Infinite Sets of Properties
Hartman goes on to consider infinite sets of properties. Hartman claims that according to a theorem of transfinite mathematics, any collection of material objects is at most denumerably infinite. This is not, in fact, a theorem of mathematics. But, according to Hartman, people are capable of a denumerably infinite set of predicates, intended in as many ways, which he gives as . As this yields a notional cardinality of the continuum, Hartman advises that when setting out to describe a person, a continuum of properties would be most fitting and appropriate to bear in mind. This is the cardinality of intrinsic value in Hartman's system.
Although they play no role in ordinary mathematics, Hartman deploys the notion of aleph number reciprocals, as a sort of infinitesimal proportion. This, he contends goes to zero in the limit as the uncountable cardinals become larger. In Hartman's calculus, for example, the assurance in a Dear John letter, that "we will always be friends" has axiological value, whereas taking a metaphor literally would be slightly preferable, the reification having a value of .
Read more about this topic: Science Of Value
Famous quotes containing the words infinite, sets and/or properties:
“What infinite heart’s ease
Must kings neglect, that private men enjoy!
And what have kings, that privates have not too,
Save ceremony, save general ceremony?”
—William Shakespeare (1564–1616)
“Nothing sets a person up more than having something turn out just the way it’s supposed to be, like falling into a Swiss snowdrift and seeing a big dog come up with a little cask of brandy round its neck.”
—Claud Cockburn (1904–1981)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)