Philosophy that is served by mathematics is served badly. Here are examples to show that set theory, which can be applied to philosophical logic, is fundamentally misguided.
Is a ‘set of recipes’ waiting to be cooked?
Is a ‘set of cows’ a herd?
Is a ‘set of unforseeen movments’ often misspelt?
Obviously not. Why then does mathematics insist that the members of a set confer their properties on the set, like the examples above? For example:
The set ‘a set of numbers’ is not a set of ‘numbers’ because the numbers from which ‘a set of numbers’ takes its numbers, are numbers only in the application from which they are taken - their ‘numberness’ is not conferred on the set.
There are no subsets. The members of a set are completely defined by the name of the set. Any factors in the members of a set that are not considered in the name of the set, do not confer these properties on the name of the set as a ‘subset’.
A set of numbers means a set of things with properties called ‘numberness’, eg the property 'one, or ‘twenty seven’, etc. You are right in that a set of numbers does not define what numbers are. I could have just as well say a set of wookiwookis, and wookiwooki are things with the properties of ‘numberness’. ‘Numberness’ is defined elsewhere.
But when we say a set of numbers we know what is meant. It is language limitation and not a fundamental flaw in mathematics. It is, so to speak, a matter of convention.
I would like to know what the mathematician means when he says that that there are infinite members in the set ‘set of numbers’. Because I think, and have said, that the mathematician doesn’t know what he means by ‘infinite’.
JJ
In mathematics, infinite is defined by a ‘set’ that’s components will never reach an end, i.e. {1,2,3,4,5…} Is defining an infinite set of real numbers because no matter how high you can count (thinking only in real numbers) there will never be a number that defines the end of the set. Hence the … after the last digit. Infinite is also defined a any line, if you put a line on a graph, there are infinite possibility to parallel that line, or stick a perpindicular line with it, for the lines themselves are infnite (no definite end) and as are the graphs. ‘Mathematicians’ know exactly what they are talking about when the say infinite, do you?
The mathematician does not know what he means by ‘infinite’, nor what he means by ‘set’. The idea ‘largest number’ is also misconstrued.
First, ‘infinite’. There is no application for ‘repeat’, or ‘…’ in mathematics except ‘repeat to this limit’. Only until a limit is specified, is a number created. No limit is specified by ‘infinite’, so infinite number is not a number, nor a mathematical function. This argument also applies to the ‘possible’ positions on a line. There are no positions on a line until we name them, i.e. set their limits.
‘Largest number’. A number is a number in its own application. Numbers are not shared between different applications. Accordingly, if I count to 8, then 8 is the largest number, and it is true that 8 is the largest number. If you now tell me that 136 is the largest number, you are either i) referring to a different application altogether, or ii) presenting a numeral, which is the sign of a number prior to its presence in an application.
There are no numbers in a set. A number is not a number if it is taken from its application. Therefore, a set of numbers is a set of numerals. Unless these numerals are named in the name of the set, then the set ‘the set of numbers’ is not only referencing numerals, but is not a set at all, as the numeral is not known outside the set.
The members of a set are not countable. All the members of a set are indistinguishable, because they are equally defined by the name of the set. So there is no framework within which a count can be made.
Mathematics borrows the concepts of common parlance - 'infinite, ‘set of’, and ‘largest’ and erronously associates them with mathematical applications, within which these words are entirely out of place.
JJ
Mathematics is a precise language in which infinite is NOT a number, it never was and never will be. Infinite is merely a concept of which states no boundaries of a given object, i.e. set. ‘…’ is NOT a number, it never was and never will be. ‘…’ is merely a concept of which states a continuation of the earlier pattern to an undiscernable number in the future. ‘…’ and infnite are arguably the same thing where set builder notation says {x|xER} x is a variable only deicided by the equation of that variable, therefore has infnite possibility. Once x is discovered by working out the equation, we are able to reduce the possibilities to the set of real number in which we may say {x|xE(1,2,3,4,5,…)} Meaning simply that x such that x is an element of the set {1,2,3,4,5} and so on to any other infinite possibilities following that set.
Your understanding of infinite is based on non-mathematical basises, in mathematics, infinite is just assigned to the definition that is something without boundaries following the same pattern, end of discussion, in mathematics, to understand infinite is to understand that definition, that definition IS the concept of infinite.
Your discussion is flawed in that all you have to support your argument is that you don’t agree with a set definition of some name that was given to that definition.
What is an indiscernible number? This is just another way of saying ‘…’.
Also, it is not number to which the terms ‘indefinite’ and ‘possibility’ refer. For number in isolation is numeral. By these terms you refer to the function for creating number. If you say ‘carry on indefinitely’, or ‘possibility’ then I would suggest to you that ‘indefinite’ and ‘possibility’ are not limits. Without a limit placed on our function for creating number, which is the same as specifying the act of applying the function, then we have no number at all.
So what do you suggest? wookiwookis, zybzigy, and konks? Or is your objection also of the associated concepts such as infinity? I have still not heard from you what is the error-free concept of infinity. What is it?
JJ, I am afraid I have no idea what your argument is, a number in isolation is a numeral? Of course it is! 4 is IV, is this what you are suggesting? There is no argument there… The definition of indefinate is something that is not defined. I have no idea where you are coming from so please, rephrase your last statement.
A number in isolation is a numeral. So, if we are asked to continue a number series, we do not continue with numbers, but with numerals. In order to maintain the idea of number, and to stop number collapsing into numeral, the injunction to ‘carry on counting’ must refer to the function for making numbers and not the numbers themselves. Numbers ‘themselves’ are numerals.
Now, if I do not define a limit to applying a function, then I do not apply it at all; and hence no numbers are created.
JJ
Stop it. Stop it right now. Your whole fucking arguement is meaningless. math is built on certain basic axioms, such as the properties of numbers, sets, and so on. You are saying, essentially, that our concept of math doesn’t work, that our ideas of numbers and set theory is wrong. All you’re doing, however, is coming up with your own crackheaded axioms to replace the ones that we know, (the ones that actually work). Everything you ahve mentioned about numbers and sets is either wrong or irrelvant (numbers vs. numerals, for instance). You haven’t proven a goddamn thing except that you really have no idea what you’re talking about.