Questions tagged [logic]
Use this tag for general questions about logic that are not categorizable under some more specific tag, like "mathematical logic", "informal logic", "classical logic", etc.
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Law of excluded middle in intuitionistic formalism
Does intuitionistic formalism accept the law of exluded middle?
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Skeptical hypothesis as undecidable statement
Does anybody support the idea that the skeptical hypothesis (like the possibility that we are brains in a vat) is not assessable? By that I mean that the skeptical hypothesis may resemblance the sort ...
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Could you help me with this logic problem? [closed]
I need help proving validity of this:
((A ∧ B)∨(¬A ∧¬B))<==>(A<==>B)
This is how we did it in class, but I don't actually understand this very well. Could someone explain to me how to do ...
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Is there an intrinsic hidden modal logic within ordinary Boolean algebras?
Is there an intrinsic, hidden modal logic within ordinary (abstract) Boolean algebras?
I do not question whether interior or closure algebras are Boolean algebras. Nor do I seek for an explanation of ...
user13738
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Proof of a Conditional and Discharged Assumptions
Currently, I am self-teaching myself formal logic from E.J. Lemmon's Beginning Logic. So far, the book is discussing the rules of derivation for propositional logic, and I've struggled to fully ...
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Every argument is an instance of an invalid argument form
This was a question posed to us in a lecture.
I have been thinking about it for ages.
Can I say that since all argument are instances of this invalid form p => q, the statement is true?
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Double arrow elimination
I know that P <=> Q becomes (p => q) ^ (q => p)using double arrow elimination but how about the following ?
~(P <=> Q) becoming ~(p => q) ^ ~(q => p) ?
Also
(~P <=> Q) ...
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Does a beginning imply an ending? (In regards to the universe)
In regards to the universe if it said to have a start (Beginning) does that imply that it will have an end? Are beginning and ends implied when either ones is said to be true of a proposition or can ...
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What is the proper name for the group comprising "must" and "must not" (see disambiguation below)
In logic (or philosophy) jargon, what do you call the generalization of the two mutually exclusive condition states must and must not? I assume mustness isn't the correct term but it conveys what I'm ...
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Logical Form of an Appeal to Probability
How can you express an "Appeal to Probability" argument in a logical notation? Feel free to use any forms or renditions of logic, including APL, as I know there are different symbols that can be used. ...
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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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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 ...
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What does Samir Okasha mean in this quote about converting invalid to valid argument?
I'm reading Samir Okasha's article "Does Hume’s argument against induction rest on a quantifier-shift fallacy?" and in page 240 there is this:
Consider a typical
inductive inference of the sort ...
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The logical and psychological differences between the conjunctions "and" and "but"
The following question comes from Logic for Mathematicians by J. B. Rosser on page 17.
Exercise II.1.1 Write two short essays (not more than five sentences apiece) concerning the use of “and” and “...
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Disentangling Conditional Statements from their Corresponding Inference Schemes
Suppose we're looking at two objects:
(i) the conditional statement (A --> B)
(ii) the inference A |- B
In propositional logic, we have that (i) is true if and only if (ii) is valid. My ...
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How does one explain (apparent) nonexistence?
There is quite a bit of fun in building a little web of questions and answers throughout StackExchange. (Let's call it an exercise in interdisciplinarity.)
"Molecular biologist Robin Holliday has ...
user3164
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Distinction Between Deontic Logic and Formal Ethics [closed]
What, if any, is the distinction between "formal ethics" and "deontic logic"?
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What is a good table format for diagramming logical conclusions?
I am looking for a visual organization format that can help group logical conclusions. Basically, If people are given 3 options, and I am looking to interpret their vote, what is a clean manner of ...
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How do I solve logic derivations with disjunctions?
My premise is ((P v R) → S) and the desired conclusion is R-->S. I cannot understand how to get disjunctions out in problems like this.
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Is there any self-contradiction in this statement that "everything is beautiful"?
'Everything is beautiful.'
If you deny the proposition of 1), it is 'something is not beautiful'.
The proposition 'something is not beautiful', which comes from 2), is included in 'everything'.
In ...
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How can you know if premises are true?
In logic, you start with premises to obtain conclusions. But how do you know that the premises themselves are true?
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Facts and the denial of "Iff it is true that A, then it is true that it is true that A"
The SEP article on axiomatic theories of truth goes over a theory in which "the truth iteration axiom ∀A(T[TA] ↔ TA) is inconsistent." Apparently (and this sentence is an edit), it's ...
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Do philosophers do research in mathematical logic at the same level as mathematicians? [closed]
I am neither a philosopher nor a mathematician but I am assuming that philosophers don't know a lot of math. So, does that keep them from doing similar research in mathematical logic as mathematicians ...
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Is affirmation of the consequent always invalid?
Examples that I've seen usually go something like
"If the lamp is off, then the room is dark. The room is dark, therefore the lamp must be off."
However, what about the following example
&...
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What do the meanings of ponens and tollens have to do with Modus Ponens and Modus Tollens? [closed]
There are two inference rules in propositional logic called Modus Ponens and Modus Tollens. I was wondering how the meanings of ponens and tollens have to do with the rules? That is, how does the ...
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Do the following two derivations imply each other?
https://plato.stanford.edu/entries/square/ says
A proposition is a subaltern of another iff it must be true if its superaltern is true, and the superaltern must be false if the subaltern is false.
...
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Intro to formal logic
We homeschool our kids, and "The Great Courses" offers a lot of good intro college classes that are suitable for 6-12th grade as well.
I'm really not into math or logic so please forgive me ...
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Question about disjunction elimination in Fitch
I was recently using https://proofs.openlogicproject.org/ and realized that their version disjunction elimination is fairly restrictive.
I had a proof set up something like this:
p∨q (Premise)
p∨r (...
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What does it mean "to provide semantics" in the context of formal logic?
When reading some SEP articles, this is a phrase I commonly came across, "this provides a semantics for this logic". But what does it mean?
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How would a logician define the phrase "all other things being the same"?
Here are some Examples of the Phrase
All other things Being the Same
All other things being the same, the juice of a Granny Smith Apple is more acidic than a the juice of a Red Delicious Apple.
All ...
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"This seems to abolish logic, but does not do so."
If language is to be a means of communication there must be agreement
not only in definitions but also (queer as this may sound) in
judgements. This seems to abolish logic, but does not do so. -- It ...
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Does it make sense to relate something to itself
We have reflexive relations in mathematics like equality that maps an element x with itself such that xRx is always true.
These are called relations however, xRx really can be seen as a self-identity ...
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Could our natural numbers be non-standard?
This question is related. It asks: "Can truths about the natural numbers vary across possible worlds?". One comment says: "Well, no, if they use same definitions and axioms about ...
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Can you lose something that you don't care about?
I'm new to philosophy and as of now, I don't have any knowledge related to what he said in order to properly redirect him to a source that mentions something similar. His philosophy goes like this:
If ...
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Universal affirmative propositions and the similarity of individual objects?
I'm trying to understand what counts objects as being members of a class. I'm getting stuck when there are variations for each object of a class but they might still be said to be part of that class.
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When does a mathematical predicate have a truth value?
Say we have a predicate in a domain of real numbers, P(x), 2x+10=20 we know that we can existentially quantify this and say that the value x=5 makes this true, but we cannot talk about P(x) being ...
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What is the Difference between a Claim and a Fact? [closed]
I know for a fact a computer must somehow add numbers but since I can only suggest it, it is forced to be a claim.
In that case, how could I ever state anything as a fact if I can only ever claim it?
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How can we name objects that we do not know?
Imagine that you are a detective and you are investigating a crime. Suppose you can't point to a criminal yet. However, you can name him in your reasoning. You can call him the criminal, the murderer, ...
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How does Aristotle show that 'particular deductions can be reduced to universal deductions in the first figure'?
In Prior Analytics I.7, 29b15-20, Aristotle states that
And so since the syllogisms in the middle figure can all be reduced to
the universal syllogisms in the first figure, and the particular
...
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Restrict logical negation
Let be:
p: is A a rational number.
Not p: A is not a rational number.
Hence, A can be a tree, the moon, etc...
But I would like to obtain something like this:
p: A is a rational number.
Not p: A is ...
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How to write a formal proof of Euclid's Theorem, specifying every logic rule used?
Euclid's Theorem is the statement that there is no largest prime. We might put it this way in first-order logic:
∀x ∃y (y >= x & Prime(y))
An informal proof is pretty straightforward:
Let n be ...
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Do all true statements express the same proposition?
Do all true statements express the same proposition? I know that, for example, the statements "2=2" and "1+1>1" are distinct sequences of symbols. However, I want to know, do ...
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Prove that if S tautological consequence of P, S tautological consequence of Q, then S tautological consequence of P | Q
Consider the following argument:
S is a tautological consequence of P.
S is a tautological consequence of Q.
Therefore, S is a tautological consequence of P | Q.
I wish to give an informal proof of ...
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If humans lack non-deterministic free will, is rationalism invalid?
I have an argument regarding the validity of rationalism in a universe without non-deterministic free will.
If human being's theories, thoughts and ultimate conclusions are inevitable, (bound by ...
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How can we know (with absolute certainty) that our logic is correct?
How can we know (with absolute certainty) that our logic is correct?
Even statements like Descartes’ “I think therefore I am” relies on our logic: that I exist is a logical consequence of my ...
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bad practices in statistics - ratio of a ratio
I haven't been able to think of good search terms for my question, and I'm happy to be redirected to another stackoverflow site.
I frequently see statistics presented in scientific summaries (written ...
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Can a response to an unanswerable question that says that the question is unanswerable be considered to be answering the question?
Let's say someone has asked a question: "How can one do X?"
But it turns out in fact that one cannot actually do X.
So someone posts a response saying that X is impossible to do.
Can this ...
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Checking translations of predicate logic
Let Dx = "x is a detective", U12 = "1 is the uncle of 2", and appropriate lowercase letters for names.
If there are any detectives, John is the only detective.
No detective is ...
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What are some strong arguments for logical holism?
What are some strong arguments for logical holism? The idea that the world operates in such a way that no part can be known without the whole being known first seems extremely foreign to me. This is ...
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Is Tarski's theory of truth widely accepted
Tarski's truth theorem asserts that a truth definition for a (reasonably strong) theory cannot be formalized within that theory.
It seems that Tarski's theory of truth has met with a lot of criticism. ...
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