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closertotruth.com
Crows "counting to three" is one I recall. But that's explicable in terms other than maths.
I don't think so. Rather, maths is everywhere in our interpretation of the natural world. I mentioned above that we can't count anything without designating WHAT we want to count and the FIELD in which we want to count it. No human, no numeration
That's an abstraction. Abstractions are only found in brains, which is largely the point I'm making. The number 2 is an abstraction, which is why, as I said, we don't find uninstantiated 2s at large in the wild. And we don't find 2s at all unless we, the relevant individual, first determine the WHAT and the FIELD for that counting.
Because that's how we think, indeed have to a large extent been taught to think. The innumerate shepherd used to count his flock by the pebbles-in-the-bag method or the notches-on-the-stick method (one-to-one correspondence means of tallying) rather than muttering '101, 102, 103 ...'.
I think of it as the result of working with the logical consequences of particular axioms, very usually provoked by particular precedents. That is, I think logic is the universal-seeming element rather than mathematics itself.
You cannot be a physical realist and a mathematical non-realist.
This is because math is a logic-based language. Human languages don't exist outside the brains of humans and other animals that can understand it. And just as humam language is, there isn't only one way to do it and even other animals have their own languages, including some that have been observed using their own version f math.
Math is connected to written language, more than to spoken language. If we did not have written language; could not write math, spoken math would be very limited, and would be much harder to do. Written language allows one to record what you counted; placeholder for memory, instead of having to place the sum into memory, while also doing calculations and operations in your heads. Writing allows to document, so we can pause and reflect. If you are solving simultaneous equations, it is much easier to write them down and then ponder what you see. You try things until they work; many pages. All in your head, like spoken language would be very difficult beyond just basic math, even keeping track of where you have been; aborted efforts.An interesting discussion...
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Animals could never understand the human's perception of numeration, period.
I guess you missed the point of what I said. Do you think a monkey's brain is capable of understanding the human brain's perception of numeration? No. Monkey's are quite capable of scrolling through an iphone but do they know what they are looking at on the phone too? No. They don't do math the way humans do it, period.
Its more than three, and you can call it whatever you like but recognizing, organizing, and reacting to quantity is inextricably related to math. SO that's a fail.
Math may be everywhere in our interpretation of the world, but it does not follow that that is the only place it is. Regardless of whether I am consciously interpreting it as such, the number of trees in my yard still has a quantity. Sounds like you're running aground of a basic map/territory confusion.
No, or at any rate its not only an abstraction. Combining two collections of two objects still yields 4 objects, regardless of whether a human is doing the counting or not. OR would you disagree? If a monkey has 2 grubs in one hand and 2 in another, and there is no conscious observer to use mathematical language to describe the situation, isn't it nevertheless true that the monkey has 4 grubs? Quantities exist in nature, and they combine and divide and substract and all the rest, just like our theories describe, regardless of whether they are interpreted mathematically by a mind capable of such.
Idk if this is a deliberate strawman or if you're just a bit out to date in the philosophy of mathematics, but their are realist positions wrt ontology/truth in mathematics that do not involve "Platoland". Structuralism, for instance.
Humans are animals so your statement is invalid, and yes indeed some other animals do math. Of course probably not the same way we do it, but about the only communication we do strictly have in common is when we teach some gorillas sign language. All other languages we all have we all just all do them different.
I can be a physical realist and point out that maths exists only as concepts in human brains, not out there in nature but only in how we interpret nature.
Yes, mass is found in nature and energy is found in nature (nature being the world external to the self which we know about through our senses).
Maths is purely conceptual, a tool we use for organizing our perceptions of reality.
Where else do you say it exists, other than as concepts in a human brain?
No, it doesn't have a quantity until you choose to interpret it in terms of quantity. Maths is the human-made map, not the objective territory. Without humans there are no plants, trees, flowers, grass, grain, no mountains or hills, no bees, spiders, fish, birds, animals, just aggregates of things.
I disagree. There's no such thing as collections, categories, examples, unless you, the observer, choose to see things that way. Which we've evolved to do. so from a survival point of view that approach works.
Not unless and until YOU decide (as you've evolved to do) that this thing is a monkey and this thing is a grub and this thing is a grub and this thing is a hand and this thing is a hand and this thing is a grub and this thing is a grub.
Again, we've evolved to categorize the world. In our absence the world simply is.
Mathematical platonism requires belief that maths exists independently of our concepts of maths, ie independently of humans, but does not exist materially. Therefore it exists somehow in Platoland, an alternative universe somehow overlapping ours; and Platoland is a notion I reject.