Questions tagged [philosophy-of-logic]
Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.
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What are the differences between philosophies presupposing one Logic versus many logics?
I was wondering in light of the historical developments of logic since ancient Greeks and well into the nineteenth and twentieth centuries: What kind of a philosophy assumes only one Logic, and what ...
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What is the philosophical ground for distinguishing logic and mathematics?
I was wondering why the field of mathematics and that of logic are perceived as two distinct fields. Although could be pleased with the intuition that logic is rather meta-mathematics, still would ...
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References for the justification of the use of Logic
Following that question : How to justify the use of logic?
I'm looking for references of the justification of the use of Logic (the question above didn't ask explicitly for resources but rather for a ...
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What justifications have been given for using particular systems of logical calculus?
I think that using any particular system of logical calculus should be properly justified.
This justification should be seen as particularly important and pressing in science and technology, and ...
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Is Logic Empirical?
We use the logical system that we know from observations (empirical data) holds true in the world we live in (please correct me if I am wrong). Hence the axioms of logic we choose are themselves ...
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What are the current topics in philosophy of logic?
I'm contemplating another attempt at completing my long delayed MA in Philosophy, and I need a new thesis topic. As a student I excelled in advanced symbolic logic, but my connection with academic ...
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What is the difference between the "is" of predication and the "is" of identity?
What is the difference between these, the "is" of predication and the "is" of identity?
For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
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What were the historical interpretations of Aristotle's definition of validity/logical consequence?
What were historically the various interpretations given to Aristotle's notion of validity, implicit in his syllogistic?
Here is one authoritative translation of the relevant text:
A syllogism is ...
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Can paraconsistent or other logics make the impossible happen?
A paraconsistent logic system it is defined as
"a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
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What is the difference between Law of Excluded Middle and Principle of Bivalence?
Law of Excluded Middle:
In logic, the law of excluded middle (or the principle of excluded
middle) is the third of the so-called three classic laws of thought.
It states that for any proposition, ...
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Exactly what was Wittgenstein's argument against identity?
Roughly Speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing. (Tractatus, 5.5302 and 5.5303)
Like Russell ...
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How is the nature of logical principles commonly defined in contemporary philosophy?
In contemporary philosophy, how exactly is the nature of logical principles defined? For example, the way I've commonly seen logical principles construed are as true propositions which described the ...
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What does the truth-value of a material implication represent?
This question comes from my attempts to understand what the truth value for a material implication with a false antecedent represents. I have seen several justifications for this convention, usually ...
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Can hypercomputation compute the impossible?
There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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Why did the mid-19th century and earlier thinkers fixate on one-place predicates?
A book I'm reading mentions the following:
A major barrier to the development of first-order logic had been the
concentration on one-place predicates to the exclusion of many-place
relational ...
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Why is it that the statement "All goblins are yellow" does not contradict the statement "All goblins are pink?"
From what I know, I think it has something to do with vacuous truths, but my understanding is not quite there yet.
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Why did we define vacuous statements as true rather than false?
I have been trying to understand why implications about the empty set are treated as "true". It seems to me intuitively that vacuous statements should be false.
For example consider the sentence:
...
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Introductory book on philosophy of logic?
I know that there are quite a few questions like this here already, but I haven't yet found an answer that would satisfy me.
I'm looking for an introductory logic book. My main goal is to work ...
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Logic and Computation: a philosophical viewpoint on Curry-Howard isomorphism
The link between logic and computation is stronger than ever, especially since the establishment of the Curry-Howard isomorphism specifying that proofs can be seen as programs and formulas as program'...
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What are lucid examples of non-truth functionals?
I wanted to understand the concept of non-truth function (which I found when reading about conditionals in logic). The definition of non-truth function that I have is (from reddit):
If a connective ...
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A proposition is non-falsifiable. So what?
Does Karl Popper argue that non-falsifiable theories are not true/have no truth value, or simply that they are not provable? Put another way: according to Popper, could a non-falsifiable theory ...
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Tractatus 3.333 and Russell's paradox
Can anyone explain to a non-logician how Tractatus 3.333 refutes (or fails to refute) Russell's Paradox? Please explain his use of symbols!
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What does the term "mathematical logic" mean?
What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical?
Also, is "quantificational logic" a particular type of "...
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What do we mean when we say there's only one type of logic/mathematics and that they can’t change?
Do we want to say that if they changed, they would not be logic/mathematics (as we know) anymore? How can we be sure that there's no other type of logic/mathematics?
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How do we know that if the statement "A → B" is correct, "¬B → ¬A" is correct?
All examples that I can come up with confirm that If "A → B" is correct, "¬B → ¬A" is correct, but is it possible to rigorously prove that negating a true implication always will result in another ...
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Can different varieties of modality be used with existential quantification?
I'm wondering if it makes sense to talk about worlds which aren't this one being real.
It seems like you can claim that something possibly exists.
Now I'm wondering, because it seems to amount to ...
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Is Deductive Reasoning Alien to the Material World?
A quick survey of literature:
Goel V. Anatomy of deductive reasoning. Trends Cogn Sci. 2007 Oct
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2685028/
García-Madruga JA, Gutiérrez F, Carriedo N, ...
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What is the intension of the concept “intension”? [closed]
I think that it should be possible to assign to all concepts a plausible intension, consisting of just one or two words. However, in textbooks or encyclopedias I never found such focused appointments ...
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What is the axiom of reducibility? And what philosophical controversies did it incite?
Trying to come to terms with basics concerning philosophy of logic, and wish to ask about some particular issue: What is in simple words the axiom of reducibility put forward by Russell? And what is ...
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How do we separate rules of logic from non-logical constraints?
I think that very often the idea of 'constraint' appears in mathematics.
For example, when a triangle is considered, 3 points are constrained not to be co-linear,
and then we try to discover the ...
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Does the Fallacy Fallacy make logic useless?
I should note that I'm not a formal student of philosophy and haven't studied it in any serious depth. I just like logic, and logical fallacies. I like to spot them, and I like to debate using them, ...
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A Question Regarding Russell's Paradox
Consider the 'set' behind Russell's Paradox:
R = { x | x is a set and x ∉ x }
in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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What exactly is informal logic and is this what I'm looking for?
I've been reading and researching about formal and symbolic logic for some time now, mainly out of interest in rationality. But I've come to a point where the various logical systems seem more like ...
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What is the origin of the truth table in logic?
Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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Is finding truth possible?
Consider the following argument:
If want to know that something is true, I need to first know what
is truth. If I need to know what is true, I need to find the truth.
(Is there ...
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What does Russell mean by "term" in Principles of Mathematics?
Bertrand Russell in Principles of Mathematics defines a term as "Whatever may be an object of thought, or may occur in any true or false proposition or can be counted as one." Can someone elaborate on ...
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Is there any reason for the heavy focus on binary relations in formal logic?
As a fan of C. S. Peirce, I'm surprised that, at least triadic relations, aren't investigated as much as binary relations are. What I mean is that with binary relations, they have already been ...
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Is Herbrand semantics a kind of term formalism?
Michael Genesereth and Eric Kao describe Herbrand semantics as follows:
Herbrand semantics is an alternative semantics for First Order Logic based on truth assignments for ground sentences rather ...
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What distinction is there between logic, philosophy of logic and philosophical logic?
I'm not clear on where logic in the broad sense of the word stands with respect to philosophy.
I do know there is mathematical logic which would be a subset of something.
If philosophy of logic and ...
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What is the difference between Aristotle's theory of categories and Russell's theory of types?
A partial answer might come through an introduction. Well, we know that Russell's efforts to understand the contradictory appearance of the class of all classes not members of themselves (a notion ...
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Is Rule-Based Machine Learning an Example of Inductive Logic in the Philosophical Sense?
Human beings are capable of deciding upon rules based on intuitions and observations their neurons presumably provide (certainly metaphysical presumptuous). According to WP, this is inductive ...
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Is there anyone who believes that all modal statements are meaningless or trivial?
It is often useful to interpret statements in various modal logics using possible-world semantics. For instance "it is necessary that P" means "P is true in all possible worlds", "it is possible that ...
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If the premises of an argument CANNOT all be true, then said argument is valid
Based on the fact that a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, I am ...
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What are the advantages of Aristotle's term logic over predicate logic?
I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic:
"I come to semantic ...
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References for the Realism/Anti-Realism debate in Logic
The concept of anti-realism in logic seems to be an interesting and growing idea.
I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
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Prerequisites for Michael Dummett texts
I want to read Michael Dummett's The Logical Basis of Metaphysics. Is it hard to read ? I would like an answer for the same question regarding his other texts.
Do I need a prior exposition to other ...
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Stephen Yablo's Aboutness and logical subtraction
I was finishing reading Aboutness by Yablo, but there is an intuitive definition that I do not get:
He says on page 148 that:
What is this relation of adding falsity, or being additionally false, or
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What, at present, are the major unsolved problems of logic?
In the 1900s, Hilbert published a list of 23 (later 24) unsolved problems in mathematics, which sparked increased research into each of them and the subsequent resolution of several of these problems. ...
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Natural Language and Implication
I understand that relevant logic deals with a natural-language interpretation of implication, but it seems too restrictive. It does seem a bit of a reach to say that there is a conceptual link between ...
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Infinite Regress in Language and Logic?
I had this idea, and it seems novel to me, but I'm wondering if there is a philosopher that addresses this issue already because I think it's kind of interesting.
When making a logical statement, you ...
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