Questions tagged [logic]
Use this tag for general questions about logic that are not categorizable under some more specific tag, like "mathematical logic", "informal logic", "classical logic", etc.
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How can we reason about "if P then Q" or "P only if Q" statements in propositional logic?
When you have a propositional sentence of the form P ⊃ Q — which we might read as "if P, then Q" — how can you tell when it is true, or false, based on the truth-values of P and ...
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What is the difference between Fact and Truth?
I'm curious about the difference between Fact and Truth. I was searching on the internet if I could find it. But still I'm confused about the exact meaning.
I first read the forum discussion here
Fact ...
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Is God either amoral or not omnipotent?
The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which ...
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What is the difference between depth and surface information?
I was looking for an answer to this question: Was Euclid's method of proof axiomatic?
While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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Philosophers or philosophical traditions that reject symbolic reasoning
I'm most familiar with philosophy in the context of discussing various flavors of logic, such as independence-friendly logic, various extensions of first-order logic with plurals, relevant logic, and ...
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Is infinite regress of causation possible? Is infinite regress of causation necessary?
For a number of reasons — including perhaps a desire to feel that we have a complete understanding of where we came from, or at least an understanding which is completely sufficient for all of ...
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What fallacy dismisses problems by presenting "bigger" problems?
Wasn't really sure how to phrase this, but I'm thinking of an instance in which someone diminishes a problem by presenting one of larger scope - as a rather shoddy example, "x political problem in ...
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What are the differences between philosophies presupposing one Logic versus many logics?
I was wondering in light of the historical developments of logic since ancient Greeks and well into the nineteenth and twentieth centuries: What kind of a philosophy assumes only one Logic, and what ...
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What are the more complex/interesting examples of synthetic a priori statements?
The usual examples of synthetic a priori statements are – it seems at least since Kant:
"Nothing can be simultaneously red and green all over"
7 + 5 = 12 (or any other basic arithmetic statements).
...
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What is the philosophical ground for distinguishing logic and mathematics?
I was wondering why the field of mathematics and that of logic are perceived as two distinct fields. Although could be pleased with the intuition that logic is rather meta-mathematics, still would ...
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Why does the material conditional have the truth table it does?
Can someone provide me with the simplest possible argument for why the material conditional has the truth table it does?
Googling doesn't help at all, providing only flimsy and clumsy arguments. I ...
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Is it possible to know anything with certainty?
I have been thinking about objectivism vs relativism recently.
It is easy to prove by contradiction that there exist objective truths. However, is it possible to know anything?
If you assume a human ...
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Existential import: in logic, do propositions default to true or false when objects in them do not exist?
In this hypothetical:
Firefighters always tell the truth, while politicians always tell lies.
Suppose three people, who are either a mix of firefighters and politicians, all politicians, or all ...
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?
Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes
But do you know whether his hypothesis also allows/accept universes described by other types ...
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References for the justification of the use of Logic
Following that question : How to justify the use of logic?
I'm looking for references of the justification of the use of Logic (the question above didn't ask explicitly for resources but rather for a ...
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Do all epistemologies suffer from the "regress of justifications" problem?
Aristotle describes the regress problem in his logical work Posterior Analytics I.2:
b5. Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. ...
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Why are conditionals with false antecedents considered true?
I don't understand what conceptual sense this scenario makes, or what the motivation behind the decision to make conditionals with a false antecedent true was. Can anyone help me understand this?
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How do I check if two logical expressions are equivalent?
For example:
Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as
(A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C &...
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In how many and which ways can a logic be non-classical? Are there systems for organizing them?
I asked on MathSE What are the various respects under which a logic can deviate from classical logic, thus being “ non-classical”? and received one short answer. So, I'm interested in responses from ...
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What is the logical form of the definition of validity?
My text book gives the definition of validity as "An argument is valid IFF if the premises are true, then the conclusion must be true". Using a conditional elimination on the RHS of the IFF yields "An ...
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What formal logical systems "resolve" the Liar Paradox?
Short version of my question.
What formal logical systems can represent, and seem robust against, the Liar Paradox?
N.B. I would like to avoid reference to truth-values, except inasmuch as they ...
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Is there a deduction analog to the problem of induction?
Aren't deductive and inductive reasoning equally unjustified? So, inductive reasoning is going from specifics to general, whilst deductive reasoning is going from general to specific. But in deductive ...
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Are omniscience and omnipotence mutually inconsistent?
I see this in The God Delusion by Richard Dawkins:
If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But
that means ...
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Is free will a third option aside from chance and necessity?
The determinism dilemma is that if our actions are predetermined they are not free, and if they are random they are not willed, either way there is no free will. Even if will causation is a mixture of ...
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What is the relation between the material conditional in logic and conditionals that we use every day?
The material conditional has a truth-value of T in every case except where the antecedent proposition is true and the consequent is false. However, this means that many conditionals are true (if only ...
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Is there modal logic without possible worlds?
Would it be desirable to carry out a deflationary research programme in modal logic? In other words, would it be desirable to re-think modal logic without the possible worlds semantics? The original ...
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What fallacy dismisses a conclusion because supporters give invalid arguments for it?
A person dismisses an otherwise valid argument, because some of its proponents support it for the wrong reason.
How is this fallacy called?
EDIT: Here is an example. A person defends the idea that ...
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Can logic be used to prove any belief?
I have witnessed a lot of debates and arguments of different beliefs, and noticed that each side uses logic to prove its point. So, can any belief be proven by logic regardless of its nature (...
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Is the use of inconsistent definitions a logical fallacy?
I am not asking for a defense of or pro/con of the existence of an omnipotent (or multiple omni-x) being, or for the existence of square-circles or any other similar thing. These arguments are well ...
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Why do people use the material implicaton over alternatives?
It isn't because it works. There are numerous alternative, fully-functioning implication systems.
If people have a problem with conditionals with false antecedents, and with true consequents, always ...
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What justifications have been given for using particular systems of logical calculus?
I think that using any particular system of logical calculus should be properly justified.
This justification should be seen as particularly important and pressing in science and technology, and ...
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What is the difference between a statement and a proposition?
I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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Is Logic Empirical?
We use the logical system that we know from observations (empirical data) holds true in the world we live in (please correct me if I am wrong). Hence the axioms of logic we choose are themselves ...
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What are the current topics in philosophy of logic?
I'm contemplating another attempt at completing my long delayed MA in Philosophy, and I need a new thesis topic. As a student I excelled in advanced symbolic logic, but my connection with academic ...
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Why did we define vacuous statements as true rather than false?
I have been trying to understand why implications about the empty set are treated as "true". It seems to me intuitively that vacuous statements should be false.
For example consider the sentence:
...
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Why do we prohibit consensual incestuous relationships?
When talking about sexual relationships between brothers and sisters, our initial intuition might be, “Well that’s just wrong. There’s something immoral about that”. Now, to examine the logic, I ...
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What fallacy argues that we should do nothing because we can not do everything?
A says to B "we should recycle because it is better for the environment," and person B says "if we wanted to be better environmentally, there's lots of things we could do that we don't, so we shouldn'...
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Can reason be precisely defined?
Reason, or rationality, is classically defined as deriving a conclusion from observations. Again, classically this is achieved by the application of logic. Aristotle explained it in this way. There ...
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How does actual infinity (of numbers or space) work?
Is infinity just continuous generation of numbers, or can space be actually infinite? If it is finite can we see it expand if we went to the edge?
When I say "I am counting to infinity" does it mean ...
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How does Plantinga's free will defense of God's benevolence work?
The purpose of the defense is to show that omniscient, omnipotent and benevolent God is consistent with the existence of evil in creation. The most popular version of the defense is due to Alvin ...
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Is there a suppressed premise in Anselm's Ontological Argument?
Source: 5 minutes 20 seconds juncture; Lecture 1, Video 4 (transcription);
MITx: 24.00x Introduction to Philosophy; by MIT Associate Prof Caspar Hare PhD (Princeton)
[...]
Suppose God existed in ...
user8572
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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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Motivations for dialetheism?
At the request of the moderators, I've reformulated this question to change the emphasis of the question to something perhaps a little more broad-ranging:
Question. What are the major modern ...
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Was Locke right that analytic knowledge is vacuous?
According to Locke, it is impossible to obtain substantive knowledge from analytic propositions. Statements like "triangle has three sides" are analytic, but one cannot derive the Pythagorean Theorem ...
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Can there be a valid argument which has a tautology as a conclusion?
Given this definition:
A deduction is valid if and only if its conclusion is true whenever all of its hypotheses are true.
Can an argument be valid if it has a tautology as a conclusion?
An ...
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What are the arguments for and against "one true arithmetic"?
This question was born out of a discussion Is the real number structure unique? on Math SE, but since it is more philosophical than mathematical I decided to ask here.
From Gödel completeness and ...
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Is logic subjective?
If logic is constructed from axioms, and axioms are depended on observation which in term could be subjective, does this means that logic could be limited to our observation, and not really absolute ...
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What is the difference between the "is" of predication and the "is" of identity?
What is the difference between these, the "is" of predication and the "is" of identity?
For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
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Are arguments based on conceivability refuted by ideas from fantasy and sci-fi?
There are several arguments in metaphysics which are based on "conceivability":
The ontological argument for God's existence.
Hilary Putnam's Twin Earth argument for semantic externalism (the idea ...
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Why is Tarski's notion of logical validity preferred to deductive one?
Its flaws are well-known and serious. To recall, an inference from A to B is valid iff all interpretations of "non-logical constants" that make A true also make B true. What are interpretations, a.k.a....
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