Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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2answers
119 views

Derivation using inference rules

Suppose I have the premise: ~(AvB).(Negation A or B) How can I get to the conclusion: A<=>B (A if and only if B) using inference rules like introduction or elimination and also ...
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0answers
57 views

Language confusion; necessary/nomological/true in all worlds

I got confused by the way different people use language in the context of physicalism. In particular, Kripke seems to equate "necessary truths" with something that is true in all possible worlds. Is ...
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68 views

How and why Aristotelian essentialism is a problem for Quine?

I cannot understand how and why the Aristotelian essentialism is problematic for Quine. I have tried to read articles on the theme but probably I am not smart enough to understand them. Could you ...
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21answers
13k views

Is the “omniscient-omnipotent-omnipresent” definition of God consistent?

God is commonly defined as an omniscient (infinite knowledge), omnipotent (unlimited power), omnipresent (present everywhere) entity. Is there any logical inconsistency in this definition? I have ...
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0answers
40 views

Can a Rigid Designator still exist if there is only one possible world?

According to Kripke, a rigid designator is a pronoun (but not all pronouns are rigid designators) and they pick out the same unique individual in each possible world. I understand this, however, if ...
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1answer
133 views

Which problem is Russell focusing on while providing a solution, in his introduction to the Tractatus?

In the final part of his introduction to the Tractatus Logico-philosophicus, Russell provides a possible solution to the problem of the impossibility of self-reference of logic: There is one ...
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2answers
69 views

Existential quantifier proof help

I know I have to use the existential elimination rule twice but I'm still having troubles. ∃x∀y((Kyf ↔ x = y) ∧ Bx), ∃x(Kxf ∧ ¬Bx) ⊢ Fa ∧ ¬Fa
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1answer
273 views

What does this table regarding the 'connectives' '&' and '~' mean?

I'm a modern philosophy student and I'm reading content on the truth-value of sentences in logical structure, but I had trouble underatanding how connectives contribute to the truth-values of say ...
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0answers
111 views

Did Wheeler's “It from Bit” allow inconsistencies to exist?

Physicist John Wheeler proposed a model of the universe based on "It from Bit" asserting that the world is fundamentally information. I've been told both that Wheeler's It from Bit is compatible with ...
4
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4answers
670 views

How to find redundant premises?

Suppose I have this simple argument: ( P ⊃ Q ) R P Therefore, Q Here's the truth table I made in an excel worksheet: As you can see this comes out valid but in reality it isn't valid ...
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1answer
86 views

Logic. Having problems with interpretations

My question asks me to specify a true and a false interpretation over the domain {1,2,3} of (∃x¬Fx → ¬∃xFx) So I have said that the extensions of a,b,c are 1,2,3 Do I just need to find extensions ...
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56 views

Can a solipsist doubt?

I've been thinking about epistemological solipsism, which seemingly necessarily follows from metaphysical solipsism. Namely, that the "world" of the solipsist is one and the same with the self of the ...
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3answers
297 views

Analogy between an unknown in an argument, and a contradiction in the principle of explosion

Context I like to argue that, since we do not know what consciousness is, we can not specify what it can not do. Therefore we can not state we can't do something now, nor in the future. Up to the ...
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1answer
74 views

Why can some arguments be proven only through Conditional or Indirect Proof?

For brevity, abbreviate as CP 'Conditional Proof', as DM 'Direct Method, and as IP 'Indirect Proof'. Source: p 445, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Indirect proof ...
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0answers
115 views

Modal logics - philosophical paradoxes using modeling by possible worlds

I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) ...
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1answer
67 views

Does the Münchhausen trilemma negate its validity?

https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the ...
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1answer
66 views

Fitch Questions Please Help Me

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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3answers
124 views

Why are non-logical predicates of 0-arity treated as logical variables?

In the "Non-logical symbols" section of Wikipedia, it states: A predicate symbol (or relation symbol) with some valence (or arity, number of arguments) greater than or equal to 0. These are ...
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2answers
56 views

Another logic proof problem I'm stuck on :(

sigh stuck on another problem Premises P Conclusion (( ~(Q → R) → ~P) → (~R → ~Q)) I am allowed to use Modus Ponens, Modus Tollens, Hypothetical Syllogism, Simplification, Conjunctions, Addition, ...
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2answers
58 views

Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : [![enter image description here][1]][1] How do I reach this goal? Which rules do I use and with which ...
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0answers
31 views

Is marxist dialetic according to Aristotle classical logic?

Is a static binary logic compatible with one based on dynamic evolution by overcoming?
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2answers
49 views

Interpreting conditional statements

If we have the conditional statement: a -> b -> c Do we interpret it as "if a, then b, if b, then c" or "if a, then if b then c"? In other words, which of the arguments would be valid: 1) a -...
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3answers
185 views

Why do we need model theory to express semantics?

https://en.wikipedia.org/wiki/Model_theory Why can't semantics be directly expressed in the formal language? This is the key part of model theory that I don't understand: https://www.lesswrong.com/...
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6answers
859 views

Are there degrees of truth ?

I do not assume bivalence - that every proposition or declarative statement - is either true or false but not both. I do not raise the issue of 3-valued logics or offer or invite any theory of truth. ...
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3answers
260 views

Can Camus' 'The Absurd' Be Arrived At Through Reason?

I am currently reading The Myth of Sisyphus by Albert Camus. In it, he gives a fair outline of his philosophy. Camus says that absurdity isn't just the scrutiny of a single fact; it's the paradoxes ...
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2answers
64 views

Fitch Question Help

I'm having trouble understanding quantifiers in proofs. The proof I'm working with is : ¬∀x Tet(x) -- Premise ¬∀x (Tet(x) ∧ Medium(x)) -- Goal How do I reach this goal and also get to the goal ...
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1answer
93 views

Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...
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2answers
141 views

Can classical logic have deduction with infinite steps

I've been reading the Stanford Encyclopedia of Philosophy article on classical logic, and I've been confused about Theorem 9, and the preceding statement. They mention how (*), the clause which ...
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2answers
64 views

Are there truth tables for strict implication?

Lewis defined the concept of strict implication to resolve some problems of material implication. Basically, strict implication is defined as [](p --> q), where [] denotes the predicate 'is necessary" ...
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1answer
80 views

The essence of real Europeans [closed]

I'm a European living in America. A fellow countryman is trying to coerce me into doing something for him. He claims that if I was a "True European", I would do what he wants. I've not done a lot of ...
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5answers
7k views

Why is argument by analogy invalid?

There is a well known fallacy called the "argument by analogy" fallacy. As I understand it, the fallacy occurs in a situation where someone makes a reasonable comparison between two situations and ...
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0answers
49 views

De Re, Counterfactuals, and rigidity

This is going to come off as vague or obscure; but, I hope the idea is performatively expressed: Two questions: Do you think that Kripke would argue that the impossibility of de re counterfactuals ...
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2answers
72 views

Hard Predicate Proof Help

I have been working on this proof for over a week now, and I can't seem to figure it out: Pd ⟷ (Hj & Mj), Gsd, ∀x∀y∃z(((Gxy & (Py ➝ Pz)) & Rxyz) ➝ Gxz), Pe ⟷ ∀x(Hx ➝ Mx), Rsde |- Gse I ...
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2answers
142 views

What is a natural deduction proof from ~(A↔B) to ~(A→B)?

It feels intuitively correct, but I cannot work out how to prove it. I would appreciate any help.
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2answers
66 views

Logic of associated rights

I am trying to understand the logic of associated rights (i.e. if I have right A, then I must also have right B). Imagine I have the right to own the white house (which is a property), then it ...
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4answers
821 views

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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3answers
2k views

Why does Carnap say 'Caesar is a prime number' is meaningless?

I don't get it. Assuming there exists an individual Caesar, we can look at the set of prime numbers and not-(prime numbers), and Caesar will be in one of them. I just don't see, even though it may be ...
3
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4answers
131 views

How to give proof for Q ∧ R with the premisse ¬(¬¬¬P ∨ P)?

I'm trying to use Fitch to get to an answer, but I'm really confused right now. Can someone help?
2
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0answers
47 views

Circularity between truth and meaning?

These two common claims are equally appealing: (1) the meaning of a ( declarative) sentence consists in its truth conditions (2) the truth of a sentence depends on its meaning But are we moving ...
5
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1answer
258 views

Isomorphism vs homomorphism in the Tractatus' picture theory of language

People often mention that there is an isomorphic nature between language and the world in the Tractatus' conception of language. As far as I can see it, according to Wittgenstein (it's been a few ...
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1answer
128 views

Cause and Effect - Finished infinity [closed]

I have a question it's best if I give you an example right away. Our universe has its limits. in terms of the effect or cause e.g. if we kill a human for some reason will also have the effect. I'm ...
3
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2answers
159 views

Are the fundamental laws of logic always true in every field known to man?

the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity. These are the three fundamental laws of logic and while ...
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2answers
550 views

What are the conditions for RAA?

My textbook states that: In this case, however, what about situations where we can get Q ^ ~Q (sorry, unfamiliar with this formatting) without depending on P? For instance, the proof of EFQ: 1 (1) ...
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3answers
165 views

Aristotle's Logic and Human Thought

Is Aristotle's logic sufficient to model human reasoning? If not, why not? Are there counter-examples, certain cases where we reason differently? Let's assume we're talking about sound reasoning,...
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1answer
52 views

Negation of equality in FOL

I am unsure if there is a rule in FOL that allows me to make this derivation ¬(a = b) Assumption a ≠ b ??? Is this derivation allowed, and if so what notation should I use to justify it?
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2answers
52 views

Solving a proof in which the goal is the negation of a variable in Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. A ^ B (A ^ ~C) --> ~D A -> ~C (B ^ E) --> (C v D) ~E I ...
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1answer
91 views

Has there been any philosophical guidance regarding when to use logic vs empirical testing?

One obvious disadvantage of testing a given claim with scientific constraints is that one may never know the number of possible constraints to try, in which combinations, and in which order to modify ...
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1answer
70 views

Can a different universe be built with three dimensions? [closed]

Can you theoretically create a universe that will have the same dimensions but will look different? For example, a paper that has a limit, or another similar dimension can it be different?
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4answers
105 views

Finite Alphabets

This is a question based on section 2.5.6 from the book Logic, laws of truth, by Nicholas J.J Smith, page 48. What does Nicholas mean when he says: Note that we can further specify exactly what we ...
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2answers
2k views

Fitch Proof - LPL Exercise 8.17

I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise. I am finding it ...