Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
2,527
questions
0
votes
0answers
28 views
What are 'counterfactual definiteness'?
Without much gibberish, I am wondering what are 'counterfactual definitive statements' made across possible worlds?
And, most importantly how do they obtain?
0
votes
1answer
34 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 ...
0
votes
0answers
37 views
Possible worlds and accessibility relations [on hold]
Is there anything preventing possible worlds from meeting one another in a plane of existence that intersects both possible worlds?
And if not, how would you describe such a plane that intersects ...
2
votes
1answer
60 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
50 views
Formalisation of an Argument
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
27 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
24 views
Logic Philosophy question [duplicate]
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
42 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
47 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 ...
0
votes
0answers
26 views
Is There a Maximally Consistent Set That is Not $\omega$-complete? [closed]
I was going back through Mates 2nd edition Elementary Logic and am having a bit of trouble on one of the exercises; it says,
"Find a counter example to the following assertion: for any set of ...
3
votes
1answer
79 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
60 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 ...
1
vote
1answer
34 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 ...
0
votes
1answer
49 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
140 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
41 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
58 views
Tableaux for normal modal logics
Does ⊢ ◻p ⊃ ◻◻p hold in Kρ? Check with tableaux and if the tableau does not close,
define and draw a counter-model.
0
votes
1answer
43 views
How to prove ~(~A v ~B) |- A & B by natural deduction? [closed]
Help with proof please.
I can't seem to see a proper way to go about this specific proof.
0
votes
1answer
51 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
84 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
97 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
36 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
66 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
39 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
34 views
0
votes
2answers
123 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 ...
0
votes
1answer
67 views
Complement of “at least two people share the same birthday”
Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday?
So this is actually a question on probability, but I'm really confused in the logic and ...
0
votes
2answers
77 views
Is every reason reducible to a sequence of tautological statements? [closed]
I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
2
votes
2answers
84 views
Do Aristotle's three laws of logic apply to statements about the future?
I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply ...
0
votes
1answer
24 views
Logic Question in a fitch style system - disjunction elimination
I am having difficulty in formally proving two arguments.
Firstly, given the premises
A ∨ (B∧C)
¬B∨¬C∨ D
derive A v D.
I can see why it has to be either A or D, because if it's B and C, ...
3
votes
1answer
278 views
Proof Using Model Universe
Suppose I am trying to prove the following argument
(∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx)
Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
4
votes
1answer
102 views
Difference between “neither true nor false” and “either true or false.”
What is the difference between "neither true nor false" and "either true or false."?
I was reading about definitions
And I read a line saying "Lexical definitions are either true or false".
After ...
1
vote
2answers
57 views
Clarification on what is and isn't a logical statement
After reading the article from Wikipedia I feel more confused on what the scope of the definition of a 'logical statement' or proposition is. First, is the statement "It is raining" considered to be ...
0
votes
1answer
43 views
What is the difference between a function and a relation in first-order logic?
Consider this definition of first-order (or Herbrand) logic syntax. Here is the vocabulary:
Definition (Vocabulary): A vocabulary V consists of:
A set of relation constants {r1, ...,...
2
votes
0answers
43 views
The perfect definition of impossible [closed]
When i think about the true impossible, for me is a very dark area, that causes depression, because when we think about this simple question that begins whit, an example, "God creates the Human ...
2
votes
1answer
67 views
What's the difference between a second-order relation and a relation between objects?
I was reading an article in philosophy and found this:
Some philosophers have denied that there is such a relation as
identity. Thus Ludwig Wittgenstein writes (Tractatus 5.5301): "That
...
0
votes
2answers
76 views
How should one symbolize “and then” in logic?
Graham Priest observed that not all uses of "and" in English commute: (page 15)
...according to the truth table for &, 'a and b' always has the same value as 'b and a', namely, they are both ...
1
vote
2answers
51 views
What's the difference between “All A are B” and “A is B”?
I'm having trouble catching the difference between these two forms. I tried to draw some Venn diagrams but it's not helping.
"All A are B" means A is contained in B.
Does "A is B" mean A is also ...
1
vote
1answer
38 views
logical fallacy (or pseudo-logical, or rhetoric) corresponding to unduly extending my argument to make it false
This is probably similar to my preceding question:
What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?
but I'm not sure ...
10
votes
9answers
3k views
How to prove (A v B), (A → C), (B → D) therefore (C v D)
Obviously since A → C and B → D then if A v B one of C or D must be true.
My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
0
votes
3answers
68 views
What is an example of a true contradiction in a paraconsistent logic?
While reading the Wikipedia article on trivialism I noticed the following:
In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
1
vote
4answers
176 views
Is metaphysics justified in its conclusions?
I'm curious of the modern meta-philosophical viewpoints on metaphysical knowledge. That is, is it possible for arm-chair theorizing or rational pure thought alone to gain true knowledge about any ...
7
votes
11answers
3k views
What is the logical distinction between “the same” and “equal to?”
We all understand that
Given A = C, and B = C,
Then A = B.
However, A is not “the same as” B.
Example:
A is the question, “What animals have feathers and can fly?”
B is the question, “What was the ...
1
vote
4answers
244 views
Is there any exception that proves or suggests that the law of non-contradiction does not always apply?
Is there any exception that proves or suggests that the law of non-contradiction does not always apply?
I am thinking, because the law of non-contradiction is very similar to the law of excluded ...
1
vote
3answers
75 views
Is this ad hominem or in general acceptable behavior during an argument?
Person A: What is considered socially acceptable should be common sense regardless of outside influences.
Person B: What is considered common sense or obvious can be very different depending on ...
3
votes
3answers
59 views
Does a biconditional necessarily imply a causal relationship?
Supposing A if and only if B, is it necessarily true that either A causes B or B causes A?
I'm considering this question where the truth values of A and B are both True, not both false.
In theory, ...
4
votes
2answers
265 views
Is there a difference between equality and identity?
Is there any difference between equality and identity, or are they the same concept?
2
votes
2answers
55 views
Is there any exception that proves or suggests that the law of identity not always apply?
The law of identity is rather simple, so I feel like there can be absolutely nothing that can contradict it or suggest it to be false, it's like a tautological truth that doesn't say anything. But is ...
