Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
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Translations into TFL (truth functional logic)
I've been struggling with truth functional logic translations (very new to this) and I was wondering if someone can help me with strategy at getting better with this stuff. I feel super all over the ...
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What kind of fallacy is in that situation?
What kind of fallacy is there in saying that it is improbable that people will do radical actions, (like becoming religious) if there isn't a bit of truth to it.
Could there be fallacies that were not ...
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What reasons philosophers give to justify the claim that the Liar is paradoxical?
Most philosophers seem to see the Liar as paradoxical. Typically, they would say:
(L) -- If the Liar is true, then it is false; if it is false, then it is true.
According to what I have read, (L) ...
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Existential vs. universal alternation
Is there a difference between trivial and nontrivial negation? It occurred to me that we could think of the following series of negation operations/relations:
Empty negation = primordial double-...
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Is Validity or Justification Always Valuable?
Although it is debatable that justification is a necessary or sufficient condition for knowledge, many philosophers make the claim that it is. African-American philosopher of culture Alain Locke ...
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Is logical entailment possible without the logical connectives, quantification, or equality?
Can you think of any possibility of logical deductive argument without the use of logical symbols (negation, material conditional, all, some, etc.), or equality?
I was at first thinking perhaps the &...
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Can omnipotent beings exist? [duplicate]
Through an omnipotent being, all things are possible. Can such beings exist? For example, can the Flying Spaghetti Monster be omnipotent?
Prior discussion:
This question is supposedly relevant, but ...
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Modal system K - prove ⊢ (□p ∨ □q) → □(p ∨ q)
I am trying to prove the following:
⊢ (□p ∨ □q) → □(p ∨ q)
However, I think that I am lacking the knowledge of a tautology in classical logic that would help me prove this.
I tried something, but it ...
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Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K
This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so.
□(A ∨ ¬B), ¬□...
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Proof of □P ⊢ □¬¬P in modal logic system K
I need to prove the aforementioned formula in modal logic system K, which I am having trouble to do.
Of course, this should be easy to prove if I had access to axiom T, but since it's system K, we can ...
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Modal Companions and Trivially Strict Conditionals
The classical material conditional is given a truth-functional definition that can be determined with truth-tables. Intuitionistic implication is a kind of strict implication that can be translated to ...
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Can a totally ordered set with a last element but no first element exist, or is this contradictory?
Can a totally ordered set with a last element but no first element exist, or is this contradictory? An example of such a set would be a set that is ordered from largest to smallest, with there being ...
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How is the completeness of first order logic reconciled with the incompleteness of set theory?
First Order Logic (FOL) is complete in the sense that:
there is a proof procedure for FOL such that just the statements(/wffs) of FOL that are true and remain true under any re-interpretation of their ...
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Infinitary modal logic
Let 'L' and 'M' denote the necessity and possibility operators. In Modal Logic, the following theorems hold:
L(p and q) <--> (Lp and Lq)
(Lp or Lq) --> L(p or q)
M(p or q) <--> (Mp or ...
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Substructural skepticism
The SEP article on substructural logic mentions an issue of repeated premises:
So, I might have X, X ⊢ A, which says that I can use X twice to get A. I might not have X ⊢ A, which says that I can use ...
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What is this "going to the other extreme to make it look stupid to prove something"?
I don't know why I see this so often.
When I say, it may not be good to sell 35 years of your life to the corporate world in a stressful way being golden handcuffed by a high salary or stock, somebody ...
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What does it mean "to provide semantics" in the context of formal logic?
When reading some SEP articles, this is a phrase I commonly came across, "this provides a semantics for this logic". But what does it mean?
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Confusion about "This statement cannot be proven"
I'm wondering why this statement is taken to mean the below when it's true or false.
T: there is no proof (implying a true statement with no proof)
F: there is a proof (implying a false statement with ...
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Mill's methods - logic
Which Mill's method (not considering their limitations) would you use if you need to rule out the identity of a murderer based on the murders he already committed?
The only possible answers are method ...
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Should I ever be influenced by an argument that I can't understand?
[Edit: Please read the whole question, or at least the new "N.b" paragraph, that I added just now to the end of the question, before attempting to answer it.]
I'm asking this because ...
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If it is trivial that 𝘟, is it trivial that it is trivial that 𝘟?
Differentiate between empty, trivial, and nontrivial solutions to problems. From a category-theoretic point of view (or maybe just mathematics/logic historically), one has that empty solutions are ...
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Entry points from philosophy into mathematics at higher levels?
Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
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A resolution to liar's paradox
Let's consider the famous liar paradox's statement:
This statement is false
Now, in classical logic, principle of bivalence could be stated as "All statements can either be assigned a value of ...
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How can one refute this argument that claims to do away with omniscience as a divine attribute?
Definition of omniscience: X is omniscient = for the whole preposition P, X knows the value of P.
Let T be the set of all true propositions. An omniscient being knows all these propositions (T).
Let ...
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What logics/philosophies deny the law of excluded middle (LEM)?
What logics/philosophies deny LEM, the law of excluded middle (tertium non datur)?
This law is expressed as Philosophical Axiom 4.2:
Tertium non datur (Non est medium inter esse et non esse. ‑ ...
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How would a logician define the phrase "all other things being the same"?
Here are some Examples of the Phrase
All other things Being the Same
All other things being the same, the juice of a Granny Smith Apple is more acidic than a the juice of a Red Delicious Apple.
All ...
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On the logical modeling of reality and human reason
What is the system of logic which models reality and, furthermore, which models human reason?
Preface:
Of course, objective reality (that is, reality as it is before it's perceived) may operate under ...
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Correlating epistemic logic types with quantifiers?
Pursuant to my question about a logic of "understanding" as a distinct, same-level concept vs. "knowledge", I have had cause to try situating at least ∀ and ∃ in relation to the ...
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Why shouldn’t I be a skeptic about the Necessitation Rule for alethic modal logics?
Alethic modal logics for metaphysical possibility and necessity usually have the Necessitation Rule:
From ⊢P, infer ⊢□P.
Doesn’t this commit us to the meta-notion that logical necessity modulo some ...
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What logical differences are between "if" in conditional clauses and "provided that" in proviso clauses?
In Keller's Learn to Read Latin:
The conjunction dum, sometimes strengthened by the adverb modo, "only", may introduce a subordinate clause stating a provision under which the event of the ...
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Is there a system of logic which denies DNI?
From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE.
DNI: p -> ~~p
DNE: ~~p -> p
and denies DNE ...
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Why does no modal logic use an anti-symmetric (partial order) accessibility relation?
Several sources includes catalogs of many modal logics, often arranged into a lattice of inclusion, showing increasing power, from K to S5. Naturally, for each logic there is a corresponding ...
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https://proofs.openlogicproject.org/ - Double negation introduction - [duplicate]
How can we introduce double-negation? For example, p is the same as ~~p.
I am not able to find how to introduce ~~ in https://proofs.openlogicproject.org/
Is there anything like DNI, similar to DNE?
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What logical fallacy is made in this argument that seems to prove that learning is futile?
To learn is to gain more knowledge.
Having more knowledge means having more that one can forget.
∴, the more one learns, the more one forgets.
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Double-negation deduction rule in https://proofs.openlogicproject.org/
How can we use double-negation deduction rule?
For example, ~~p is the same as p.
I am not able to find how to eliminate ~~ in https://proofs.openlogicproject.org/
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Proof of A & B from ¬(A → ¬B) using rules of inference
I have been tasked with proving A & B from −(A → −B). However, I'm only allowed to use the following rules:
ModusPonens,
ModusTollens,
ConditionalProof,
DoubleNegation,
AndIntroduction,
...
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What are the arguments of philosophers against the reasoning which justifies the horseshoe from truth-functionality?
There is a reasoning in mathematical logic which is meant to prove that the horseshoe is the only logical operation which fits our notion of conditional.
The reasoning starts from the idea that the ...
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Essentialism and concepts
I've been reading an old logic text (Deductive Logic. George Stock. 1888) and he describes something very like Aristotle's notion of a definition, but in his description, it is clearly a matter of ...
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Modelling glass half full vs half empty using logic
Suppose we have a glass of water, and it is filled till half. One could either say, it is half full or it is half empty. These are two distinct propositions, but are complement to each other in some ...
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Do computers use logic?
I know we refer to computers as using logic, logic gates and the like, but is this just us ascribing human capacities to the machines? It sounds like a case of us giving more meaning to the machines ...
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Natural language into logic and proof
I'm working through Logic by Paul Tomassi, and there is one particular problem I'm stumped with. The problem is on pg 186 and involves representing an argument in English as a sequent and then ...
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Is there a logic with negation as (primarily) a binary relation?
The only search results I got for the exact phrase "negation as a binary relation" were a cryptic essay and/or book about "Chinese opposites." Now, what I have in mind is something ...
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ls elementary mathematical equality essentially a self-identity statement?
In a lot of places equality is defined that for two expressions A=B, A=B means that A and B have the same value (A=B). This relationship seems strange as we are slightly abusing use/mention, if '=' ...
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What to make of properties as unary relations?
Take for example the property or the unary relation, Man(x). It seems to "really" be a binary relation between x and {true, false} "under the hood." So would this make the notion ...
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Would the imaginary unit be the truth-value of sentences formed using √𝐧𝐨𝐭?
Section 4.3 of "Sentence Connectives in Formal Logic" discusses a concept of demi-negation or what is (for the sake of the text) resolved to a concept of "the square root of negation&...
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How the hell could it be a valid argument if the premise and conclusion are two different things [closed]
The premise is: John is a married bachelor
The Conclusion is: Pigs can fly
There is only one premise and one conclusion. Why are they connected and in what way can we say this argument is valid?
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Halting Problem Oracle
Halting problem is unsolvable. There is no method to solve it, so no human can solve it.
So why is any theory utilising an oracle (which can solve halting problem) not simply nonsense?
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Is this a problem with verisimilitude talk, many-valued-logic talk, or something/nothing else?
A perhaps naive characterization of verisimilitude is "closeness to truth," the proximity coming from the similarity. At least, the SEP article uses, "The number of planets is 9," ...
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Are there conjunctive facts and disjunctive facts?
Facts are supposed to be the grounds for truths. However, consider a conjunctive statement like "Paris is in France and New York City is in the USA". What fact grounds that? Is there such a ...
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Identity in Quantified Modal Logic
Why is ¬(◇(a=b)∧◇¬(a=b)) a validity in Quantified Modal Logic (QML)? For example, let a:=“the present King of France” and b:=“the richest bald person alive”. Then, it seems ◇(a=b)∧◇¬(a=b) is not a ...
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