Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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Is there a sheaf-theoretic description of para-consistent logics?

Paraconsistent logics drop the notion of global consistency, instead they have a notion of local consistency. In sheaf-theory, or categorical logic, as in topos theory, there is a notion of local ...
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25 views

Self determination in non atomistic time?

I am reading the book " perspective in whiteheads metaphysics" by Stephen David Ross. On page 182 he says" whiteheads theory of events is atomistic-primarily to allow for self determination, but the ...
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25 views

Is there provably a largest cardinal consistent with ZF

Reinhardt cardinals are the largest cardinals yet defined in ZF (they are the critical points of a non-trivial elementary embeddig of V into itself), are they provably the largest possible? Is there ...
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1answer
172 views

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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5answers
338 views

Inductive argument for infinite number of cities

Think of a city, say the capital of Germany, Berlin. Now I can easily come up with another city, like San Fransisco. Now with two cities in mind, I can still come up with another city (Stockholm, for ...
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26 views

Why do people threaten each other? [closed]

My question is why people sometimes threaten each other. Answers will be appreciated. Thank you.
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2answers
96 views

Argument where premises cannot all be true

Is an argument whose premises logically cannot be true at the same time a valid one? It seems it would be "vacuously" valid but I'm not sure about the precise definitions. Ie, is the following a ...
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49 views

Non-Self-Referential Derivation of Inference rule

Prove the inference rule below "non-self-referentially," i.e., without using the inference rule to be proved itself, by deriving its corresponding conditional or biconditional without any premise. (at ...
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2answers
136 views

Semantic vs syntactic consequence

I see that the double turnstile ⊨ denotes the semantic consequence of some sentence of logic, and single turnstile ⊢ denotes the syntactic consequence of some model. This seems equivalent to me. Why ...
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1answer
63 views

Is Deontic Logic applicable in Computer Science?

Deontic logic gives rise to a number of paradoxes when applied to our reasoning about moral values. These days it is starting to be applied in computer science. My worry is: doesn't the presence of ...
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2answers
98 views

Provable and contradictory?

For each consistent formal theory T having the required small amount of number theory, the corresponding Gödel sentence G asserts: "G cannot be proved within the theory T". This interpretation of G ...
2
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1answer
62 views

When translating universal affirmatives should we use implication or conjunction?

Sometimes, when translating a sentence like "All dogs are animals", I often see it represented like this: (∀x)(Px ⊃ Qx) However, I feel like the following is also a good translation: (∀x)(Px ∧ Qx) ...
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1answer
54 views

Provide an example of two sentences , the first formally implying the second, the second analytically(but not formally) implying the first

Provide an example of two sentences , the first formally implying the second, the second analytically(but not formally) implying the first. Are two such sentences formally equivalent? Are they ...
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1answer
156 views

Can a valid argument with formally consistent premises have an analytically impossible conclusion? What about the converse?

Can a valid argument with formally consistent premises have an analytically impossible conclusion? What about the converse; analytically compossible premises, but a conclusion that is a formal ...
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3answers
81 views

How not to judge?

People constantly say not to judge people, but how is this possible? We all make mental remarks based on our past experience, for instance if I see a single mother smoking cigarettes, I will judge ...
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1answer
48 views

If A: P implies Q and B: Q implies P, then A is the *what* of B?

I have two propositions A: P implies Q B: Q implies P is A then the converse of B, or is there a term that is more exact?
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1answer
46 views

What is this special, general type of atomic sentence?

There is exactly one atomic sentence form of L (call it 'A'), which is always a tautology, and whose negation 'negate A', is always a formal contradiction. What is this special, general type of atomic ...
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1answer
58 views

Tractatus 3.333 and Russell's paradox

Can anyone explain to a non-logician how Tractatus 3.333 refutes (or fails to refute) Russell's Paradox? Please explain his use of symbols!
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1answer
55 views

Are the following relations reflexive/irreflexive/neither? Symmetric/asymmetric/neither? Transitive/intransitive/neither?

Are the following relations reflexive/irreflexive/neither? Symmetric/asymmetric/neither? Transitive/intransitive/neither? 1) x is a biological father of y 2) x is between point a and y. (Here, let ...
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1answer
83 views

Which of the following sentential operators are truth functional ? Why?

Which of the following sentential operators are truth functional ? Why? 1) '___ 'formally implies '__' in L. 2) '_____' analytically implies '__' in L. 3) Were it not true that '__', then '_' L. ...
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1answer
52 views

Judging the Logical Conclusion for this Epistemological Debate

I was involved in a debate with my friend a few days ago. He proposed that the most logical answer for questions that can't be judged with science, logic and reason should be polar, i.e., either ...
3
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1answer
37 views

Are there any large cardinals that are inconsistent with ZF?

Reinhard cardinals are the largest cardinals yet defined that are consistent with ZF. This suggests that there are large cardinals that are inconsistent with ZF - are there in fact any?
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1answer
54 views

References for intuitionistic meta-logic?

It seems to me that arguments about logical theories itself are often done using classical logic. For example, one says that a theorem is provable or not provable, which is not automatically valid ...
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65 views

Formalized monotheist religious system

I'm interesting in analysing religious arguments, the most popular ones, e.g, monotheistcs ones, in a logical formal way, but I didn't find such formalization anywhere. It appears that the concept ...
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1answer
33 views

Qs about interpretations on Parmenides's claim

Parmenides's classic claim is that what does not exist cannot be thought about. (It has been read as a claim that every truth-bearer must have a truth-maker, since otherwise the truth-bearer is not ...
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2answers
69 views

What is this type of logical fallacy called?

If the Principal of a school says that unruly boys will not be allowed to play games and if someone concludes that it is perfectly fine for unruly girls to play games, what is the fallacy called as?
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What's the word for anything is true if the antecedent is false?

(1) If A then B. (2) A is false. Then B can be anything (true or false) and (1) remains true. So B is true by __. What's the word or words in the blank?
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77 views

Is Graham's number bigger than the smallest inaccessible cardinal?

Someone says Graham's number is the biggest number with a name. Is Graham's number bigger than the smallest inaccessible cardinal?
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2answers
168 views

What exactly is it that Gödel is supposed to have done that an algorithm can't

I've heard a lot of people say that Gödel's proof shows that human intelligence somehow goes beyond what a computer could ever do. It's only ever been articulated to me very badly, though not for want ...
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2answers
413 views

What's the difference between a contradiction and a paradox?

Why can't we just claim a paradox invalid, just as the way we treat contradiction in mathematical proof? (i.e. if we arrive at the proposition inconsistent with the assumption, then we can immediately ...
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0answers
66 views

Logic as a (bad) model language

Can someone name the most well known philosophers to explicitly put forward an idea along the lines that formal systems can only be used descriptively, not prescriptively - that they're just a model, ...
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2answers
68 views

How important are equality, functions and constants for first order logic?

Many non-classical logics are first introduced without a corresponding first order version. I'm thinking about things like modal logic, intuitionistic logic or partition logic here. My experience and ...
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3answers
89 views

Is the UNIVERSE trying to discover itself? [closed]

We are all made of atoms. We are trying to discover the universe(which is made up of atoms) . So can I say the universe is trying to Discover itself?
2
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1answer
92 views

Were we born to believe?

This is a controversial question and not one that necessarily implies a Super Natural intervention, but I am curious about your opinion. Many of you I would hope is aware of the fact that living our ...
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3answers
73 views

Is something without a solution a problem?

Is an inconvenience without a solution still a problem? An example would be you are stuck in a war. You obviously cannot fix the war (safe to assume that), so would it be a problem to you, or simply ...
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4answers
99 views

Is it possible to logically derive moral statements from factual statements?

Yes, this is essentially the is-ought problem posed as a question. The reason I am asking however, is that I have so far found absolutely no satisfactory arguments for this being the case anywhere ...
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1answer
43 views

In modal logic what is the difference between: M,w |= p and M | q, w |= p

Where p designates some proposition, M designates a model and w designates a world. Sorry if this question is too basic, but I think it is so basic that none of the basic textbooks and articles which ...
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2answers
71 views

Is the real number line actually real when we construct it?

Intuitionism is akin to constructivism in mathematics but not quite the same from what I can tell. In the usual treatment of the real line, the additional numbers are found between the rationals by ...
2
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1answer
82 views

Truth is singular. Its “versions” are mistruths. [closed]

In the beginning of the legendary movie called Cloud Atlas... Somni 541 is sitting in a room, and an "Archivist" comes in. The conversation starts... Archivist: On behalf of my Ministry and the ...
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1answer
36 views

What distinguishes logical necessity, logical consequence, logical truth, and tautology from one another?

The text I'm reading distinguishes logical necessity, logical consequence, logical truth, and tautology from one another; however it doesn't make their distinctions especially perspicuous. As far as ...
2
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3answers
82 views

How does logic reference fictional characters?

The sentence, The Current King of France is ill, presupposes the existence of an extant French king. That sentence translates to, ∃!x(Kx ⋀ Ix), which is false. Similarly, the sentence, The ...
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2answers
39 views

Logical reasoning: What is the difference between NOT-elimination and False-introduction?

What is the difference between derivation rules: NOT-elimination and False-introduction? My book says they are similar, but they differ in use. I think my book lacks the description of the difference ...
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3answers
113 views

How can we represent 'nothing' or 'nothingness' in predicate logic?

The question says it all. I'm at lost for how to do this edit: what had motivated this was Heidegger's "What is Metaphysics." This was my first stab at philosophy of a continental persuasion and ...
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4answers
96 views

How to prove: (P v (P ^ Q)) iff P

How to prove (P v (P ^ Q)) ≡ P? I am not sure how to get rid of proposition Q. I am allowed to use Leibniz and apply Substitution. I already came across most calculation rules in the book: ...
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3answers
50 views

Describe the result of the xor of n logic variables with a sentence of everyday language

What I mean is, for example, we can understand A xor B as "true if A is different from B, false otherwise". Is it possible to understand the "collective xor" of multiple logic variables A1 xor A2 ...
4
votes
2answers
67 views

Desirable features in an introductory logic textbook?

I have been very unsatisfied with the quality of the free, open-source textbooks in logic I have found so far. Some, like P. D. Magnus's forall x and the wikibooks Formal Logic text seem overly ...
2
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1answer
80 views

What step in this argument is the least valid?

I know this is not a totally formal argument, and it is not mine, I just tried to distill it as much as I could to find where the weakest point is. Please help me if you want. It goes like this: H ...
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52 views

What is it that you don't know?

Imagine the following situation of a pretty wise master and his best student. Master..: I know everything. Student: So, what is it that you don't know? Master..: How to solve a paradoxon. How ...
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74 views

What were Peirce's trinary conception of logic?

Peirces conception of the trinary structure of thought is mentioned in passing in the SEP on Hegels Logic Hegel's later treatment of the syllogism found in Book 3, in which he follows Aristotle's ...
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1answer
68 views

BHK Semantics and Homtopy Type Theory

There are different ways of associating interpretations to intuitionistic propositional logic, one of which is to interpret it by Heyting algebras this is the analogue of the standard interpretation ...