Questions tagged [logic]

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

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What is the exact form of law of non-contradiction that dialetheism rejects?

Dialetheism asserts that there are sentences that are both true and false, e.g. the Liar. This seems to, quite obviously, go against the law of non-contradiction (LNC), and indeed Priest seems to ...
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How to translate a set of sentences into logic symbols

For example If there is justice in this life, then there is no need for a future life. If, on the other hand, there is no justice in our earthly life, then we have no reason to believe that God is ...
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Are there modern approaches to logic that aren't *grounded* in math?

Are there any modern approaches to logic that are non-mathematical in nature or not grounded in math? The introduction to Thoughts, Words and Things, referenced in this answer, contains an ...
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Variant of free logic that accepts domain emptiness but rejects non-referring terms

To my naive perspective, domains that might be empty and terms that fail to denote (via constant symbols that don't refer or partial functions) feel radically different. The former seems ordinary and ...
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Hume's Law on the principle of explosion

The WikiPedia page of Hume's Law stated the following: An alternative definition of Hume's law is that "If P implies Q, and Q is moral, then P is moral". This interpretation-driven ...
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Is this a fallacy?

Julie wrote in her diary. At the end of his life, James asked God to forgive him for his sins. There is further historical evidence to show that James performed various public welfare activities ...
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Trying to understand the fallacy in my inductive reasoning regarding this conclusion? [closed]

Consider the following statements: Anna told you she failed her physics midterm. Anna hasn't been in physics class since the teacher graded the exams. Anna has been in sociology class, which meets ...
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Do you know any Fitch proof for ~p=>(p=>q)? [closed]

Please, somebody know A FITCH proof for this tautologu?
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How can I prove A(x) from ¬∀x(Q(x) → x 6= a)? [closed]

I am trying to study for my exam Monday, and I was doing some exercises but I got to this one and I can't figure out how to get to A(X) from the premise ¬∀x(Q(x) → x 6= a) using Fitch proof system, ...
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Why is the class of basic statements permitted by “p” a subclass of the class of basic statement permitted by “q”?

Excerpt from section 37 "Logical Ranges. Notes on the Theory of Measurement" of "The Logic of Scientific Discovery": If a statement "p" is more easy to falsify than a ...
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Understanding [(a→b).(c→d)] formula in section 36 of The Logic of Scientific Discovery

Excerpt from footnote 1 in section 36 of Popper's "The Logic of Scientific Discovery": In the present section, the arrow is used to express a conditional rather than the entailment relation....
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Did Zeno of Sidon really write that any geometrical system must have some unstated assumptions?

According to this site Zeno of Sidon argued that even if we admit the fundamental principles of geometry, the deductions from them cannot be proved without the admission of something else as well ...
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What is 'expendable' in logic and how to explain 'tautology' given this image?

This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
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Structure of a deductive argument

I wonder if this is true for all deductive arguments, a deductive argument must have at least one premise where the term "ALL" or "NONE" or an equivalent word appears Is it true? ...
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Principle of Parsimony and Epistemological Economy [closed]

Why aren't definitions in other sciences (especially humanities) parsimonious in that they word themselves so as to provide the least necessary&sufficient logical conditions? The Principle of ...
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Looking for the correct english term for [closed]

I just remembered a conversation I had (in german) about 18 years ago and the other person used the (german) term "All Theorie", which in this context was not related to the theory of ...
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Is perspective a human limitation or a property of reality? [closed]

This might be an unremarkable observation but the further away someone is to an object the smaller it becomes and vice-versa. From an evolutionary standpoint it doesn't seem to be any type of benefit ...
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Is it consistent to say “X is possible but false”?

Is it consistent to say something like "Possibly there is a cat in my room, but in fact there is not"? Basically, is it consistent to assert that something is possible but in fact not the ...
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55 views

Non-equivalence of `i`-form and a claim of existence

What's the difference in meaning between an i-sentence and its corresponding existential claim? In traditional logic, the following inference is valid All As are Bs. AaB ----------------- --...
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1answer
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Optimal truth assignments for minimizing variation from credences

Suppose I have a set of propositions and "exogenous" credence levels for each proposition i.e. how likely I think it is to be true. Then suppose Ι know that certain logical relations hold ...
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Term Logic Paraconsistency — Is it just a meta-level manifestation of existential import?

This lecture by Graham Priest contains an interesting claim, namely that term logic is paraconsistent. I have two questions about this: Is paraconsistency in this context ever considered a meta-level ...
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Is it possible and meaningful to substitute the Laws of Identity into the variables of the Laws recursively? [closed]

Normally when working with logical formulae, we can substitute other formulae into the variables. For instance: Let p≡avb, q≡m∧n, then (p⊻q)↔(avb)⊻(m∧n). This ability to perform substitution is a ...
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132 views

Is the material implication the correct model of conditional reasoning in mathematics?

Question: Do you believe that the material implication correctly models the kind of conditional reasoning necessary in mathematics to prove a theorem? Example: If x > y and y > 0, then x > ...
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Do contemporary logicians generally claim that classical logic can be simply reduced to these 5 logic principles?

Do contemporary logicians generally claim, as Wikipedia does, that classical logic can be simply reduced to the 5 logical principles below? Or is it more complex than that and are there principles not ...
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Why is the definition of the real numbers not contradictory? [closed]

I understand that a set whose members can, in principle, be enumerated (by having a formula) can be considered as a well-defined set. Therefore, set of all even numbers, multiples of 3, and so on ...
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What are some logic rules that are true for every kind of logic?

What are some logic rules that are true for every kind of logic? Some rules from conventional logic are ignored like in paraconsistent logic, but I am wondering if there are logic rules that are true ...
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92 views

What does it mean for two distinct people to know a fact?

Let there be two people A and B. They both encounter a strange object O. What do they know about each others knowledge about O? More strictly, we are speaking of a situation where, say, you and me ...
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212 views

What is the relation between a priori and tautologies?

I have just started learning Epistemology. I am not sure about the relation between a priori and tautologies. My textbook has given definitions for a priori and tautology. A priori: knowledge which is ...
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56 views

What type of logical fallacy happens here?

This has been going on a lot lately in my country. Usually, in a discussion where some antisocial behavior of an organization is being criticized, a supporter of the organization, usually a member of ...
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“Inference to the Best Explanation if the Best is Sufficiently Good”

The reliability of Inference to the Best Explanation (IBE) is sometimes contested because it may end up recommending the best of a bad lot, which might require a modification of IBE (e.g. contra ...
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Does software exist to automatically validate an argument?

I'd like to Derive logical arguments from English, and test their validity using a program. Does software exist for step 2? It would be fine if it were to give up because The validity isn't ...
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332 views

Why are some things considered “impossible” even in other universes?

For example, I often hear that life could not develop in a universe where the fundamental constants were even slightly changed, or where certain physical laws were different. But if we're dealing with ...
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Contradiction and existence

I would have liked to know if this argument was logical and if it had already been made: Everything exists. The principle of non-contradiction applied to existence is a postulate that does not hold. ...
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List of books which teaches historical Aristotelian logic

Background: I want to study philosophy and I think a good way is to first learn logic, so I tried reading The Categories. But even after trying so hard, I didn't understand it. The writing is very ...
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Is 1=2 a logical contradiction, or merely a false statement?

I know that (1=2 AND NOT 1=2) is a logical contradiction, but what about 1=2 by itself? Is it a logical contradiction, or merely a false statement? And what about something like NOT 1=1?
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Is there more than one form of logic in mathematics?

Is there more than one form of logic in mathematics? I would be inclined that mathematics only cover one type of formal logic, but I would be interested to know if there are variants thereof or ...
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1answer
61 views

How do you work with a non-classical metatheory?

What are non-classical metatheories like? How do you use a metatheory that isn't classical? It is straightforward to use a classical system to analyze simple non-classical ones. However, this is the ...
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True Thinkables - with regards to the Identity Theory of Truth

What exactly is a 'true thinkable'? According to John McDowell, 'true thinkables' are identical with facts(1996:27-8,179-80). This seems, if i may, a bit truistic and am left with no concrete ...
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68 views

Does Grice's quotation have a coherent meaning, and if so, what is it?

What is the meaning of this, and is this an example of bad writing? "For it will be possible to construct in terms of the formal devices a system of very general formulas, a considerable number ...
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Guessing the past - Bayes - Throwing Dart

I'm trying to understand how Bayes formula helps us make guesses about the past. What are your thoughts about the following philosophical metaphor regarding claims about events in the past? Whenever ...
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2answers
88 views

How do I prove ∀x(A(x) -> B(x)) from ~∃x(A(x) ^ ~B(x)) using a fitch proof? [closed]

What would the formal fitch proof for this be? This question came up in my practice problems and I'm really stuck on how to proceed. I'm assuming that you start with an assumption, but I can't figure ...
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What type of logical fallacy leads to a false conclusion of expertise?

If someone says they have never taken an action, and never had any issues, therefore that action is problematic, and they are now an expert what logical fallacy(s) is that? For example: "Driving ...
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273 views

What is the philosophical term for using half-truths to intentionally mislead?

Our local school district has been distributing propaganda to support keeping schools open during an uncontrolled pandemic. There has been a common pattern among these statements, where a half-truth ...
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What did Husserl mean by logically composite?

In the philosophy of arithmetic on page 119, Husserl says that only things that are logically composite can be given formal logical definition. He does not define and term beyond that and only gives ...
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Is there any exception to the rule of non-contradiction?

Is there any exception to the rule of non-contradiction? In physics, mathematics or philosophy? Is there any system where the law of non-contradiction doesn't apply for a good reason? I can't think of ...
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1answer
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Valid or invalid? ( from a CSU Exam, instructor Tim Black)

Source : http://www.csun.edu/~tab2595/PRAC_EXAM_1.pdf Is the following argument valid or invalid? (1) No email messages are written carefully, (2) but every love letter is very carefully written. ( ...
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Is it possible to draw the line with “hasty generalization”?

At what point does a generalization become fallacious and hasty? If I say people who smoke get cancer and the data shows that 90% of smokers get cancer, is that still a hasty generalization? Or 60%? ...
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How are objective probabilites and statistics (frequency in the world) of groups related to individual cases?

I'm a bit confused about why frequentist measures of probability based on groups are relevant to individual cases. It seems that moving from the group to the individual is somehow a violation of the ...
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What is the philosophical term used to describe flawed logic?

A freak snowstorm strikes Washington, D.C. Climate change deniers hail it as evidence of global COOLING, not warming. It seems logical since snow is popularly associated with cold. However, it seldom ...
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an argument that is clearly valid but invalid in a sentence logic

I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...

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