was looking at a recent closed question, on natural deduction, ...
0
votes
2answers
32 views

In First-Order Logic, can you deduce an existential quantifier purely from other existential quantifiers?

Let's say we have: ∃x(Fx → Gx) and ∃xFx can we deduce ∃xGx? I've been throwing myself at this problem for days and every time it just seems like the entire enterprise is flawed. Existential ...
0
votes
1answer
30 views

How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
-1
votes
1answer
44 views

Cogito corollaries and meaning [closed]

Doubt implies thought. I'm doubting. So I'm thinking. [(d→t) ∧ d]→t Thought implies existence. I'm thinking. So I exist. [(t→e) ∧ t]→e d→t; ¬t→¬d; [¬t ∧ (d→t)]→¬d t→e; ¬e→¬t; [¬e ∧ (t→e)]→¬t [(d→...
11
votes
16answers
10k views

Does the notion of an all-powerful God conflict with the idea of free will?

In Abrahamic religions, God is often believed to be wholly omnipotent. People also seem to believe that humans have "free will", especially insofar that they feel they are in control of their own ...
2
votes
3answers
799 views

How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?

Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
7
votes
11answers
2k views

Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
20
votes
10answers
3k views

Is the universe isomorphic to a universal turing machine?

I often think about problems that require an understanding of the very essence of computation and its inherent limitations. So, my questions are as followed: Is the universe isomorphic to a universal ...
1
vote
1answer
99 views

Lists and predicates on lists in classical first order logic

I have to express some basic Prolog code in classical first order logic (FOL). In Prolog i use lists, together with member/2 and append/3 a lot. Could you give me some tips for writing clauses like ...
3
votes
3answers
149 views

Concerning the definition of “valid”

I studying graduate math (not very far into it) and I realized that some of the higher level math texts I would like to read are hard to access without a strong basis in logic. Now I've taken ...
-2
votes
2answers
80 views

Trouble with cookies [closed]

Matter cannot be created. Cookies are matter. So cookies cannot be created. I know this seems absurd but I'm using this to make an important point about arguments. The argument appears to be valid ...
3
votes
2answers
260 views

References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
-2
votes
2answers
151 views

Does the Universe make sense? [closed]

When faced with a paradox, we say: well this can't be because it doesn't make sense. p = "x doesn't make sense" q = "x doesn't exist" The contrapositive preserves validity: p implies q (not q) ...
2
votes
3answers
279 views

Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
2
votes
2answers
258 views

Can someone explain this logical statement?

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced ...
5
votes
0answers
63 views

The enunciation clause (Lyotard & Levinas)

As kind of introductory remark, let me state that I'm not academically-trained in philosophy, so my apologies if this comes up as a rather simple question. I was reading Logique de Levinas by JF ...
2
votes
3answers
76 views

Why is there an O type conclusion in modus celaront

Modus celaront is type logical syllogism. No reptiles have fur. (MeP) All snakes are reptiles. (SaM) ∴ Some snakes have no fur. (SoP) The conclusion is of a O type(Some .. are not ...). Why is ...
2
votes
10answers
2k views

Can there be cause and effect without time?

Our usual understanding of cause and effect operates tensely; that is in time. But consider a basic statement in some generic computer language: if x then y Is this in time? Well an actually ...
1
vote
2answers
89 views

Trying to decide if the terms “proper education”, “real world education”, “successful life” are vague or ambiguous? [closed]

I feel that all three of these terms can have different meanings, but are they all vague as well? For example, proper education could mean a university education/college education/education in the ...
-1
votes
3answers
62 views

A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...
3
votes
4answers
353 views

What is the difference between logical consistency and logical entailment in deductive logic?

I am having a little trouble sorting out two definitions from the first chapter in my logic textbook, The Logic Book by Bergmann, Moor and Nelson. I am under the impression that a set in a sentence ...
10
votes
3answers
1k views

When is pointing out a person's hypocrisy not considered to be a logical fallacy?

People keep using the word "whataboutism" and it seems people don't really know what it means, and I don't see how it's a logical fallacy if it's a very good argument. For instance, if the U.S. says ...
2
votes
2answers
91 views

Incorrect statement in Suppes' Introduction to Logic

Chapter 2 of Suppes' develops the notion of sentential inference and how to construct rules of inference. However, there is one part in his development that seems incorrect no matter how I look at it. ...
1
vote
1answer
90 views

Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
1
vote
2answers
64 views

Negation of a relational quantified term?

Formally, when you negate a quantified term which is attached to a relation, is a distributed term always made undistributed and vice-versa? For example, consider this statement : Anyone who assists ...
21
votes
4answers
35k views

What is the difference between a statement and a proposition?

I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
2
votes
2answers
222 views

Has anyone developed a “restricted English” notation for logic (first-order or otherwise)?

I ask because Kleene mentions the possibility in Mathematical Logic, but I am not sure if he meant this as something he's aware of, or as a hypothetical possibility. I also enjoy the first part of ...
1
vote
3answers
115 views

Logical Necessity

Logical necessity is that which is necessary by definition. Otherwise it is sometimes considered to be that which cannot possibly be false, or cannot be otherwise metaphysically. The usual example is ...
0
votes
2answers
163 views

Who first studied asymmetric relations qua relation?

Who first asymmetric relations qua relation, viz., the fact that A relates to B by some relation does not always/necessarily imply that B relates to A by the same relation. ?
2
votes
0answers
52 views

Using solipsism's incoherence with doubt as proof of the external world?

I have the following rough outline of utilizing solipsism as a proof by contradiction to the goal of asserting an epistemological proof of the external world. A solipsist (Wittgenstian) lives in a ...
2
votes
2answers
108 views

Wittgenstein's solipsist, from Tractatus?

According to the early Wittgenstein of the Tractatus, the solipsist is one and one and the same with the world. He then makes the claim that solipsism coincides with realism. 5.64, Wittgenstein ...
1
vote
2answers
114 views

De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
1
vote
1answer
221 views

De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
2
votes
1answer
246 views

Does this argument make sense?

Consider the following argument: (A) Either sales or expenses will go up. (B) If sales go up, then the boss will be happy. (C) If expenses go up, then the boss will be unhappy. (D) ...
1
vote
3answers
82 views

Having trouble starting a proof

I am given the following premise: ( Q --> R ) and the following conclusion (( ~ Q --> ~ P ) --> ( P --> R )) I am allowed to use Modus Pollens, Modus Tollens, Hypothetical Syllogism, ...
2
votes
4answers
120 views

What is an argument with necessarily true conclusion?

I cannot understand what an argument is with a necessarily true conclusion. Could you explain to me what it is and write here some examples? Moreover, what is the meaning of “necessarily true” and “...
0
votes
2answers
359 views

How to derive: F(xy)→∼F(yx) ∴ ∼F(xx)

This is from Logic 2010, Derivation 4.021: F(xy)→∼F(yx) ∴ ∼F(xx). The book we use is Parsons', but I cannot even make sense of these symbols stand-alone F(xx) without any quantifier. This problem ...
4
votes
1answer
105 views

Who first studied “logical (ir)reversibility”?

Who first studied "logical (ir)reversibility" philosophically? By "logical (ir)reversibility" I mean questions like:Why is it easier to multiply large numbers than to factorize them? understand a ...
1
vote
3answers
109 views

Unproven premises leading to true conclusion imply valid premises

Suppose that we have a bunch of premises which are unproven but lead to a valid conclusion, how much of a leap of faith it is to assert that the premises can now be seen as valid? I have said "a ...