75
votes
Accepted
If I said I had $100 when asked, but I actually had $200, would I be lying by omission?
I would say it depends on the situation. Specifically, it depends on whether the person asking you the question wants to know whether you have at least $100, or exactly $100. The question could ...
- 22.9k
44
votes
If I said I had $100 when asked, but I actually had $200, would I be lying by omission?
tl;dr- It's a lie if the speaker intends to deceive the listener(s).
More specifically, it's a lie-by-omission if the speaker intends to deceive the listener(s) by neglecting to mention something ...
- 1,939
34
votes
Accepted
Why is it that the statement "All goblins are yellow" does not contradict the statement "All goblins are pink?"
Edit in response to your comment: Okay, long answer:
What is the meaning of "the"?
(A previous version of the question had the statement "The goblins are pink"; this is an ...
- 2,489
33
votes
Accepted
Do computers use logic?
Allow me to be precise about this. Logic (in the formal sense) is a system of manipulating symbols according to rules. Computers can manipulate symbols according to rules — that is more or less ...
- 18.5k
25
votes
Accepted
If you used intuitionistic logic in real life, would you not sound absurd?
As Conifold comments, a real-life intuitionist would not shy away from assuming LEM ... when appropriate. Intuitionism merely permits the failure of LEM, it doesn't assert that it always occurs. For ...
- 3,210
20
votes
Accepted
Why did the mid-19th century and earlier thinkers fixate on one-place predicates?
Because there was a calculus for one-place predicates, Aristotle's syllogistic, roughly equivalent to monadic predicate calculus. Aristotle does discuss "relatives" in Categories, which ...
- 42.5k
17
votes
Accepted
What is the philosophical ground for distinguishing logic and mathematics?
Let me give you a historical background first. Until the end of 19th century logic was almost exclusively associated with Aristotelian logic, the syllogistic. This logic did not have quantifiers, or ...
- 42.5k
17
votes
Why is it that the statement "All goblins are yellow" does not contradict the statement "All goblins are pink?"
There are two ways in which these statements can be non-contradictory:
Option A: Non-mutually exclusive
It is possible for a goblin to be both pink and yellow, therefore it is possible for a goblin to ...
- 171
15
votes
What is the origin of the truth table in logic?
You can see:
Irving Anellis, The Genesis of the Truth-Table Device (2004)
as well as:
Irving Anellis, Peirce's Truth-functional Analysis and the Origin of the Truth Table (2012).
Before Bertrand ...
- 36.2k
15
votes
Accepted
Why are there two fundamental laws of logic?
They're not equivalent, but they do seem very close together in most contexts when you assume a bivalent (two truth valued) logic.
But they pull apart when it comes to several controversial ...
14
votes
Why did we define vacuous statements as true rather than false?
We do NOT define vacuous statements as true.
A vacuously true statement is vacuously true.
A "vacuously false" statement is vacuously false; although nobody ever gives this type of statement any ...
- 2,890
12
votes
Do premises need to be valid conclusions themselves?
Validity in logic is a somewhat tricky notion to understand as it is different – though only subtly – from related, pre-theoretic notions. For instance, not every valid argument is ‘convincing’ or ‘...
- 743
11
votes
Accepted
What is the axiom of reducibility? And what philosophical controversies did it incite?
To put it in simple words we have to describe in a couple of words the project of Principia Mathematica, which Russell inherited from Frege: reconstructing mathematics from logic alone. For a broader ...
- 42.5k
11
votes
Accepted
How come intuitive thinking is related to constructing a proof?
Intuitionism is a philosophy of mathematics that was introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966): he developed a very personal philosophy of mathematics that founds ...
- 36.2k
11
votes
What is the difference between 'accidental' and 'contingent'?
Colloquial meanings of the two words are pretty close, accidental is "occurring unexpectedly or by chance", contingent is "subject to chance; occurring or existing only if (certain circumstances) are ...
- 42.5k
10
votes
Is finding truth possible?
You've stumbled upon an old problem in philosophy, The Paradox of Inquiry, first formulated in Plato's Meno.
The problem can be reformulated as follows:
Either you know the answer to a question, or ...
- 6,466
10
votes
Accepted
Logic and Computation: a philosophical viewpoint on Curry-Howard isomorphism
I think you are right to be impressed with the Curry-Howard correspondence. It is a detailed and extensive rule-by-rule and feature-by-feature isomorphism. This strongly suggests that proof and ...
- 22.9k
10
votes
If I said I had $100 when asked, but I actually had $200, would I be lying by omission?
Your question is about lying by omission, and this requires that you define lying. The definition I use is a communication with the intent to deceive. Thus, whether or not you are lying is a function ...
- 23k
10
votes
If you used intuitionistic logic in real life, would you not sound absurd?
Propositions in intuitionistic logic are probably best understood as statements about provability. P ʌ Q means that you can prove P and prove Q, ¬P means that from P you can derive a contradiction, ∃x....
- 1,169
10
votes
Is there a system of logic which denies DNI?
Yes there is. As you say, intuitionistic logic has DNI but not DNE. There are also dual-intuitionistic logics whose connectives operate in a fashion that is dual to those of intuitionistic logic. Dual-...
- 22.9k
9
votes
What is the explicit reasoning behind proof by contradiction?
There seem to be several overlapping concerns in your issue with proof by contradiction.
You have an objection to the truth table for material implication:
I've never been satisfied with the ...
- 24.6k
9
votes
Accepted
What are the differences between philosophies presupposing one Logic versus many logics?
It is more complicated than a merely instrumental/metaphysical division. The "logics as mere instruments" were not meaningful until well into the 20th century, after the general ...
- 42.5k
9
votes
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 ...
- 27.1k
9
votes
Accepted
Is there an English language example where modus tollens is valid but contraposition is not valid?
Here's the example from David Lewis's Counterfactuals (1973):
If Boris had gone to the party, Olga would have gone.
Now suppose that Boris wants to go, but not if Olga goes, because he wants to ...
- 6,466
8
votes
Accepted
Does the Fallacy Fallacy make logic useless?
Short answer: definitely no, that does not make logic useless.
When someone makes an invalid argument, they're committing some sort of a formal fallacy. That is only to say that the conclusion does ...
- 6,466
8
votes
What are lucid examples of non-truth functionals?
Conditionals in English are used for a lot more than just expressing simple truth functions. Here are some general cases where the truth functional material conditional doesn't fit.
Claims about ...
- 22.9k
8
votes
What, at present, are the major unsolved problems of logic?
One should keep in mind that the meaning of "logic" changed over the last century, and is now more confined to formal logic, although it is broader than deductive or mathematical logic in the narrow ...
- 42.5k
8
votes
Accepted
Do premises need to be valid conclusions themselves?
Short answer : NO.
Arguments are either valid or not.
Premises and conclusions are sentences, and thus they are either true or false.
See Valid argument :
In logic, an argument is valid if and only ...
- 36.2k
8
votes
Can paraconsistent or other logics make the impossible happen?
Logic, paraconsistent or not, does not exactly make something happen, it is applied to reshuffle information already contained in a system. Paraconsistent logic does not even have to be applied to ...
- 42.5k
Only top scored, non community-wiki answers of a minimum length are eligible