You have a lot of one’s in today’s date. Five digits. Where was I that day I wasn’t here, orndorff? I was in a digit. How’s that? – Amorella.
I’m glad you put your name, otherwise I would have thought I was creating the paragraph out of thin air. Merriam-Webster’s 11th Collegiate Dictionary says: “Middle English, from the Latin digitus: finger, toe; perhaps akin to Greek deiknynai: to show.”
Orndorff, use the first present day definition.
“1a: any of the Arabic numerals 1 to 9 and usually the symbol 0 b: one of the elements that combine to form numbers in a system other than the decimal system.”
You are fooling with me, Amorella. I had to look up decimal system on Wikipedia which was at first interesting, then slowly I lost interest. It was most interesting to find that some cultures use other basis besides ten, and that the Arabic system may have first been used in China. This however has nothing to do with a place value, at least I don’t think it does. I don’t know. I was never good in math. My old high school math teacher, Bob Short, was my second cousin as his mother was my grandfather Clell’s oldest sister, Gretchen. It was embarrassing getting C’s in Algebra I; C’s in Geometry; and D’s in Algebra II. I was kindly advised not to tackle Trigonometry/Calculus in my senior year, or Physics either. That’s the way I remember it. I love science and physics except for the math. How can you be in a digit anyway? Numbers are made up abstractions. Oh. – So you were in an abstraction?
Boy, this definition is really funny (in this context).
“Abstraction: 1a: the act or process of abstracting: the state of being abstracted b: an abstract idea or term; 2: absence of mind or preoccupation; 3: abstract quality or character; 4a: an abstract composition or creation in art; b: abstractionism.”
What is funnier is the fact that it doesn’t mention numbers as abstractions. – Amorella.
I have read some material online from The Metaphysics Research Lab at Stanford and Philosophy Forums discussion on the question: “Are numbers real?”
Let’s include selected material from your recent online research.
The Theory of Abstract Objects [Stanford University]
[An online version of Principia Metaphysica can be found by following the link to The Theory of Abstract Objects (see below). In published work, the theory has been applied to problems in the philosophy of language, intensional logic, the philosophy of mathematics, and the history of philosophy.]
Introduction
The equations at the top of this page are the two most important principles of the theory of abstract objects. The first principle expresses the existence conditions for abstract objects; the second expresses their identity conditions. In this document, we try to give you some idea of what these principles say.
Metaphysics vs. Physics
The theory of abstract objects is a metaphysical theory. Whereas physics attempts a systematic description of fundamental and complex concrete objects, metaphysics attempts a systematic description of fundamental and complex abstract objects. Abstract objects are the objects that are presupposed by our scientific conceptual framework. For example, when doing natural science, we presuppose that we can use the natural numbers to count concrete objects, and that we can use the real numbers to measure them in various ways. It is part of our understanding of science that natural laws exist (even if no one were around to discover them) and that the states of affairs that obtain in the natural world are governed by such laws. As part of our scientific investigations, we presuppose that objects behave in certain ways because they have certain properties, and that natural laws govern not just actual objects that have certain properties, but any physically possible object having those properties. So metaphysics investigates numbers, laws, properties, possibilities, etc., as entities in their own right, since they seem to be presupposed by our very understanding of the scientific enterprise. The theory of abstract objects attempts to organize these objects within a systematic and axiomatic framework.
It would be a mistake to think that a theory postulating abstract objects is incompatible with our theories of natural science, which seem to presuppose that the only things that exist are the things governed by our true scientific theories. To see that the theory of abstract objects is compatible with natural scientific theories, we only have to think of abstract objects as possible and actual property-patterns. These patterns of properties objectify a group of properties that satisfy a certain pattern. For example, it will turn out that the real number π can be thought of as the pattern of properties satisfying the open sentence "According to the axioms of real number theory, π has the property F" (where "F" is a variable ranging over properties). There are an infinite number of properties satisfying this pattern (and an infinite number that don't). Our theory of abstract objects will "objectify" or "reify" the group of properties satisfying this pattern. So, on this view of what abstract objects are, we need not think of them as some ghostly, imperceptible kind of nonspatiotemporal substances. Instead, they are possible and actual patterns that are grounded in the arrangement of particles in the natural world and in the systematic behavior and linguistic usage of mathematicians and scientists as they discover, state, and apply theories of the natural world.
From: mally.stanford.edu/theory.html
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Below, is selected conversation from the UserGroup connected with Philosophy Forums:
Do Numbers Exist?
No. At most, numbers subsist (i.e. 'possible' objects sans actuality, including 'impossible' objects); they neither exist (i.e. 'actual' objects) nor are "real" (i.e. other-worldly, super-sensible, Platonic).
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"That mathematics can be applied so well to the real world" may be a historical fact rather than a meta/physical condition since we cannot know, on this account, whether some other, non-mathematical, way of compressing information (i.e. patterns) is possible which works as well as, or better than, mathematics. Mathematics is a convention, the most rigorous we have so far, and that's all we can intelligibly say about it.
Besides, most of mathematics does not (directly) concern numbers and most mathematical domains are not (directly) applicable to the physical world, so it doesn't follow that numbers are any more "real" than (e.g.) words, or mathematics is any more "real" than (e.g.) grammar. You don't think the 'rules of chess', truth, are as "real" as, or more "real" than, physical 'chess pieces & board', do you?
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Most of the mathematicians hold to the Platonist view when it comes to numbers and mathematical relations. They feel like 'discovering' theorems rather than 'inventing' them.
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"Experience without theory is blind, but theory without experience is mere intellectual play."
-Immanuel Kant
From: forums.philosophyforums.com/threads/do-numbers-exist-41938.html
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I feel I have some validation from the above anyway. In high school I did not have the words to express what I found today on ‘numbers’. I guess I do not have a brain malfunction after all. I better understand my problem with communication. I have to admit though this exercise today makes me wonder what it would be like to sit down with a real extraterrestrial and have a discussion. Every one sheorhe spoke or wrote in English I would no doubt be checking the dictionary and having herorhim verify the definitions. It would be a very slow but quite interesting process because I would gain some inference into how the alien actually thinks. Some people take grammar for granted and gloss over what is actually said or written in context.
This is true for the readers of these books and blog, old man, including yourself. – Amorella.
I suppose this can be so. I write the words but do not spend a lot of time afterwards studying what they are actually saying. I am focused more on the grouping of words that best suggest, at that moment, the conveyance of a concept or thought. For instance, here I sit suddenly realizing that I have yet to understand what you mean when you said “I was [not here in your mind I was in another location]in a digit.” Do I have that right?
Close enough. I was located in a metaphorical ‘finger’.
Do you mean the first finger, the pointer, the ‘index finger’ mentioned in the conclusion of the chapter six?
Yes.
Totally bazaar. How did you move from my mind to the book?
How do you read?
This is suddenly giving me a dull headache both in the frontal lobe and the cerebellum at the same time.
Accurate enough for all intents and purposes.
Are you suggesting the books are a mind unto themselves?
No, I am saying as you are haunted by old Uptown Westerville I haunt the books. – Amorella.
I have never heard of such a thing.
I don’t suspect you have.
I am at a loss of words.
Put the loss to work, orndorff. All for today. Post. – Amorella.
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