Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [logic]

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

1
vote
1answer
61 views

De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
1
vote
1answer
63 views

De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
2
votes
2answers
150 views

What is the fallacy when someone refuses to be specific

A Muslim apologist was debating two Atheists on DW channel in Arabic, the host asked him whether he agrees with "executing atheist apostates". The Muslim apologist knows that apostates are to be ...
2
votes
1answer
104 views

Why is first-order logic defined as a collection of formal systems?

I think I understand what a formal system is and what formal languages are. But I have trouble grasping why first-order logic is referred to as a collection of formal systems whereas propositional ...
3
votes
3answers
521 views

Equivalent forms of “if p then q”

I'm wondering if "If p then q" is equivalent to "p unless q" or "p or not q" in regards to philosophy?
2
votes
3answers
186 views

Is this argument about abortion being both right and wrong valid or invalid?

Abortion is either right or wrong. If it is right, then people should be allowed to kill fetuses. Killing fetuses is wrong. Hence, abortion is not right. If it is wrong, then women won’t have the ...
2
votes
1answer
37 views

Prove the rule that proves X(P) from X(a) preserves derivability in modal system K

I'm trying to solve a problem which asks me to show that the meta-rule defined by deriving X(P) from X(a) preserves derivability (i.e. if ⊢X(a) then ⊢X(P) in modal system K, where a is a sentence ...
2
votes
2answers
63 views

“Syllogisms which produce understanding”

I remember reading somewhere that the aim of Aristotle's Prior and Posterior analytics was to show which kinds of syllogisms produce understanding. I do not remember where I read this but I think it ...
2
votes
2answers
161 views

Suppose you have an argument with false premises and a false conclusion. Given this information, what do you know about the validity of this argument?

The argument is almost valid. The argument is neither valid nor invalid. The argument must be valid. The argument must be invalid. The argument may be either valid or invalid.
2
votes
0answers
30 views

Grice: Comparing Natural Meaning, Non-Natural Meaning, Conventional Implicature and Generalized Conversational Implicature

I am currently reading "Meaning" and "Logic and Conversation" by Paul Grice. I find it a little difficult to differentiate clearly between his concepts "natural meaning", "non-natural meaning", "...
3
votes
1answer
88 views

S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P)

I'm trying to construct an S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P). I know that ϕ∨ψ is equivalent to ~ϕ→ψ, and so what I'm really trying to derive is ~◻(◻P→◻Q)→◻(◻Q→◻P) (which is equivalent to ◊~(◻P→◻Q)→◻(◻Q→◻...
1
vote
1answer
50 views

Axiomatic proof of ⊢ □P → □◇□P in S4

As the title explains, I'm trying to give an axiomatic proof of ⊢ □P → □◇□P in S4. This is simple to prove in B, but I'm struggling to see how it's done in S4. I'd really appreciate any help you ...
3
votes
0answers
71 views

Formal logic to describe causation?

I'm looking for any formal work that has been done on describing causation the way people understand it. I am not looking for logical implication, more a way to talk about "Why?" questions. Basically, ...
14
votes
10answers
8k views

What fallacy is assuming something is the case because of past events

I'm sure this is a simple question. What I am referring to is disbelieving someone on Day 20 because they have lied every day previous to Day 20. Another example is the boy who cried wolf. The 50th ...
1
vote
1answer
84 views

Modus Tollens / Popperian Syllogism for the Black Swan

If it is a swan, then it will always be white. It seems like Popper is not asking so much people to build syllogisms, but rather DEPENDING on Modus Tollens as an engine for falsification. So that, ...
1
vote
1answer
60 views

Inductive Logic on Existence

Because we, only by inductive reasoning, are sure about next moment 'happening' (or more precisely, not worried about it not happening), does this mean that there is no logical guarantee that next ...
1
vote
2answers
43 views

A necessary condition for being P applies to all things that are P. does a sufficient condition for being P apply to only things that are P?

My textbook says that a definition of P has to apply to 'all and only things that are P.' How does this map onto necessary and sufficient conditions? If being F is a necessary condition for being G, ...
2
votes
1answer
54 views

What does “E!” mean in free logic?

Reading John Nolt's "Free Logic" article I see the symbol "E!" in the "2.1 Axiom Systems". The following axioms are special for free logics. (A4) ∀xA→(E!t→A(t/x)) (A5) ∀xE!x (A4) modifies ...
0
votes
2answers
73 views

Can the existence of something be proven by logic alone [duplicate]

I want to know if proving the existence of something by using only logic is possible.
3
votes
1answer
59 views

What is reflexivity in temporal logic?

According to Stanford Encyclopedia of Philosophy, reflexivity can be defined by : ∀x(x ≺ x) Where ≺ means "Precedes" : For all x, x precedes x But what does it mean for an instant in time x ...
0
votes
2answers
35 views

Why is this sentence containing “except” translated into this conjunction?

All except students are invited This proposition was translated into No student is invited, and all non-students are invited Why was it translated into this conjunction of form A∧B and not ...
4
votes
2answers
74 views

What kind of circularity, if any, is it acceptable for a philosophical argument to contain?

I'm studying circularity in arguments and was wondering if there is any acceptable circularity possible in a good philosophical argument. For instance, I gather that some regard rule-circularity as ...
2
votes
1answer
76 views

Equivalence of strings of modal operators in modal logic

I'm trying to solve a question which asks me to show that for any two finite strings O₁ and O₂ of □s and ◊s, (e.g. □□◊□◊□), that i) if O₁≡O₂ then OO₁≡OO₂ and ii) if O₁≡O₂ then O₁O≡O₂O where O is ...
2
votes
3answers
78 views

What does it mean to be a 'consequence'?

A Logical Consequence, in terms for formal language, is derivable from a given set of statements by manipulating symbols according to fixed rules. That I understand, for that is the only way to move ...
4
votes
2answers
101 views

Why do I doubt my logical reasoning?

I have been wondering for several years why I just can't trust my own proofs in math or when giving some logical arguments. I keep thinking I might be making a mistake at some step of the proof and ...
1
vote
2answers
69 views

Logical expression that non-existent things don't do anything?

How could we express the idea that "something that doesn't exist cannot possibly do anything" using a logical argument? And if so, it is at all possible to prove that kind of proposition?
0
votes
0answers
145 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
4
votes
2answers
123 views

How much the world is logical [closed]

In her book The Art of Logic in an Illogical World, Eugenia Cheng writes:"I have already asserted the fact that nothing in the world actually behaves according to logic. So how can we use logic in the ...
2
votes
2answers
115 views

Justification of existing methods of formal logic [duplicate]

What is it that mathematicians, and more likely perhaps philosophers, give as an explicit justification that any method of formal logic, which is actually used by mathematicians, or even by automatic ...
2
votes
1answer
181 views

Classical logic, symbolic logic, higher-order logic, First-order logic? Learning from scratch

I'd like to ask you a question about logic. I study philosophy in a Spanish Christian university. In the first year, we study logic but it's the classical one, following Aristotle's Organon, the ...
2
votes
4answers
73 views

How would i go about using natural deduction to prove this argument is valid?

How would I use natural deduction to prove this argument is correct? It's always either night or day. There'd only be a full moon if it were night-time. So, since it's daytime, there's no full moon ...
1
vote
2answers
52 views

What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
4
votes
0answers
143 views

Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
0
votes
2answers
115 views

Validity of a modal argument?

Would you say that the following argument is valid? And if not, why exactly? For all we know, A may be the state of B; What C does is determined by the state of B; Therefore, for all ...
1
vote
1answer
87 views

What does Tarski mean when he says that truth is a property of sentences?

A fundamental statement of Tarski's Theory of Truth is that truth is a property of sentences. What does this statement mean? What kind of Truth is it referring to? What is the formal definition of '...
2
votes
1answer
170 views

Finding desirabilities and probabilities in Jeffrey's Logic of Decision

I'm trying to solve problem 16 (Ch. 5) of Jeffrey's Logic of Decision. The problem says: Suppose that A and B are pairwise incompatible propositions, and suppose that the preference ranking is as ...
1
vote
1answer
85 views

What fallacy is this?

I am curious about what fallacy the following kind of reasoning represents. Let's say we are questioning if something is true. I would argue that in order for us to question if something is true we ...
8
votes
1answer
144 views

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?" ...
2
votes
1answer
40 views

Descartes on Llull's logic

I recall from readng long ago that Descartes described Llull's logic as something that would allow one to speak on many subjects without knowing any of them That quote from Bonner, Art and logic ...
2
votes
2answers
79 views

How to get the refutation of (OP ⊃ OQ) ∴ O(P ⊃ Q) in Deontic Logic

In Deontic Logic, one could easily infer "If it is obligatory that P, then it is Obligatory that Q", from "It is obligatory that if P then Q" O(P ⊃ Q) ∴ (OP ⊃ OQ) Where the ⊃ is an implication (...
1
vote
3answers
92 views

Is this an example of Denying the Antecedent?

Is this an example of Denying the Antecedent? Harry is not an inexperienced driver, and thus must not be irrational, seeing as all inexperienced drivers are irrational. At first, I thought it was ...
0
votes
2answers
64 views

Is this an example of Undistributed Middle?

Is this an example of Undistributed Middle? John is not a teenager, since all teenagers are impulsive, and John is not impulsive.
0
votes
2answers
84 views

Is deduction based on induction?

I'm wondering if deduction is in the end based on induction. The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported ...
3
votes
1answer
188 views

Is the problem of logical omniscience intractable?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
2
votes
3answers
273 views

Interpretation and symbolic notations of operations in mathematics

As we know a mathematical operation is a function. And a function is a special type of relation. Ultimately a relation is a set of ordered pairs. For example, what is addition of natural numbers? At ...
1
vote
2answers
72 views

What's the fallacy of relevance here?

To know absolutely that there is no God one must have infinite knowledge. But to have infinite knowledge one would have to be God. it is impossible to be God and an atheist at the same time. Atheists ...
-2
votes
2answers
89 views

How to prove : P v ( P → Q ) by Natural Deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 9) : P v ( P → Q ) I have to use natural deduction and the only rules I know are: • assumptions, • modus ...
1
vote
1answer
43 views

What's the difference between XY=F and XY=0 in Jeffrey's Logic of Decision?

I'm stuck solving problem 14 in Chapter 5 of Jeffrey's Logic of Decision. The first part of the problem says: Show that in presence of prob is nonnegative (prob X≥0) and prob is normalized (T=1)...
3
votes
0answers
95 views

What are the consequences of rejecting identity of indiscernibles

What kind of system are we in if we explicitly take its negation as an axiom? Here's the identity of indiscernibles. (1) ( ∀P.P(x)↔P(y) ) → x = y Here it is written in prenex normal form (2) ∀x∀y.∃...
2
votes
3answers
145 views

What is the premise and conclusion here?

"Half of the American population believes that the universe is 6000 years old. They are wrong about this. Declaring them so is not 'irreligious intolerance'. It is intellectual honesty." -Excerpt ...