What is the basis for reason? And mathematics?

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RCSaunders
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surreptitious57 wrote:
Fri Feb 07, 2020 3:36 am
A more profound question other than are numbers man made [ yes they are ] is was mathematics discovered or invented
One that sadly does not have a definitive answer to it although then again neither does any other philosophical question
All knowledge methods, like language, mathematics, logic, and geometry, are human inventions and the purpose of them all is to make it possible for human being to conceptually identify the facts of reality. Numbers were invented to make it possible to identify those facts of reality that have quantity as one of their attributes, like collections of animals, coins, and family members, and counting is the method invented to establish those quantities.

So both questions are easily and exactly answered. Mathematics was invented to deal with the fact some aspects of reality have quantity as attributes (an ontological fact), but the mathematical concepts, as inventions, only exist in human minds (epistemologically).

RCSaunders
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jayjacobus wrote:
Fri Feb 07, 2020 3:49 am
The question is similar to asking if words are manmade. Of course words are manmade and so are numbers.

Numbers were created to represent amounts. As such, numbers are a frame of reference for amounts.

Without numbers, referring to amounts would be vague. Without numbers, someone might "many, few, massive, some, a lot, etc." but each term is not specific. Numbers give people the ability to be specific.

Saying I have many chickens and some cattle is not specific but saying I have 32 chickens and 4 steers is specific. Not only that I can specify the weight and value of each animal and the total value as well.
That's right. If there were no human beings there would be no mathematics. While much of reality would have attributes of quantity the human method of identifying those attributes (mathematics) would not exist.

Eodnhoj7
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RCSaunders wrote:
Sat Feb 08, 2020 2:10 am
surreptitious57 wrote:
Fri Feb 07, 2020 3:36 am
A more profound question other than are numbers man made [ yes they are ] is was mathematics discovered or invented
One that sadly does not have a definitive answer to it although then again neither does any other philosophical question
All knowledge methods, like language, mathematics, logic, and geometry, are human inventions and the purpose of them all is to make it possible for human being to conceptually identify the facts of reality. Numbers were invented to make it possible to identify those facts of reality that have quantity as one of their attributes, like collections of animals, coins, and family members, and counting is the method invented to establish those quantities.

So both questions are easily and exactly answered. Mathematics was invented to deal with the fact some aspects of reality have quantity as attributes (an ontological fact), but the mathematical concepts, as inventions, only exist in human minds (epistemologically).
How does one invent a quantity that stems across multiple symbols as having the same meaning?

commonsense
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Eodnhoj7 wrote:
Thu Feb 13, 2020 2:11 am
How does one invent a quantity that stems across multiple symbols as having the same meaning?
By “stems across multiple symbols as having the same meaning” do you mean there would be multiple symbols that express the same quantity?

Eodnhoj7
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commonsense wrote:
Thu Feb 13, 2020 8:30 pm
Eodnhoj7 wrote:
Thu Feb 13, 2020 2:11 am
How does one invent a quantity that stems across multiple symbols as having the same meaning?
By “stems across multiple symbols as having the same meaning” do you mean there would be multiple symbols that express the same quantity?
Yes.

commonsense
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Eodnhoj7 wrote:
Thu Feb 13, 2020 10:02 pm
commonsense wrote:
Thu Feb 13, 2020 8:30 pm
Eodnhoj7 wrote:
Thu Feb 13, 2020 2:11 am
How does one invent a quantity that stems across multiple symbols as having the same meaning?
By “stems across multiple symbols as having the same meaning” do you mean there would be multiple symbols that express the same quantity?
Yes.
Got it.

Here are some symbols that have the same meaning:

1, I, i, uno, echad, one, lone, singular, unitary, unique

Although there are many symbols—and we can invent more—that express the same quantity, we cannot invent quantities in the sense that we cannot create them. It’s just like the difference between numbers and numerals.

Eodnhoj7
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commonsense wrote:
Thu Feb 13, 2020 11:44 pm
Eodnhoj7 wrote:
Thu Feb 13, 2020 10:02 pm
commonsense wrote:
Thu Feb 13, 2020 8:30 pm

By “stems across multiple symbols as having the same meaning” do you mean there would be multiple symbols that express the same quantity?
Yes.
Got it.

Here are some symbols that have the same meaning:

1, I, i, uno, echad, one, lone, singular, unitary, unique

Although there are many symbols—and we can invent more—that express the same quantity, we cannot invent quantities in the sense that we cannot create them. It’s just like the difference between numbers and numerals.
Now do we invent the symbol making process?

commonsense
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Eodnhoj7 wrote:
Fri Feb 14, 2020 12:36 am
commonsense wrote:
Thu Feb 13, 2020 11:44 pm
Eodnhoj7 wrote:
Thu Feb 13, 2020 10:02 pm

Yes.
Got it.

Here are some symbols that have the same meaning:

1, I, i, uno, echad, one, lone, singular, unitary, unique

Although there are many symbols—and we can invent more—that express the same quantity, we cannot invent quantities in the sense that we cannot create them. It’s just like the difference between numbers and numerals.
Now do we invent the symbol making process?
Yes, the symbols are human inventions. The quantities exist without human intervention. I think we are in agreement.

Eodnhoj7
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Joined: Mon Mar 13, 2017 3:18 am

commonsense wrote:
Fri Feb 14, 2020 1:44 am
Eodnhoj7 wrote:
Fri Feb 14, 2020 12:36 am
commonsense wrote:
Thu Feb 13, 2020 11:44 pm

Got it.

Here are some symbols that have the same meaning:

1, I, i, uno, echad, one, lone, singular, unitary, unique

Although there are many symbols—and we can invent more—that express the same quantity, we cannot invent quantities in the sense that we cannot create them. It’s just like the difference between numbers and numerals.
Now do we invent the symbol making process?
Yes, the symbols are human inventions. The quantities exist without human intervention. I think we are in agreement.
Do we invent the symbol making process?

commonsense
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Eodnhoj7 wrote:
Fri Feb 14, 2020 2:46 am
Do we invent the symbol making process?
What rules are there, if any, to the process of assigning symbols to numbers (or assigning symbols to anything)?

Skepdick
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Joined: Fri Jun 14, 2019 11:16 am

Eodnhoj7 wrote:
Fri Feb 14, 2020 2:46 am
Do we invent the symbol making process?
In so far as the invented/discovered distinction doesn't matter - yes we do.

Aristotle started it all. Law of identity. A is itself.

And he created A.

Skepdick
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commonsense wrote:
Fri Feb 14, 2020 3:32 pm
What rules are there, if any, to the process of assigning symbols to numbers (or assigning symbols to anything)?
Whatever rules we say there are, they are subject to Wittgenstein's rule-following paradox.

In Philosophical Investigations §201a: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule.

That is where logical positivism began insisting on testability criteria. How do I determine (a posteriori) whether I've followed a rule correctly?

commonsense
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Skepdick wrote:
Fri Feb 14, 2020 3:37 pm
Eodnhoj7 wrote:
Fri Feb 14, 2020 2:46 am
Do we invent the symbol making process?
In so far as the invented/discovered distinction doesn't matter - yes we do.

Aristotle started it all. Law of identity. A is itself.

And he created A.
He created A, but did he create whatever steps are involved in creating a name for a (new) thing?

And is the law of identity part of the naming process or the result of the process?

Skepdick
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Joined: Fri Jun 14, 2019 11:16 am

commonsense wrote:
Fri Feb 14, 2020 3:46 pm
He created A, but did he create whatever steps are involved in creating a name for a (new) thing?
A is itself.
A rose is a rose is a rose.
commonsense wrote:
Fri Feb 14, 2020 3:46 pm
And is the law of identity part of the naming process or the result of the process?
Sure. Recursion.

commonsense
Posts: 1832
Joined: Sun Mar 26, 2017 6:38 pm

Skepdick wrote:
Fri Feb 14, 2020 4:00 pm
commonsense wrote:
Fri Feb 14, 2020 3:46 pm
He created A, but did he create whatever steps are involved in creating a name for a (new) thing?
A is itself.
A rose is a rose is a rose.
“That which we call a rose by any other name would smell as sweet.” ~ W.S.Shakespeare

How did a rose come to be associated with its name, I.e. the word “rose”?

I don’t think we are quite there yet as far as a functioning process goes.
commonsense wrote:
Fri Feb 14, 2020 3:46 pm
And is the law of identity part of the naming process or the result of the process?
Skepdick wrote:
Fri Feb 14, 2020 4:00 pm

Sure. Recursion.
Makes sense.

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