Mathematics
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pgwenthold
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How did two non-empty cups suddenly become two empty cups?
I put 1 cup of popcorn in a two cup measuring cup. I add one cup of water.
Where's the second empty cup?
A good example of how you are thinking too narrowly.
Almo
Masterblazer
This is just a hit and run. OP hasn't come back.
Perpetual Student
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This argument about popcorn and water is just plain silly. There are many examples in nature of two objects losing their identity when they come together, but that has no bearing on the universal concept of number. When an electron and a positron come together we can have two photons or even more particles depending on the original energy of the particles.
However, we can have oxygen in atomic form or we can have O2 (typical atmospheric oxygen) or O3 (ozone). Nature routinely keeps track of the number of things.
However, we can have oxygen in atomic form or we can have O2 (typical atmospheric oxygen) or O3 (ozone). Nature routinely keeps track of the number of things.
pgwenthold
Penultimate Amazing
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I disagree. Not only does it have bearing, it begs the whole question of what constitutes a
"number"
(NOTE: I can't take credit for coming up with the issue, it's a point John Allan Paulos made in many of his works)
psionl0
Skeptical about skeptics
The statement in the second column (the conclusion) is either true or false. If the statement in the first column (the premise) is false then it doesn't matter whether the conclusion is true or false so the conditional statement is true.
In this instance it makes sense to say that you can't conduct the experiment so you can't get an answer of 2.
Contrary to what many illogical people think, a conditional statement says nothing about the truth or falsity of either the premise or conclusion. It doesn't even presume that there is a causal link between the premise and the conclusion - merely that some combinations of true or false for the premise and the conclusion are not allowed.
To take a perfectly logical medieval belief:
IF the earth is flat and bounded THEN ships can sail off the edge of the world.
Neither the premise nor the conclusion is true but since we can't show that the earth is flat yet ships can't sail off the edge of the world, the conditional statement is true.
To take a slightly sillier example,
IF the moon is made out of green cheese THEN the earth orbits the sun.
Again, since we can't show that the moon is made out of green cheese but the earth does not orbit the sun, the conditional statement is true.
Perpetual Student
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You just don't get it. Some processes in nature preserve number; some don't. So what? That does not refute the reality that number exists in nature!
pgwenthold
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You are right, I don't get it. What are these things that you call "numbers" that exist and what are their properties?
Thank you. I suspected I was missing something.
If I understand you now, then the conditionals in both of these are true?
If you put one apple on the table and put another apple on the table, then you will have two apples.
If you put one apple on the table and put another apple on the table, then you will not have two apples.
hecd2
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Well as I see it that's a huge question. I would say that the work to answer both parts of that question is number theory. I can't see how the proofs of number theory, relating, say, to the infinity of primes could be anything other than they are without violating the basic rules of logic. In that sense, my view of number theory is that we discover it rather than it being a product of our cognition. We can certainly be more certain about anything proven within number theory than we can be about any proposition realting to nature.
It's true that number theory is built on certain axioms, but I can't see how those axioms could be other than they are in this universe. You might insist that because the axioms themselves are not proven, then numbers are solely human concepts but I think that is tantamount to solipsism.
Perpetual Student
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I'm certain that you can do your own research concerning number theory. Number is a property of objects and aspects of nature, like spin, charge, mass, chirality, etc. The existence of these properties is empirically determined.
psionl0
Skeptical about skeptics
Assuming that you are being serious, your two statements contradict each other so one of them must be false.
To disprove or negate a conditional statement, you need to find a counter-example. Since your first conditional is true, it will always serve as a counter-example to the second. So your second conditional is false.
But we are back where we started - I claimed the first statement was false, and you walked me through how conditionals cannot be false, and now assert the second statement is false.
Where did I go off track this time around?
psionl0
Skeptical about skeptics
No, you claimed that the experiment was impossible.
ie You could not "put one apple on the table and put another apple on the table" which, if true, would mean that either conditional could be assumed true (but not both simultaneously).
ie You could not "put one apple on the table and put another apple on the table" which, if true, would mean that either conditional could be assumed true (but not both simultaneously).
annnnoid
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It does not seem to me that pgwenthold is the one who does not ‘get it’! You claim something that you call ‘number’ exists in nature. Does this thing you refer to as ‘number’ have the same phenomenology as what is commonly referred to as the vocabulary of mathematics as it is generated by human cognition?
Perpetual Student
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Does ozone exist in nature? How many oxygen atoms does one molecule of ozone have? Is it different from one ozone molecule to another? Is it a specific number of oxygen atoms? Is the number of oxygen atoms a characteristic of ozone? -- like electric charge is a characteristic of electrons?
This number of atoms in ozone is one more than the number we call two. In nature O3 has one atom more than O2. We labeled these quantities in antiquity referring to sheep, apples, stones, whatever and have discovered that nature is quite rich with number as a property of objects and collections of objects.
As I said above, number is a property of nature as are charge, spin, mass, etc. properties of nature. These are determined empirically.
Rather than repeating the same ontological dribble over and over, address what I have demonstrated above!
TheGnome
Thinker
Well, as Leopold Kronecker once famously said:
"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk"
"God made the integers, all else is the work of man"
Anyway, this thread has motivated me to read Richard Dedekind's treatise
"Was sind und was sollen die Zahlen?"
"What are numbers and what should they be?"
which I think offers some insight into the nature of numbers.
"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk"
"God made the integers, all else is the work of man"
Anyway, this thread has motivated me to read Richard Dedekind's treatise
"Was sind und was sollen die Zahlen?"
"What are numbers and what should they be?"
which I think offers some insight into the nature of numbers.
Jules Galen
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Nonsense statement.
I'm a bit disappointed that the members of this forum have not called you out. Perhaps this forum is not as full of Skeptics as I had thought.
psionl0
Skeptical about skeptics
I'm rather skeptical about your response.
annnnoid
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Ontological dribble!?!?!? A more succinct explanation is required.
Human beings create math…numbers…etc. They (we) do this in our minds…somehow. Nobody knows how. Nobody knows what variety of thing meaning (human consciousness) is either. To you it may be ontological dribble…but to the horde of cognitive scientists around the globe, it is the holy grail.
The universe creates…the universe. There appears to be mathematical precision to this universe thing. But…from the POV of the universe…it may be some other variety of thing entirely. We have NOT located math in this universe outside of our minds. How do we KNOW this? We KNOW this, in part, because we don’t even know what math is (or consciousness)… and we KNOW this because we don’t know what this universe is.
You insist that this thing you call ‘number’ has some variety of definitive phenomenology …but you refuse to substantiate this position (except by ridiculing the notion of phenomenology). Until you do so, you do not have one (a position).
...and to answer your question. No...ozone does not exist in nature. Something we call ozone exists in nature ( …how is an ozone molecule explicitly defined???...by where its relevant electromagnetic-strong nuclear – weak nuclear – gravitational forces begin / end ????). Does the color 'red' exist in nature? Obviously not.