Sentences can be associated with quantities, sure. Words are just symbols with a different form.
"If you take three apples and add them to three apples, you'll have a total of six apples." That concept can be expressed, "3a + 3a = 6a".
Post by twetch#1832
Mathematical language just uses a different set of symbols. Like sentences, some constructions are valid and some are invalid.
I can write down the symbols "15/0" and say the words "fifteen divided by zero." Doesn't mean that refers to any real quantity.
What the chain says
- Block
- 662 180
- Time
- 2020-11-20T23:52:45Z
- Signer
- 1Jj8TsZnm1bosAJFjkbS8J2MckEGx6sGot
- App
- twetch
- Type
- post
- Content type
- text/plain
- Name in tx
- twetch#1832
Fields the transaction did not carry are omitted. Open the payload to see the bytes as stored.
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Ultimately people aren't going to agree on what is valid or not. We are talking about ideas, not about real things. I don't think there is such a thing as a "real" quantity.
In math we define things in terms of axioms. That defines what is valid or not. We can have opinions about whether we like a given set of axioms or not but I don't think we have some automatic shared idea on what is valid or not in mathematics.
Few mathematicians would have ever thought that until the 20th century. "Axioms" used to mean a self-evident or easily demonstrate truth. Now, because of the blunders modern math, "axioms" mean "any set of assumptions we take as a given and cannot prove."
There's no such thing as "self-evidence"
A theory that doesn't talk about real things, or makes no attempt at connecting fictions to the world, is a bad theory.
Math can talk about real things, and it can say important things about the world.
"Quantity" is a real feature of the universe.
Is the distance along the diagonal of a square a quantity?
If we're talking about actually-existing geometric objects - not Euclidean nothings - then sure. A "square" is a composite object, made up of a finite number of points. The "diagonal" is another composite object whose units can be counted.