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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If I said I had $100 when asked, but I actually had $200, would I be lying by omission? [closed]
If you had $200 cash on you right now, and I asked you if you had $100 on you, would the correct answer be yes (always/no matter what other conditions there are), no (always/no matter what other ...
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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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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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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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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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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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Do computers use logic?
I know we refer to computers as using logic, logic gates and the like, but is this just us ascribing human capacities to the machines? It sounds like a case of us giving more meaning to the machines ...
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If you used intuitionistic logic in real life, would you not sound absurd?
Intuitionistic logic does not include the law of the excluded middle and double-negation elimination.
I imagine a real-life conversation with an intuitionist might go like this:
Amy said you didn't ...
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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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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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Why are there two fundamental laws of logic?
We have the law of non-contradiction and the law of excluded middle, but looking at it, it seems that both of them are the same thing, or at least one of them logically implies the other.
Is there a ...
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Do premises need to be valid conclusions themselves?
I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a ...
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How come intuitive thinking is related to constructing a proof?
I am researching Constructivism and Intuitionism. I can't understand why Intuitionism and Intuitionistic Logic are named as they are.
Intuitionistic logic requires constructing a proof of every ...
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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?
While reading Logicomix, I came across a scene that I don't quite understand.
Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
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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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Is there a system of logic which denies DNI?
From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE.
DNI: p -> ~~p
DNE: ~~p -> p
and denies DNE ...
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Why don't we have consensus in more complicated areas of logic?
When I once realised I don't really understand how and why proof by contradiction works, I started reading about it. And apparently I wasn't the only one who felt there's something wrong about it - ...
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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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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 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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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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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 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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What is the difference between 'accidental' and 'contingent'?
What is different between 'accidental' and 'contingent'?
I thought that accidental contains intentional notation while Contingent does not. But there could be an intentional action that turns out 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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Why isn't Cantor's diagonal argument just a paradox?
Cantor's diagonal argument concludes the cardinality of the power set of a countably infinite set is greater than that of the countably infinite set.
In other words, the infiniteness of real numbers ...
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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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In predicate logic, do we necessarily have to restrict the domain of discourse?
Can we combine formalized statements in predicate logic from widely different domains of discourse (say, one regarding integers, one regarding the fruits in one's garden) by using logical rules/...
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Can you list examples of problems that can not be solved within a formal system but human beings have solved through construction or creativity?
This kind of problem is mentioned in a book I have read, but the book did not give a concrete example.
If any such problem existed, this might help me understand human creativity. I think it would ...
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Why aren't Kripke semantics "syntax in disguise"?
The Wikipedia article on Kripke semantics suggests that they were considered a major breakthrough in part because algebraic semantics were seen as merely "syntax in disguise". But Kripke ...
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What are the philosophical implications of using inconsistent mathematics?
Why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything can be proven unless changing the logic used)? In particular, how could working with an ...
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What exactly is a first-order logic?
Can someone explain in simple terms what exactly is a first-order logic?
From my amateur standpoint, I think that first-order logic is a some kind of a system of symbols and general logical rules and ...
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Are the "laws" of deductive logic empirically verifiable?
"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on.
That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
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What is the explicit reasoning behind proof by contradiction?
From my understanding, proof by contradiction consists of the following steps.
1. Show that p -> q, where "->" is the conditional.
2. Show that q is false.
3. Deduce from a truth table that p must be ...
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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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Can animals follow logical rules of inference?
I've been trying to recall a thought experiment, which I very vaguely remember to have come across either in Davidson or Dennett, that considers the following scenario: A hound is chasing its quarry ...
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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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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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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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How could mathematics and logic exist without us, if they are concepts created by us independent of reality?
Would maths and logic exist if we didn't exist despite we created them, and do not have correspondence with reality?
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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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What, if anything, is the difference between studying logic mathematically and studying it philosophically?
There seems to be a distinction between studying logic mathematically and studying it philosophically and, in practice, it is reasonably clear which framework one is using when one studies logic.
I've ...
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Do logically incoherent statements still have meaning?
My reading of Carnap's "The Elimination of Metaphysics Through Logical Analysis of Language" suggests to me that it is possible to form sentences in a language that are grammatically correct but ...
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Is Modal Logic Logic?
What makes "Modal Logic" Logic? Why are symbols that stand for "necessary", for example, taken as symbols of Logic (of the same level of symbols that stand for "exists")? What are the limits that ...
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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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Are there any strong reasons to still consider logical monism or a "One True Logic" in light of all the non-classical logics that have been developed?
I know there has always been some debate concerning whether or not a certain logical system (like classical logic) is the correct one, especially when it comes to propositional claims about the ...
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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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Which philosophers have considered irrational conviction
It seems a characteristic of humans to be convinced about a matter in the absence of overwhelming evidence, even where logic suggests that are other valid alternative positions to take. We see this in ...
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