39
votes
Accepted
Why would infinite monkeys not produce the works of Shakespeare?
Yes, the monkeys will do it. No, they don't have to.
It's mathematically true that after removing all logistical constraints - which is what we mean when we say there are infinitely many monkeys, ...
- 640
31
votes
Is there just one Zero?
In group theory, the "zero" is better referred to as the identity element, usually within what are additive groups.
This is not the same in every group.
For matrices, it is the n × n zero-...
- 5,460
19
votes
How many Platonic ideals are there?
Although Plato's Theory of Forms presents as a consistent, "scientific" system of metaphysics, it doesn't really hold up under scrutiny, and there's a strong tradition of thought that it was ...
- 30.7k
10
votes
How do we know we've defined a thing properly when all definitions seem to have exceptions?
Do not expect to find a perfect definition.
A definition is an expression of the meaning of something (the problem of the thing, what is a thing, is another), and meanings are intended normally for ...
- 8,100
10
votes
Is there just one Zero?
Try holding only a book in your hand, and asking them how many pens you're holding.
Zero doesn't exist at all. Neither does one, two, three, etc.
These are just concepts we often (but not necessarily)...
- 13.6k
7
votes
How do we know we've defined a thing properly when all definitions seem to have exceptions?
Several options to define a word.
1. Explicitly define a word in any arbitrary way you want
and then use it according to your definition. This method often works for new terms that you invented, such ...
- 18.9k
7
votes
Is there just one Zero?
There are many related issues:
the symbol 0: different in different languages/notations,
collections of objects with the same number of objects: how collections of NO objects at all can differ? and ...
- 41.1k
6
votes
Is there just one Zero?
I am reminded of Wittgenstein, because ambiguities like these where all the words seem different but seem to reflect no underlying difference in reality are really his jam in Philosophical ...
- 161
5
votes
Can nominalists believe in their own death?
I don't think there is a problem for nominalists here. I take nominalism to be the view that there are only individuals or particulars - concrete things or signs of concrete things, particular objects,...
- 36.1k
5
votes
Why would infinite monkeys not produce the works of Shakespeare?
The difference is between in principle and in practice. If you did have an infinite number of monkeys typing at random for eternity they would produce the works of Shakespeare. However, even if every ...
- 26.3k
5
votes
Is there just one Zero?
There are three zeros in 1000, but they mean different things: zero units, zero tens and zero hundreds.
- 2,253
4
votes
Accepted
If someone doesn't believe in "the" theory of category mistakes
Category-Error equivalents across fields
It is remarkable to note that from Aristotle on and through Kant, fundamental categories has been a staple of philosophy but philosophy has not dealt with ...
- 5,394
4
votes
Is there just one Zero?
This is a corollary of the fact that there exists exactly one empty set: {}. Therefore any intensional formula that defines a condition that no object satisfies, such as the three examples you gave, {...
- 973
4
votes
Is there just one Zero?
There is exactly one 'zero' in the same sense that there is exactly one 'one' or one 'two'. Numbers are linguistic quantifiers that call for a reference object. The reason people think that 'zero ...
- 24.1k
3
votes
Can nominalists believe in their own death?
All people, nominalist as well as realists, can believe in: One day, I will die. Or more general, they can believe in:
One day in his future, each living being will die.
That's the most simple ...
- 42.3k
3
votes
Do realists and nominalists actually disagree about what really is, or do they just disagree about words?
See the SEP article on nominalism:
[T]here are (at least) two kinds of Nominalism, one that maintains that there are no universals and one that maintains that there are no abstract objects. Realism ...
- 14.8k
3
votes
How do we know we've defined a thing properly when all definitions seem to have exceptions?
How do we define things?
We don't. We define words, the words we use to talk about things. To define a word is to specify what thing we use the word to refer to.
We don't define things, but we ...
- 9,882
3
votes
Why would infinite monkeys not produce the works of Shakespeare?
The odds are just too small for this to happen in any fathomable universe. From Wikipedia:
If there were as many monkeys as there are atoms in the observable universe typing extremely fast for ...
- 3,284
3
votes
Why would infinite monkeys not produce the works of Shakespeare?
This points to the danger of thought experiments. Clearly this isn't meant to be a realizable scenario. In a real-world version, even putting niceties such as immortality, feeding and materials aside, ...
- 30.7k
3
votes
Why would infinite monkeys not produce the works of Shakespeare?
How about instead of a typewriter the infinite monkeys each have a button for 0 and a button for 1 and truly randomly smacks one or the other until the end of time. We'll group up those 0s and 1s into ...
- 131
3
votes
Why would infinite monkeys not produce the works of Shakespeare?
It is fairly easy to show that it is not necessary.
First let us simplify the model. Instead of a finite set of monkeys randomly typing keys on a type-writer for all of eternity, let's have a finite ...
3
votes
Could, "If X is red, X has a coloration," possibly be not true like, "Cucumbers are vegetables," is not strictly true?
It's just multiple definitions for the same symbol.
Carrot is vegetable is not part true and part false. It's true for some definitions of carrot and vegetable and false for other definitions. The ...
- 8,405
3
votes
If someone doesn't believe in "the" theory of category mistakes
You ask:
To the extent that some (possible) person (possibly) doesn't believe in the concept of "making category mistakes," is it even possible for that person to make category mistakes?
I ...
- 35.5k
2
votes
If mathematical platonism is true, is mathematics then a discovery?
We could go through the permutations of Platonism, nominalism, intuitionism, empiricism, and fictionalism. The guts of the question is whether, if Platonism is true, we can and do discover ...
- 36.1k
2
votes
What have been the major achievements in the debate regarding platonism and nominalism?
Mark Balguer's Platonism and Anti-Platonism in the Philosophy of Mathematics is considered a critical text arguing that the ontology of mathematical objects is an open question such that there are ...
- 551
2
votes
Realist vs Nominalist views of empirical data
In sciences, such situation has been encountered where the set of experimental data leads to a variety of conclusions and the analyst has to sieve through the data with background disposition as to ...
- 871
2
votes
Why should we care about the Platonism vs. nominalism debate?
You ask for a "practical reason", its not completely clear what a practical reason would look like. For example and by way of tenuous analogy (sorry physicists) is there a practical reason ...
- 3,060
2
votes
Is nominalism generally considered to be disconfirmed?
There's consistently been an even amount of platonists & nominalists and this continues to be the case in contemporary philosophy, see the PhilPapers survey (actually, right now, there might be ...
- 138
2
votes
Does nominalism about kinds/universals entail eliminativism/nihilism about ordinary objects?
According to the SEP's article Nominalism in Metaphysics:
Nominalism comes in at least two varieties. In one of them it is the rejection of abstract objects; in the other it is the rejection of ...
- 35.5k
2
votes
Nominalistically Finding Radioactive Half-Life?
One way to express the concept of half-life without math is to fill a see-through container with pennies, marking their volume on the side with a horizontal line. Shake the container and then spread ...
- 2,350
Only top scored, non community-wiki answers of a minimum length are eligible