John Jones

Philosophy and mathematics use many of the terms and ideas of logic, such as necessary and sufficient conditions, token and type, and sets. Some of these ideas can serve philosophy badly. For example, Set theory, which has been used in philosophy, is, in the instances I have come across, misguided.

1. Is the set 'a set of recipes' waiting to be cooked?
2. Is the set 'a set of cows' a herd?
3. Is the set 'a set of unforseeen movments' often misspelt?

Obviously not. Why does logic and mathematics insist that the members of a set confer their properties on the set? for it leads to the absurdities illustrated above.

I can further illustrate this by two examples taken from logic/mathematics - the set 'a set of numbers', and 'subsets':
1. 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. A set of numbers is a set of numerals.
2. 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'.
My point is that philosophers should not automatically defer to the mathematician, the scientist, the logician, lest errors go unobserved.
JJ

epepke

It doesn't. At all.

My guess is that your understanding of set theory is through philosophy, and my experience of philosophers is that they generally don't understand set theory at all, so it probably isn't your fault.

I think it would probably be a good thing if philosophers would learn some set theory, some second-order predicate logic, and some of the information theory of Shannon et. al.; it would improve their philosophy no end, if they actually used the stuff. However, I have met few of them who want to, though there seem to be no lack of philosophers who use the terms in a pseudomathematical kind of way, making them serve the same purpose as a carnival barker's top hat.

John Jones

I gave two examples to show that it does.
JJ

Cojana

Imagination, truth,and insight,these are the elements that permit creative phylosophers to thriumph in their wares, through Imagination extraction that lingers universely can be captured, truth, will enhance its interpretation, and insight will make it imortal, certain minds are especially tuned to the excretion left over from rightious thought, left over from God,! every creature with a mind has a link to God, for a mind are as infinite as the universe itself, God's Mind,?? :wave: :thumbs:

Wiploc

Off to ~~Elsewhere~~

crc

Cojana

Sorry, member John Jones, seems that my phylosophy bothers the 'shallow' WipLock, seems that he was waiting for my name to appear to dispatch me to elsewhere; no matter where I responce its the wrong catago :love: ry,!

John Jones

<Probems with moderation? Go to the P&C forum. Don't post it here - someotherguy>

muidiri

As stated... it doesn't. Logic and Mathematics insist that members of a logical or mathematical set share the defined characteristics of that set. A group of stuff does not a mathematical set make... Also as suggested, some study of set theory would be helpful before attempting to say it is worthless.

A set is defined by a particular characteristc - e.g. a set of numbers defined as X (Primary Numbers) = {1, 2 , 3, 4, 5, 6, 7, 8, 9}. Then the set Y (Primary Primes) = {1, 2, 5, 7} is a subset of the defined set X. But the set {12, 24, 56.5} is NOT a subset of the defined set X. A mathematical set is very structured, and very well defined.

Similarly a logical set is defined by a shared characteristic - e.g. "Herd" = {geographical grouping of cows in your neighbor's yard}. Then Bessie and BlueBell can be a subset of that herd if they are in your neighbor's yard... but Ferdinand is not a subset of the herd, because he is not in your neighbor's yard. Similarly, Spot the dog is NOT a member of the set, even though he is in your neighbor's yard, because he is not a cow. Notice that if the term "herd" were defined to mean ALL cows on the planet, then Ferdinand would be a member (ignoring the implication of gender in the term "cow", and just assuming all bovines are cows...).

In both cases, the initial set is well defined, and is defined by a particular characteristic (or set of characteristics). It is a REQUIREMENT that the members of the set have the defined characteristic. The characteristic does NOT pass upward from the members to the set - it is a CONDITION for membership in the set. If used properly, set theory could be useful in philosophy. Like any other mathematical/logical device, however, use by those that do not understand it can lead to insensible results. Similarly, debunking by those that don't understand it can lead to insensible statements.

John Jones

Aren't you asking yourself why Wiploc wants me to read your reply on the elsewhere forum, away from the eyes of his philosophers?

Regarding your analysis of sets, I can say that you will find difficulty in refuting my arguments. A set of numbers is clearly not a set of numbers simply because we have lost the property of succession which distinguishes numbers from mere numerals. So, a set of numbers is a set of numerals. Again I say, the property of the members of a set are not conferred on the set.

I will try to reply to your response on this point, but I am rapidly getting tired of the auschwitz forum board and will more than likely be banned shortly.

Cojana

'Per-don', for my lack of sophistication on your philosophy intellectual arguments, I posted my personal view of philosophy as to how it are produced, my logic pulls toward the infinite Universe,where all thought has been dispersed, Imagination,truth and insight are used to extract lingering philosophy, how did great minds come to be,? Universal extraction,! am I too simple to be taken for intelligent,? :huh: :love: