I think, therefore something exists.
Is that something me?
I’m not sure about that.
Specifically, that something and me might not be identically the same.
In math, we write ‘is’ as ‘=’. It’s a unitary operator, and in English, that means that if A = B, all of A all the time is exactly the same as all of B all the time, and equivalently, nothing that isn’t B at any time isn’t A at any time. To make sense of this peculiar little bit of semantic nonsense, let’s use an example.
Men are taller than women.
That statement, while defensible, is clearly not 100% correct by the mathematical definition of ‘is’.
Every man certainly isn’t taller than every woman. That just isn’t true. So we could push the statement a little and say, ‘Men are generally taller than women.’ However that adds problems just as it takes them away.
What does this ‘generally’ mean? Are men all one height h1, women all one height h2, and h1>h2? Again, clearly not.
To begin with, people come in a lot of different heights. There are some quite tall basketball players, and many of them are taller than I am. I’m a man. Many men are taller than I am. So are many women. Among the people taller than me, there are numerous heights involved. Are men a bunch of heights, mh#, and women a bunch of heights, fh#, where # is an index, from 1 to n (the total number of possible heights for each group)? If so, all mh# must be greater (taller) than all fh#. Every height of men must be taller than every height of women.
Obviously not.
So are men one weighted average height wh1, women are one weighted average height wh2, and again, wh1>wh2?
Not definitively. What about different populations? What about different ages? Both have strong correlations with heights. Between about 6 and 10 years of age, the average height of girls is taller than the average height of boys. Is that a function of men/women?
Very Well Fit gives the average heights of men and women in the US as 5’9″ and 5’4″ respectively. They say they got their info from the NHANES. Take them at their word for a moment.
Women don’t have one height, men another. There isn’t a pair of uniform bell curves around 5’4″ and 5’9″ respectively. The curves are certainly similar but different, and very unlikely to be symmetric.
And yet, there’s something to the statement. I (me, Matt) am asserting simultaneously that the above things don’t occur and that the broad statement still has something to it. What’s that mean?
No battle plan survives contact with the enemy. No mathematical identity survives experimental verification. Put another way, if we insisted on ‘is’ meaning the mathematical definition, we could never say anything is anything else. There would always be exceptions and caveats until the word itself ceased to exist. If we want to communicate meaningfully, and the word ‘is’ does help us communicate, than we have to add some fuzz that simply doesn’t appear in mathematics. The word ‘is’ has to incorporate a certain amount of generally, a connotation of ‘for some statistical populations’, and a dash of ‘in the average.’ The semantics become meaningless and a barrier to communication, and since the existence of words depends on their utility in communicating, these semantic arguments are themselves irrelevant.
Communication can be within someone. When I’m cooking, I might ask myself, ‘Is the oven too hot?’ That sentence has meaning to me, and I don’t think it while regurgitating a dozen definitions of thermo, flash deriving dU/dS for an oven setting. I don’t contemplate the nature of dinner. No, I just look at the temp and the recipe. The sentence ‘Is the oven too hot’ has a meaning as a thought.
So I think, therefore something is. Is the something me, within a certain amount of fuzz?
How much fuzz we talking about, here?
Enough to make the statement useful.
Well, that’s the trick.
Let’s go back to men being taller than women.
Suppose you’re a women who hired a contractor to install a shower faucet. The contractor has to install it somewhere and asks how tall the shower faucet should be? Two to six inches above your head is a good figure. Without giving the contractor a specific height, the contractor explores the utility of the statement ‘men are taller than women’ and the one factoid of our problem, the faucet should be high enough for a woman, and comes up with a number.
What if you’re tall? Is that earlier statement still useful?
Being a tall woman certainly doesn’t defy statistics. By the nature of measurement and statistics, those irregular, asymmetric curves, there are going to be some pretty tall people. That’s one of the things that averages are predicated on. So is the statement still useful?
Science is any endeavor wherein the question: How do we/you/I know something? is answered: When we/you/I can predict it accurately.
Is the statement men are taller than women known?
It’s known as well as it makes accurate predictions. This is Feynman’s Bongo.