Hot answers tagged logic
15
Recall that in formal logic, your expressions are used as follows:
A if B means that B implies A.
A only if B means that A implies B
A if and only if B means that A is equivalent to B.
For example if in the morning I tell my wife "I'll buy that shirt we saw yesterday only if it costs less than 40 dollars" and she sees me wear it in the evening, she can ...
15
"Either A or B" most precisely means, in symbolic logic terms, "A XOR B", where XOR is the "exclusive or". So yes, it means "A or B but not both". It isn't always actually used with full precision, though, so, as usual, context has to be taken into account. If somebody says, "select either A or B", for example, they definitely mean that you should not ...
15
This is bordering on logic rather than language, but the answer is definitely no: Some is "an indeterminate amount", which means it can be all. If I say I have some red M&Ms in my bag, it could be that all of them are red.
But then, depending on inflection, as @codelegant pointed out, I could be using emphasis on some to indicate that not all are ...
15
This is the Cooperative Principle in action:
(link to comic)
If you have no particular reason to think I will buy you a wallet and I say:
I will buy you a new wallet if you need one.
then, under the Cooperative Principle, you can safely assume that this is all you want / need to know. But if there were other conditions in which I'd buy you a wallet, ...
12
No; the sentence "Is it true that 1 + 1 = 2?" is perfectly grammatically correct.
In logic, there are tests that depend on being able to prefix almost arbitrary sentences with "It is the case that ..." or "It is true that ..." and if the result still makes sense, then certain properties hold (it is a declarative sentence which could be a proposition). For ...
11
Fairly obviously there can be multiple X's, any or all of which may be 'arguably' the best X. To qualify for that designation they only have to be capable of being argued for – they don't need to actually be the best.
Equally obviously there may be some X's which are so bad they're not remotely capable of being considered for 'best', and some other X's that ...
10
You're correct: subsequently doesn't imply causation.
subsequent: Following in order or succession; coming or placed after, esp. immediately after.
consequent: Following as an effect or result; resulting.
(Both definitions are from the Oxford English Dictionary.)
You might use subsequently to avoid the post hoc, ergo propter hoc fallacy.
10
The original was actually Shakespeare: all that glisters is not gold, but that needn't concern us here.
OP has simply misparsed the sentence - it actually means "Not everything that is gold glitters" (which is to say, "There are some things which are gold that don't glitter").
You can always Google "every x is not y" for more discussion of why this type of ...
10
You're correct, it is indeed contradictory. Taken purely logically, then if neither can live while the other survives, then if Harry is alive Voldemort must be dead and if Voldemort is alive Harry must be dead. Since we know both Harry and Voldemort are alive, the statement is clearly false. Since the statement is part of a piece that refers to them as ...
8
To get the logical negation of "must", switch must with a different verb.
A: We must study English grammar.
B: No, we need not study English grammar.
or B: No, we don't need to study English grammar.
or B: No, we don't have to study English grammar.
or B: No, we are not required to study English grammar.
7
No, therefore should not be reserved for conclusions beyond a reasonable doubt. It is merely a transition similar to thus or as such:
Therefore, I ordered pepperoni.
Thus, I ordered pepperoni.
As such, I ordered pepperoni.
The extended conversation could have been:
I like meat on my pizza. Therefore, I ordered pepperoni.
You can test ...
7
"Consequently" contains information about causality and "subsequently" does not, but that doesn't mean "subsequently" is improper. Did B (humanity lost its resistance to the common cold) happen after A (the common cold died out)? Yes? Then of course B happened subsequently to A.
While "consequently" means that A caused B, the presence of "subsequently" ...
7
The biggest problem in finding a technical fallacy is that "absurd", in this context, isn't detailed enough. Why is it absurd? The idea that any absurd thing could be believed if it was simply absurd enough is not really true.
The idea of arguing something as true because no one would make it up is close to these fallacies:
appeal to authority — ...
7
Quoting the Wiktionary usage notes for center:
Merriam-Webster's Collegiate Dictionary observes that center around is objected to by some people on the grounds that it is illogical, but states that it is an idiom, and thus that such objections are irrelevant. It offers revolve around as an alternative to center around for those who would avoid the idiom.
...
6
In propositional calculus especially, there is a very small number of symbols available, and a very small number of ways they can combine. So it's tempting to thing of this small stock of mostly special characters ( ¬ ⋀ ⋁ ⊃ ≡ p q r s ) as an alphabet.
In fact, however, these letters don't represent parts of words -- rather, they are words, and represent ...
6
Your co-worker is misinterpreting the statement.
The "error" is in the interpretation of the word error
Error can mean:
a mistake or inaccuracy
but it can also mean
the condition of deviating from accuracy or correctness
The first is countable the second is not. I believe the intention is to say, that amendments are only allowed in 2 ...
6
It means not everything that is gold glitters. Tolkien undoubtedly was borrowing from Shakespeare here, specifically the poem that one of Portia's suitors discovers when he reads the scroll associated with the golden chest that he has (to his loss) chosen:
“All that glisters is not gold—
Often have you heard that told.
Many a man his life hath sold
...
6
Shakespeare's line is the best known example of this general phenomenon where a universal quantifier scoping over negation gives a counterintuitive meaning. The expected meaning of:
All that glisters is not gold.
Would be:
For each thing that glisters, it is not gold.
Instead, the meaning to be understood is:
Not everything that glisters is ...
5
The main problem in both cases is this: how to convert real language into logical language. In order to do this, one must choose how to interpret real language. This is often difficult, because real language deals with information that is often not apparent, such as implicit premises and the wider context.
X1: I paid $10 for that hamburger.
Y1: ...
5
The key issue is the ordering of auxiliaries in English.
(Subject) + Modal + PerfectMarker + ProgressiveMarker + PassiveMarker + (MainVerb) + (...)
An example of all the auxiliary positions being used is:
We must have been being taught English grammar.
Negatives occur after the element they are most relevant to (often the first). Since must is a ...
5
This dates back to the Coldstream Guards
The regiment is ranked second in the order of precedence, behind the Grenadier Guards. This is because the Grenadier Guards have served the Crown for a longer period of time. However, the Coldstream Guards is an older regiment, and because of this, has the motto Nulli Secundus (Second to None). The regiment has ...
5
Firstly, written expressions suffer from lack of the intonational advantage of speech.
Furthermore, there are such ambiguities galore in the English language, probably far more than in most of the other 'conservative' languages, i.e., those that well-defined and relatively static.
In writing, I might use an expression like:
"I'll buy you a new ...
4
For straight English prose, yes. It implies more than one, but not all.
However, for a discrete math homework or test question, I think it would be synonymous with "one or more". It could be just one, or it could be all of them. So if you are asking this question to try to get a couple of points back from your math instructor, sorry. :-)
4
Yes, you are right. 'Therefore' is used to link a statement which logically follows another one. It cannot be used in a standalone statement.
I would not say therefore should be used when something is being concluded beyond reasonable doubt. It can be used to connect two statements that
1) the user believes is logically
correct
2) the user ...
4
Yes, it does work (though it sounds a little technical) in common language because by saying:
I will get wet if and only if it rains.
you are saying both
I will get wet if it rains.
(meaning that if it rains there is no chance I will not be wet) and
I will get wet only if it rains.
(there is no way I will get wet unless it rains).
4
You might be looking for affirming the consequent.
People who would illegally sell weapons to foreign drug gangs would be more likely to purchase available weapons that the gangs preferred. That does not mean that everybody who purchased weapons that the drug gangs preferred intended to sell them illegally to the gangs.
However, it might add to a ...
4
Therefore is an adverb, as well as hence and thus, although used in this similar manner they are conjunctive because they denote causal relation between the two clauses in your statement.
Both of your examples above are acceptable, but there should be a semicolon in your first therefore example:
I was tired; therefore I fell asleep.
4
Remember that one of the defining characteristics of modals is that they can't function as infinitives. If you bear that in mind, it helps you predict the impossibility of what you are suggesting and similar sentnces.
So, the solution is that you need to find another periphrastic construct (usually "need to" or "have to" etc) with a similar meaning.
4
Modal means "having modes".
In the field of user interface design, a modal interface is one in which a given action has different results depending on what "mode" the system is in. For example, a button on a digital watch might advance the current time by a minute in one mode, and turn on the face light in another mode.
The opposite of modal in this field ...
Only top voted, non community-wiki answers of a minimum length are eligible
