Mathematical objects and Discernment

Differences are apparant between elements in a universe of discourse (
or objects in a framework or model) and each element within the
discourse can also exhibit differences. In the absence of a universe of
discourse, no differences can be discernible between elements and an
element exhibits no differences itself.

Similarity, identity, countability, etc., require a universe of
discourse where differences are established. Yet it is difficult to
conceive how a universe of discourse could be constructed to support
differences: objects cannot be gathered in the manner of the
collections of a set, for 'gathering' implies a physical manoevure, and
physicality already implies a framework within which differences can be
established.

It is clear then, that if we wish to construct a universe of discourse
based on the idea of the collection of the set then we need to
re-define the set. A set 'collection' could now be defined on an
experiential basis as being comprised of those elements upon which our
attention is directed. 'Attention' is hardly of the stuff on which
mathematics or Frege's third realm of arithmetical objects is based.
Nevertheless, and if we examine mathematics closely, we shall find that
'attention' is one of many hidden manoevures used by mathematics that
do not fit in well with the popular idea of mathematical objects.

.

Relevant Pages

  • Re: a union is always a join!
    ... trigger in Oracle) on a table with only a composite natural key. ... identify things in the universe of discourse. ...
    (comp.databases.theory)
  • Re: Existence and Non -Existence
    ... be a formalization. ... a domain of discourse is a set. ... the variables range over the members of ... universe for that model. ...
    (sci.logic)
  • Re: The nature of the mathematical set
    ... bouquet is a set of tuples ... union is not allowable, it is just that in this case there are no common ... sense the ultimate subject of the discourse. ... If that universe of discourse is the actual universe ...
    (sci.logic)
  • Re: a union is always a join!
    ... identify things in the universe of discourse. ... before that information is projected away, then we could specify transition ... the guy wearing the red hat, but another possibility is that the guy ...
    (comp.databases.theory)
  • Re: The empty set
    ... The things across which the quantifiers of a formal theory may range: ... The universe of discourse may, ... universe of discourse that is a proper class. ...
    (sci.logic)
Loading