Questions tagged [logic]

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

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fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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How can I prove P Λ (Q ∨ R) ∴ (P Λ Q) ∨ (P Λ R) using fitch? [closed]

I am trying to understand these but it is just hard for me. This is a formal proof without using Demorgan's law
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Is the certainty of death a result of false induction [closed]

Perhaps the simplest example of false induction is to assume that, if a statement or property is true for the first n numbers (or some amount of another entity), then it must hold true for all of them....
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If-then statements meaning in everyday vs mathematics

In mathematics when a "P implies Q" statement is true it means that every time P is true, Q is true also. What about everyday usage? For example consider the statement: "If it is raining, then I am ...
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Could we treat chess as an impossible game? [closed]

By assuming that any piece can move like any other, chess becomes an impossible game to play. Even if we emphatically denied this assumption, it could still come up and destroy our thought process. ...
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1answer
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A Classical Notion of Dividing Travel Up into Infinite Divisions

1) A man wants me to go from a to b in a straight line. 2) Suppose he can, first he needs to go to (a-b)/2. 3) Suppose he can, secondly he needs to go to (a-b)/4. 4) There are infinitely many integers....
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What is (∃!e) in Davidson 1967?

Davidson proposes a causal law for singular event causation. Here is one example of a backward-looking part of such a law (changed slightly for clarity and to avoid copyright infringement): (e)(u)((...
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Is a conjunction true when BOTH conjuncts are false? [closed]

I know a conjunction is true when both conjuncts are true, is it also the case when BOTH conjuncts are false?
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Alphabetic Substitution, Barcan, and Strict Implication

Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
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Question on the “Property of an Object” and the “Action of an Object” (+the “State of an Object”)

I have confronted a philosophical problem related to the definition of the "property of an object." What I believe is: The capability of an object (the capability to desire) is the property of an ...
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S5 proof of q or ◻ ⊢◻q [closed]

I am doing its derivation but unable to do it. I'm really at a loss as to how to actually approach this, so even just telling me how I get started would help a lot.
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Which problems do you consider as most important open problems in philosophy of mathematics?

At the "intersection" of mathematics and philosophy, or, rather, within their "union", surely some problems are still open and no general consensus is attained when those problems are discussed. ...
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Is this conditional donation morally permissible?

About a week ago, at the onset of the COVID-19 epidemic in Bulgaria, a Bulgarian entrepreneur (Ivaylo Penchev, founder of Walltopia), offered a conditional donation of medical ventilators to a state-...
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How/Why is the explanation/prediction of physical phenomena not deductive?

Why is the explanation of the triboelectric effect or the electrostatic effect(indicative examples) not deductive? How so we have a set of premises and from them follows the conclusion which is what ...
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2answers
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If this is a logical fallacy, does it have a specific name?

I had a debate with a friend regarding his uprooting of interesting plants in a woodland. He argued that it's a big forest and he only took a few plants, so doesn't cause much damage. He also ...
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Given that we do not have the ability to time travel backwards, can we prove that there will never be backwards time travel? [closed]

I have heard that if there will exist backwards time travel in some reasonable form in the future, presumably they would send the technology back so that we have it earlier. Since we don't have it, ...
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How do you form this into SL sentence?

Premise 1: All cats are animals. Premise 2: Lilac is a cat. Conclusion: Therefore, Lilac is a cat. I'm slowly learning SL but I'm having some difficulty. How do you know if it's logically valid? How ...
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5answers
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Can an omnipotent being create a world where 1+1=3?

This thought started off as 'If we are in a simulation, or if there exist a God/omnipotent being that can change the laws of physics (and everything) as we know it - is it possible for a change to ...
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Post hoc fallacy Vs. Slippery slope fallacy

What are the differences between Post hoc fallacy and Slippery slope fallacy? Why they are different?
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1answer
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Is there an or/and operator in formal logic and if so how is defined and symbolized?

I often use the and/or structure in sentences as it helps me to create many sentences more accurate than without it, which is generally important for me to do in any context. I know that in formal ...
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Is there anything beyond mathematical universe

If Mathematics is empirical , physical events which defies the rules of mathematics may also generate new mathematics?
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Can second order logic be expressed by first order set theory?

Quine called second order logic "set theory in sheep's clothing". However, some argue that the expressive power of second-order logic is greater than that of set theory. For example, the ...
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What does □□p mean?

The premises of the S5 system are: □p → □□ p ◊p → □ ◊ p (Note that □ is an actual square, not the missing-symbol placeholder). What does the first one mean? If □p is what is necessary in all ...
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This question is about materialism

Are there any Western philosophers whose thoughts are equivalent to early materialist schools of Indian philosophy carvakas or Lokatyas , Ajivikas ?
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Did Quine change of opinion towards quantified modal logic?

Willard Van Orman Quine was a strong opponent to quantified modal logic calling it unreasonable and useless. But, did he always think like that? Or did he relax his attitude towards it with time? Did ...
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1answer
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How would I create a proof In SL

H Therefore, S ⇒(B ⇒H) How would I create a proof in SL which shows the following argument is valid in SL.
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A non-circular definition of “not”

The notion of "not" is used throughout all languages as far as I know. For instance, consider the sentence, "Trees are not blue." There are various ways of expressing this notion without using the ...
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1answer
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Questions about Quantum Logic?

Carl von Weizsäcker, who worked on the topic of Quantum Logic several times, said that Quantum Logic was temporal in contrast with Classical Logic which would be atemporal (that would mean that truth ...
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What is wrong with these two conditionals?

Is it true that these two conditionals if A then B and if not-A then B cannot be both true? Example : "If I stay then I will eat fish" "If I didn't stay then I will eat fish" The reason I think ...
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1answer
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Is this Quine example of 'logically true' statements irrefutably true?

In 'The Two Dogmas of Empiricism' Quine launches quite a compelling attack on the foundations of Reductionist Empiricism, particularly in its claims concerning analyticity. While this calling into ...
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Is Classical Logic the proper model of the deductive logic of human reasoning?

Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it? The expression "Classical ...
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4answers
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Two positions at once is logically impossible

Assume that the position of an object is x1 and x2 at once, where x1 does not equal x2. Let's define the statements A and B as: A: The position of the object is x1. B: The position of the object ...
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Analogy of Set and Subset and Contracts in abstracto and Marriage in concreto/in particular

I had a talk with a professor of family law and we are frequently told that there are general ordinances for contracts in general and particular ordinances for marriage. I am problematised by the ...
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What is the difference between inductive and abductive reasoning? [duplicate]

I would deeply appreciate it if you would answer this question, since I do not know or understand exactly the difference between inductive reasoning and abductive reasoning, which is a problem for me ...
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1answer
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Does the doomsday argument assume that you will be born?

If with every birth there is some chance c that I specifically will be born, then the number of total people born (N) does not effect the odds that I will be in the first 100 billion people. My odds ...
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Why do I accept some inconsequential claims as “obviously true” without evidence? E.g. “Most people don't like to be hit on the head with a hammer.”

There are certain claims that I accept as obviously true without (much) evidence. For example: Most people don't like to be hit on the head with a hammer. Donald Trump ate dinner some time last week....
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Proof that if an inference holds in propositional logic, then the inference holds in supervaluationism

I am currently trying to work on problem 8, but I'm not sure exactly how to start it. I was thinking of starting it by trying to prove that phi is indeed PL valid. I would have to show how that is ...
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How to solve: Show that a formula is PL-valid if and only if it is LP-valid

I don't really understand this problem, but I'm going to spill out what I've taken notes on. I know that in order to solve this we would need to use the contrapositive in each direction. I'm going ...
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Homework Question on Quantified Logic Falsehood

For one of my homework challenge questions, I have a true or false type question. The question is as follows: True or False: I'm not particularly sure how to solve this. I have no information about ...
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How do I solve: Valuation of I(a v b)=1 iff VI(a)=1 or VI(b)=1 (full question in body)

Given the definition of the defined symbol 'v', show that for any PL-interpretation, I, and any wff a and b, V of I(a v b) =1 if and only if V of I(a) =1 or V of I(b)=1 So I have attempted this ...
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What is it called when the conclusion of one syllogism is inserted as the minor premise of a second?

As an example in Lewis's "Mere Christianity," he argues for objective morality with: Major: If you can judge one moral code (M1) to be better than another (M2) then objective morality exists. Minor: ...
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Classical propositional logic. Are all formulas sentences?

Let L the language of classical (two-valued) propositional logic consisting of a denumerable set of sentential variables as well as the usual operations of negation, disjunction, conjunction, ...
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Where is the fallacy in Seth Yalcin's counterexample to the modus tollens?

Where is the fallacy, do you think, in Seth Yalcin’s argument (2012) that the Modus Tollens is not a generally valid form of argument? Seth Yalcin’s counterexample to the Modus Tollens (MT) https://...
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Is this argument about the disjuncive syllogism valid and sound?

If some arguments of the form disjunctive syllogism have false premises, then some arguments with false premises are deductively valid. Some arguments of the form disjunctive syllogism have false ...
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How were formal systems and notion syntactic consequence (proof) developed?

I've looked at several resources to learn about logic and metalogic, and they first present syntactic consequence and semantic consequence as separate things and then try to show how each implies the ...
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Universal Analytic Framework [closed]

I've been working on a philosophical framework called Universal Analytic Framework. This is actually a personal philosophical project. I am in the process of designing a framework that has fluidity, ...
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1answer
92 views

Help with basic syllogism

'If A does not belong to some B, it is not necessary that B should not belong to some A' When I draw 'if A does not belong to some B' out, I get two partially overlapping circles, A and B, where some ...
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Three statements that contradict each other

In formal logic, it seems that a contradiction only arises between two statements. Is it possible to have a set of three statements that together are a contradiction, but where any two of the ...
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1answer
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Excluded middle versus bivalence [duplicate]

In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true. This principle should not be ...
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What ifluences whether a formula of a predicate logic is true/false in some particular interpretation of a language L?

It is not clear to me, what influences whether a formula in a predicate logic is true/false in some particular interpretation of the language L. In propositional logic we valuate every atomic formula ...

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