Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
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Are there inference rules for introducing and elimination implication `->` in the antecedent (the part on the left of `|-`)?
Deductive theorem says that P, Q |- S, if and only if P |- (Q->S).
I found that the deductive theorem is inference rules for introducing and elimination implication -> in the succedent (the part ...
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Are there inference rules for introducing and elimination implication `->` in the antecedent (the part on the left of `|-`)? [duplicate]
Deductive theorem says that P, Q |- S, if and only if P |- (Q->S).
I found that the deductive theorem is inference rules for introducing and elimination implication -> in the succedent (the part ...
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Is there an OR-elimination rule for antecedent?
I learned that
P, Q1 |- S,
P, Q2 |- S
--------------------------
P, Q1 | Q2 |- S
Is the converse also true?
P, Q1 | Q2 |- S
--------------------------
P, Q1 |- S
and
P, Q1 | Q2 |- S
---------------...
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What is the justification of a complex dilemma?
7.8 The Dilemma in Copi's Introduction to Logic says:
Complex dilemma: An argument consisting of (a) a disjunction, (b) two conditional premises linked by a conjunction, and (c) a conclusion
that ...
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How should an argument containing an exceptive proposition be tested?
IX. Exceptive Propositions in 7.3 Translating Categorical Propositions into Standard Form in Copi's Introduction to Logic says:
Because exceptive propositions are not categorical propositions but
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Can the relationships of contradictory, contrary and subcontrary between P and Q be represented in terms of logical operations?
In Copi's Introduction to Logic,
propositions P and Q are called contradictory, if they can't be both true and can't be both false;
propositions P and Q are called contrary, if they can't be both ...
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Classical logic with a modified law of identity and its implications
Let's take the Law of Identity and change it to the Law of Identity with Overlapping Categories:
Would classical logic with the modified Law of Identity be completely different than classical logic. ...
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Can we determine if a logic system is incomplete?
Can we determine if a logic system is incomplete? Let's say because I don't really have a good definition of what complete is that a complete logical system can be used as a foundational ground to ...
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Do the following two derivations imply each other?
https://plato.stanford.edu/entries/square/ says
A proposition is a subaltern of another iff it must be true if its superaltern is true, and the superaltern must be false if the subaltern is false.
...
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Does subalternation apply only to syllogistic logic, but not to other logic systems?
According to Copi's Introduction to Logic, in the square of opposition in Aristotle's Syllogistic Logic, there are four kinds of relationships between propositions:
contradictory: two propositions ...
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What is a false counterpart of tautology called?
A tautology is a statement which is always true.
What is the name for a statement which is always false?
Is it correct that a statement is either tautology, the false counterpart of tautology, or ...
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States-of-affairs as zero-place analogues of properties and relations?
I've been going slow through the SEP article on intrinsic properties, and came across this intriguing gem:
(The locution ‘state of affairs’ is used differently by different philosophers. Here it is ...
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If nothing is preventing something from existing, must it exist?
The question in the title; if there is no existent precluding factor (whatsoever) for the existence of some x, must such a x exist?
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Question about effect
There is an order to the Universe we live in.
Roughly speaking, little things affect big things. Not the other way round.
This is something you already know: particle physics underlies nuclear and ...
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Can you achieve the same level of 'consistency' or similar if you remove or modify the law of identity in a logical system?
Can you achieve the same level of 'consistency' or similar if you remove or modify the law of identity in a logical system? Well, first, I consider it to be impossible to maintain the same level of ...
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Do "No S is P" and "All S are not P" mean the same?
I am reading about categorical syllogism in Copi's Introduction to Logic. I was wondering what differences are between the following statements:
No S is P.
All S are not P.
Am I correct that
Their ...
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Is there any formalized logic that doesn't rely on the law of identity?
The Law of Identity is one of the fundamental principles in classical logic, stating that an entity is identical to itself, meaning that A is A, and nothing can be other than itself. Without the Law ...
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Don't some grammar rules in natural language imply or require classical logic to be true?
Languages, natural like English or French, or subject to specification
like the mathematical language or formal logic itself, do not make any
assumption, and this for the obvious reason that ...
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For what kind of P is "if P were the case, I would know that P" true?
Consider arguments of the following form for some proposition P:
If P were the case, I would know that P.
But I don't know that P.
Therefore, it is not the case that P.
I am wondering what kind of ...
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If this sentence is false, then it is true
Is the sentence "If this sentence is false, then it is true." false or true (even tautologically true), or is it a paradoxon? The sentence p claims (= is equivalent to?) that ~p → p which is ...
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Is there a distance so small it can't be further divided?
If I shoot an arrow at a target, at some point it will reach one half of the distance to the target. Then it will reach one half of that distance. It will continue to reach the half of the previous ...
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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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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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