Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
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Is there a distance so small it can't can't be further divided
If I shoot an arrow at a target, at some point it will reach 1/2 the distance to the target. Then it will reach 1/2 of that distance. It will continue to reach 1/2 of.the previous 1/2 forever. So, how ...
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Can syntactically complete theories be undecidable?
A formal system S is syntactically complete if for each sentence (closed formula) φ of the language of the system either φ or ¬φ is a theorem of S.
My confusion is the following. I've heard that a ...
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Does logic have a more proper word to mean something similar to dilemma but neutral?
Section 7.8 The Dilemma of Copi's Introduction to Logic says:
The dilemma is a common form of argument in ordinary language. It is, in essence, an
argumentative device in which syllogisms on the ...
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FOL: variable assignment and x-variant
Someone can explain me in poor words why we need an x-variant when we deal with the interpretation of quantified formula?
Let s be the value assignment and v the x-variant.
For example M \models_s \...
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Proofs by induction on the complexity of a formula [closed]
Someone can explain me with an example how does it work?
thank you
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Propositions vs sentence types and tokens and the context insensitivity of PL
I came across the following explanation for the context insensitivity of the language of propositiional logic (PL) on page 34 of The Laws of Truth by Nicholas Smith:
Because glossary entries pair ...
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Model of an argument
I have the thought that an informal argument is fundamentally about building a justification graph: a directed acyclic graph from premise propositions to intermediate and conclusion propositions, ...
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Can a valid argument be said to be unsound if the set of premises is unsatisfiable (inconsistent)?
I'm asking in a strict propositional logic sense. Suppose that I have a set of premises that is logically unsatisfiable (or inconsistent), i.e. they can not be all True simultaneously, that argument ...
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What's it called when the consequent is indifferent to the antecedent?
What's it called when the logical consequent is indifferent to the antecedent?
I'm looking for the logic term for when
P ⇒ Q
and
¬P ⇒ Q.
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Is the Law of Excluded Middle an allowed argument in court?
Is the Law of Excluded Middle a valid deduction rule in court? If not, is it reasonable to say that all arguments in court must be "constructive in nature"?
As an example, consider this ...
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Gödel's Incompleteness Theorem
I'll keep this short and sweet.
Construct Axiomatic System A in which we can do math.
Gödel Sentence G = G is unprovable in A.
Gödel's Argument (I)
If G is provable then there's proof that G has no ...
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Does natural language like English make more assumption about logic than mathematics?
Does natural language like English make more assumption about logic than mathematics? In mathematics, there doesn't seem to be any assumption made about which logic system is true, and therefore it is ...
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Can an argument be valid even if its conclusion has nothing to do with its premisses?
An argument is invalid if and only if there is a possibility where its premises are true and its conclusion is false.
Then is the following argument technically valid?
a: Alfred has exactly 20 mice
b:...
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A question on quantified modal logic
I originally posted this on math.stackexchange.com, but I’m cross-posting it since I know there are good modal logicians on here too.
Also, I already asked a similar question here: Identity in ...
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Proof of soundness of the rule of implication introduction in natural deduction calculus
From the definition of a sound calculus we can infer that a sound implication introduction has to have the form: Γ ⊢ A → Γ ⊨ A.
The rule for implication introduction goes (Γ ∪ {A} ⊢ B) ⊢ (Γ ⊢ A → B).
...
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Could law be written in formal logic?
I essentially have two questions:
Could law be written in formal logic?
If that's indeed possible, should it be?
I see possible drawbacks being:
Difficulty to express certain concepts, I can't ...
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What is the logic of the coordinating conjunction BUT?
What is the logical difference between "and" and "but"?
Is it really possible to oppose "and" and "but" in this sense?
Is it really possible to reduce the logic ...
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Are these statements tautologies?
On p22 in The Big Questions by Solomon:
A tautology is a trivially true statement. Some examples:
A man is free if he is free.
You can't know anything unless you know something.
I wouldn't be here ...
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What are the origins of the A,E,I,O notation for the four types of categorical proposition? [duplicate]
The labels A, E, I, and O are traditionally given to the four types of categorical proposition.
Each is one of the first two vowels in the Latin words affirmo (I affirm) or nego (I deny), a usage that ...
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A technical question about the limitation of z of "jointing together" or "zus(x,y)" in Gödel Arithmetization
I am recently reading Professor Carnap's Logical Syntax of Language.
In p.61 D18.1., the limitation of z is not greater than: pot [prim (sum[lng(x), lng(y)]), sum(x,y)].
Remarks: z is the series-...
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Why is Occam’s razor faulted for being a heuristic when almost everything in philosophy is?
I am confused as to why any sort of discussion about Occam’s Razor, without fail, has the addendum mentioning how the tool doesn’t prove anything. But quite literally, unless something is logically ...
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Logic of reflective equilibrium
Reflective equilibrium is the simple but compelling concept that a person reflects on conflicts between different beliefs that they hold, and revises their beliefs to reduce the conflicts, or to ...
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Is "may exist" and "may not exist" a negation that isn't a contradiction?
As usually happens, a statement (p) and its negation (~p) contradict each other. So, e.g. God does not exist, the negation of, God exists, together form a contradictory pair. A statement (p) and its ...
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How does one differentiate between the logically possible and the impossible?
The term “married bachelor” seems to be an obvious contradiction. The very definition of bachelor and unmarried are with respect to each other and so it seems nonsensical to talk about a married ...
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Is asking to align on definition during a debate a derailling or disingenuous demand?
In a recent discussion with a group of friends, we found ourselves in a situation where we appeared to be using the same word, but it became evident that we held different meanings for it. At that ...
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Type of false reasoning?
I don't have extensive background in philosophy but I try to outline my question clearly.
I am arguing with a person who always uses the same logic.
We have an outcome X such a medical disease ...
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Proof of the existence of God?
Here it is, the long-awaited proof for the existence of God (for your consideration).
I have taken the liberty of defining discretely what God is, without which there is no question to be answered (...
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Can A cause B with B preceding A in time?
I am wondering whether or not A can cause B with A occurring after B. Something about this seems nonsensical. But is it logically contradictory?
If it is not logically contradictory, does this mean we ...
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How to discuss subjects with people who are convinced by emotion, not by reason?
Sometimes I must discuss a subject with someone who has an emotional, not necessarily reasonable, connection to a subject. How can one discuss a subject or convince a person who has an emotional ...
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In logic, is there a name for a secondary contradiction that arises from operating (unkowingly) under a first contradiction?
Say I assume predicate A and B.
Say I show that A AND B is a contradiction.
If I then apply the law of excluded middle to say NOT A, this is a fallacy, no? Does it have a particular name?
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Prerequistes for mathematical logic
I have a working knowledge of calculus and linear algebra. But when I pick up books on mathematical logic (for example the ones listed in the logic study guide by Peter Smith), they often use ...
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How this principle related to Golden Rule and Eye for an Eye is called?
Had long admiration to this example:
When criminals were sent to isolated island centuries ago they suddenly realized that it's not fun anymore when everyone is criminal. And switched to one of most ...
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Does probabilistic justification exist?
Is there such a thing as how likely it is for a hypothesis to be true given evidence as a matter of fact?
It is certainly true that we might feel strongly about other minds existing based on what we ...
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Could a quantum computer simulate any system based on different types of logic?
Quantum computing is based on quantum mechanics (obviously) which has different logical rules than classical/Boolean logic.
However, does this mean that a quantum computer could simulate or process ...
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I have taken my midterm exam 1 hour ago, and I am confused about some question meaning
1 what is the defferenece between "the justification of line 6" and "the application of xx on line 6"? For example, we can find that in the line 6, the application is wrong because ...
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Is the law of identity the same for negative expressions?
Is the law of identity the same for negative expressions?
Does 'if not p then not p' have any specific meaning in philosophy?
I am asking because I am trying to work out whether the vagueness of 'p' ...
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Categorizing with metaphor, analogy, and symmetry
Continuing the discussion Categorizing with metaphor, analogy, generalization, and abstraction my next question is how two concepts metaphor/analogy equivalent to symmetry(change without change) .If ...
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The Liar Paradox: Simply a sentence of indeterminate truth value?
Some sentences are true. Some are false. However, sentences like "What time is it?" or "Wash your hands" can be said to be of indeterminate truth value. This suggests a trichotomy ...
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Is there a modal modification of the law of excluded middle that may render constructive?
Intuitionistic logic rejects the law of excluded middle, and paraconsistent logic rejects the law of non-contradiction. I wondered whether the rejected laws can still be incorporated, if they're ...
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Intro to formal logic
We homeschool our kids, and "The Great Courses" offers a lot of good intro college classes that are suitable for 6-12th grade as well.
I'm really not into math or logic so please forgive me ...
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How Does Alethic Nihlism Address The "Changing Of Subject" Objection?
I recently read this article in my pursuit to understand wtf alethic nihlism is trying to say:
https://philarchive.org/archive/ASASIT
One of the objections to alethic nihlism is that alethic nihlism ...
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Trivialism vs Alethic Nihlism
What are the similiarities and differences between the two theories (as well as arguments for and counterarguments against).
From what I know, trivialism states that everything is true (and I believe ...
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Is a naïve logical argument against god rational?
I have seen a short clip recently, in which someone used a proof by
contradiction that a being cannot be omniscient (including past, present and
future) and have free will at the same time. There are ...
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What is the philosophy that deals with concepts being correctly fitted to reality or "carving reality at the joints"?
In philosophy of science thinkers sometimes speak of certain theoretical concepts "carving nature at its joints" (I think this might have been used prominently by Hilary Putnam but I can't ...
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What's so special about Tarski's T-Schema?
It seems fairly obvious. Even a five year old could probably come up with it. Its obvious that if something is the case, it is true (literally synonyms).
So, am I missing something? Is there a gulf ...
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Liar's Paradox and Truth
I found myself thinking about the liar's paradox of the form "This sentence is false" and how it relates to one's conception of "Truth" and "Falsity". After deliberating ...
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abductive reasoning in many fields of study
In continuation of the discussion What is the relation between abductive reasoning and fallacy? my question is that if medical science judiciary history all uses abductive reasoning (almost all the ...
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Can a quantifier bind a name in FOL formulas
For example, if I have
∀a(∀x∃z(P(m) & Q(x,z,a)) || R(a,b)) (|| means OR), can I say it is a well formed formula in FOL.
If I remove the ∀a at the beginning, can I now claim it is a well formed ...
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Question about disjunction elimination in Fitch
I was recently using https://proofs.openlogicproject.org/ and realized that their version disjunction elimination is fairly restrictive.
I had a proof set up something like this:
p∨q (Premise)
p∨r (...
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FOL Equivalence and Theorems
So, this is sort of a 2-in-1 question.
There is no sentence W of FOL such that: ∀yB(y)⟛¬W
True or False?
Now, my interpretation is: There is no sentence W in FOL where for all y in the extension of B, ...
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