Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
3,090
questions
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Structure of “affirming the consequent fallacy”
The formal structure of affirming the consequent fallacy is,
P1 - If A is true, then B is true
P2 - B is true
---------------------------------
C - Therefore, A is true
Now if I transform like that, (...
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1answer
33 views
Does a proposition have to have a true conclusion?
“...understand that a belief is propositional, which means it can be expressed in a declarative sentence—a sentence that is either true or false...Recall that in logic, a proposition has been ...
5
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8answers
1k views
What the Preface paradox tells us about the principle of explosion
The Preface paradox (adopted on a classical logician): Imagine that a
classical logician has just written a textbook (on classical logic).
He has included many assertions in it and has thoroughly ...
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0answers
20 views
Can I lie saying an affirmation onto something that doesn't exists
If someone asks me where I live, and I give an addres I know doesn't exists, for example, "Sunset Boulevard 1600", being the address number 1600 inexistent, ¿Am I lying?
If I am lying, then ...
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4answers
87 views
Let P does not imply Q, and Q does not imply P. Are P and Q independent?
Let P does not imply Q, and Q does not imply P (P → Q and Q → P are both false). Would it correct that P and Q are independent? Is it possible to have R that can imply both P and Q?
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1answer
51 views
Ontology - How do we describe actions/scenarios in relation to objects?
Does anyone know how actions to do with objects are represented in ontology or first order logic?
Example: the cat sits on the mat.
I think the cat and mat have properties that relate them to each ...
0
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2answers
77 views
Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?
Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?
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2answers
121 views
Generating the simplest sort of Cosmological Argument
First, I am not a philosopher, but rather an applied mathematician. However, the Cosmological Argument has always intrigued me. At times I feel that all attempts are necessarily hopeless, at other ...
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2answers
175 views
How do we arrive at stronger theories in mathematics/logic?
A reasonable aim of formal mathematics/logic is to build systems which can "interpret" many things. As an example, ZFC can interpret a number of things. Incompleteness Theorems provide us ...
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2answers
83 views
Can a logical statement be meaningless?
Can a logical statement be meaningless? If a statement is logical, then it can be proven mathematically, but if logical statements can be meaningless still doesn't that prove that mathematical proofs ...
2
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1answer
55 views
Why is the use of the ND rule ∃E not correct in this proof?
Is there anyone who could explain to me why these errors occur? It seems to me the rule was used properly.
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2answers
36 views
Does the definition of “mutually exclusive” include the case where neither A nor B happen?
Does the definition of "mutually exclusive" include the case where neither A nor B happen?
I ask this because I remember in logic, "xor" has to be A or B and doesn't include the ...
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1answer
58 views
Why are variables logical symbols, but predicates non-logical symbols in predicate logic?
I was reading this wikipedia page on first order logic: https://en.wikipedia.org/wiki/First-order_logic
And it says variables are logical symbols and predicate symbols are non-logical.
It also says ...
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1answer
75 views
Is the statement “no form of human knowledge can justify metaphysical absolutes” self defeating?
A common objection to the statement "no form of human knowledge can justify metaphysical absolutes" is that the statement itself is a metaphysical claim.
One response is that the statement ...
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0answers
75 views
Putnam and Skolem Paradox
Why, according to Putnam in "Models and Reality", is moderate realism more affected by the so-called Löwenheim-Skolem Paradox than extreme realism?
I understand the gist of Putnam's grip ...
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2answers
91 views
How is logical form semantic?
According to Wikipedia:
In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system
How can something be a semantic version of another thing? ...
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0answers
31 views
Justification logic and set theory
I was reading the SEP article on justification logic and the question arose for me, whether the difference between intrinsic and extrinsic justifications of set-theoretic axioms (a difference that has ...
2
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1answer
81 views
Is there such a thing as ωth-order infinitary logic?
I've seen references to ωth-order logic sprinkled (sparsely) throughout my studies, though what properties this has compared to and contrasted with nth-order logics I wouldn't be able to tell you (I'm ...
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73 views
Is this a reasonable argument? Dr. Fauci on Face Masks
In a recent interview, Dr. Anthony Fauci (Chief Medical Advisor to the President of the U.S.) was asked why he advised the public against wearing masks in early 2020. One of Dr. Fauci's arguments was
...
5
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3answers
144 views
How to model “forget about” in first order logic?
The other day, my housemate said "Don't forget to not leave the spoon at the bottom of the container". I understood what he meant: "Do not leave the spoon at the bottom of the ...
5
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4answers
191 views
The relationship between Rationalism and logic
Here is an excerpt from the book An Introduction to Philosophy by Russ W. Payne (2015) which is causing me some confusion.
Mathematics had long served as the rationalist’s paradigm case of knowledge ...
23
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11answers
13k views
Is Yoda committing a fallacy?
I've been debating with a hard core Star Wars friend who loves repeating Yoda's "Do or do not, there is no try" knowledge.
I tried to explain that the DO (B) and DO NOT (C), are end results, ...
2
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4answers
792 views
Why fallacy of amphiboly exists in this sentence?
I am reading Essentials of Logic, 2e by Irving M. Copi. And I do not understand this exercise from page 87.
Identify the fallacy of ambiguity that best characterizes each passage.
...
Being ...
2
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0answers
37 views
Summary of philosophical positions on how belief revision proceeds in mathematics?
Since mathematicians have embraced classical logic, as e.g. MacFarlane points out in his 2021 intro book to philosophical logic (§ 7.4), one needs to distinguish between [meta-]reasoning and argument/...
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2answers
68 views
Question about Kenny’s critiques on Mill’s logic
Recently, I have read a book called New History of Western Philosophy by Anthony Kenny.
In this book, he starts chapter 4 Logic with a section called Mill’s Empiricist Logic, which contains an ...
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2answers
63 views
How to prove ∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy) using natural deduction? [closed]
∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy)
I tried to use reductio ad absurdum by assuming ¬∃y∀x(Fx→Gy) and then using quantifier negation to simplify it further, but it got very messy when I had to use ∃-elimination ...
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3answers
110 views
What is the name of this fallacy (if it is indeed a fallacy)?
What is the name of this fallacy (if it is indeed a fallacy):
Drinking alcohol makes me laugh
Laughing is good for me
Therefore drinking alcohol is good for me
Assuming the premises are true then ...
1
vote
1answer
59 views
Combining the knower with other paradoxes
The knower paradox concerns a sentence such as, "This sentence is unknown." Now liar sentences can be paired with honest sentences, e.g. "This sentence is true." So suppose there ...
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1answer
33 views
Proving using natural deduction ~(AvB) v (~A&B) with premise ~A [closed]
Been stuck at this for a little...
I tried proof by contradiction but got literally stuck at the first step...
So hypotheses is ~A and to derive is: ~(AvB) v (~A&B).
Would appreciate any help.
2
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2answers
174 views
How can one formalize that an argument composed of a true and a false statement is “partly true”?
In classical logic if either A or B is false then "A and B" is false. But in natural language it's often the case to hear someone say "that's only partially true" or "that's ...
0
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1answer
24 views
Making inferences from a counterfactual conditional statement about consistency
Please take a look at a passage from an LSAT:
The economy is doing badly. First, the real estate slump has been with
us for some time. Second, car sales are at their lowest in years. Of
course, had ...
0
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1answer
34 views
Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)
Does ∃x(Nx & ~Nx) contradiction itself?
Is there an error in my proof?
Thank you
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1answer
47 views
Prove (-A=-A) = [-(-A => A) = (A=>-A)]
This is not homework
I do this for fun.
I tried using prover. The result is quite confusing.
I use the Logic Book
This is the last problem I want to do in this
section.
I have to it mostly in SD+ .
|- ...
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2answers
63 views
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1answer
59 views
Is there a weaker/general version of Incompleteness Theorem which holds for every formal axiomatic system?
Is there a general version of Godel's Incompleteness Theorem which holds for any formal axiomatic system (and not just those capable of modelling basic arithmetic)?
If no, is it absurd to ask why such ...
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2answers
75 views
Questions About Complete Truth Tables
Why do you need a complete truth table to prove that a sentence is a tautology when you can just make a partial truth table starting with labeling the sentence as false and if it's impossible, the ...
2
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0answers
33 views
Analysis of Liar-like sentences in fuzzy logic
Let t0 = FALSE and t1 = TRUE. In fuzzy logic, 0 or 1 can be switched out for any real number in the interval [0,1]. This lets us construct all manner of liar/honest-like sentences, ranging from, "...
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4answers
90 views
I don't see the problem caused by the following entailment
From Forall X (p.74):
(3) ‘It’s not the case that, if God exists, She answers malevolent prayers.’
Symbolizing this in TFL, we would offer something like ‘¬(G → M )’. Now, ‘¬(G → M )’ entails ‘G’ (...
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3answers
134 views
What is the most basic reasoning that creates all kinds of reasoning?
Hypothetico-deductive method, abductive reasoning, induction, deduction, reduction to absurdity, dialectic....
There's reasoning in mathematics, too.
What is the fundamental reasoning that creates all ...
3
votes
2answers
271 views
What makes an argument objectively more “compelling”?
If person A gives an argument to person B in order to convince them about the truth of claim X, how can B determine how compelling A's argument is in a way that is as objective as possible (i.e. in a ...
2
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2answers
96 views
Can 'All S is P' ever be false if S is empty?
I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"?
In the boolean interpretation 'All S ...
0
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1answer
46 views
Help with Fitch formal proof?
I'm having trouble solving this formal proof in Fitch. I've put together most of it, but I think I need to use disjunction elim(?) at some point and am having trouble doing that.
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1answer
48 views
Show the following is valid in SD+: How to solve this derivation
This is not Homework.l do this for fun and expand my learning.
I am obviously having difficulties with SD+,thus l post many problems.
I am using the Logic Book
Problem has be done in SD+
Using goal ...
2
votes
2answers
78 views
Non catastrophic presupposition failure
In a previous question, I asked something similar but without explicitely referring to the source material of my doubt. Now I try to state it here with more precision: In "Non-catastrophic ...
-2
votes
3answers
99 views
Is rational to logical as rectangle is to square?
That is, if X is logical, is it necessarily rational? What's an example of something that is rational, but not logical. If logical does not necessarily imply rational, what's an example of something ...
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2answers
174 views
Is the concept of a “model” in logic grounded?
The concept of a "model" in logic has always seemed a little suspicious to me - as it implies statements that are not deducible from the axioms, yet are true anyway. What could "true&...
3
votes
1answer
39 views
Some minimal insightful example for the distinction between internal vs external logic of a Gentzen system?
I've read the following:
Definition (Internal logic) An argument from premises to conclusions is valid
in the internal logic of a sequent system iff the sequent G ⇒ D is derivable in that
system.
...
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votes
1answer
75 views
I need help with with to do this derivation
This is not homework
I do this fun and to expand my knowledge.
I am using the Logic Book
I am having trouble obviously doing SD+ derivations as I post several of them.
I have to show this derivation ...
0
votes
2answers
36 views
How do I symbolise this statement with a definite description in first order logic?
"If there is exactly one present King of France, then the present King of France is a present King of France"
The part I am confused about is the consequent of the conditional which equals ...
0
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1answer
60 views
Although only half of a dish is red, can I call it ‘red dish’?
Although only half of a dish is red, can I call it ‘red dish’? Or only when an entire dish is red, can I call it ‘red dish’?
