Mathematical Logic around the world:
http://world.logic.at/

On Wed, 30 Jan 2008 14:19:23 -0800 (PST), lwalke3@lausd.net wrote:

Yes, he's still with us! :-)

Proof? Did I present a proof for that? I must have missed it. :-)

Anyway, I can present an _argument_ for it: a heap consisting of a
single object (say a grain of sand) _is_ just that single object
(grain of sand). Hence: a = [a] (where a is "atomic"). On the other
hand, a heap [A] consisting of a heap A is just that heap A. Again:
[A] = A (for a heap A). Hence for every heap x: x = [x].

On Jan 31, 5:07 am, Bill Taylor math.canterbury.ac.nz>
wrote:

In ECHU IV.15.2, John Locke introduces the notion of 'degrees of
assent'. On the basis of this notion he formulates his claim in IV.
16.1 that the degrees of assent should be regulated by the degrees of
probability. This is a fairly common view in modern philosophy; you
can call to mind, for instance, Hume's famous saying, "The wise man
proportions his belief to the evidence," which Hume means quite
literally: the degree of belief should match the degree of evidence.

http://branemrys.blogspot.com/2004/12/are-there-degrees-of-assent.html

So, apart from the few important things that we can know for certain,
e.g. the existence of ourselves and God, the nature of mathematics and
morality broadly construed, for the most part we must lead our lives
without knowledge. What then is probability? Locke writes:

As Demonstration is the shewing of the agreement or disagreement of
two Ideas, by the intervention of one or more Proofs, which have a
constant, immutable, and visible connexion one with another: so
Probability...

hagman wrote:

Any big sparse sphere of dust with nonzero angular momentum, when
allowed to contract (e.g. under gravity), will become a nearly flat disk
as it much more easily shrinks along the spin axis (no centrifugal
effects) than in the plane of rotation (due to centrifugal effects).

As for why it had nonzero angular momentum, the probability of a
specific angular momentum vector, including the zero vector, is zero so
you "almost certainly" get something else given a random clump of space
molecules. C.f. "why does everything spin?" posted a week or two ago.

Straw Man. They mischaracterized your argument in order to gain their
foothold.

On Jan 30, 10:51 pm, WM wrote:

No, you've not defined an operation of division on cardinals.
Definition of an operation requires proving uniqueness and existence
clauses and then proper definitional form. You've not even hinted at
anything like that. As usual, your idea of mathematical argument is to
force whatever conclusion you desire by resort to undefined
terminology.

MoeBlee

WM says...

Yes, and that is exactly what happens. If you have an infinite
collection of finite sets, then the union is infinite.

On the contrary, that's exactly what happens in set theory.

Action implies a close connection between objects. All persons are
entitled to act; but the manner of action of each is different. The
actor maybe described as a man; but the term "man" refers to the whole
human species, and so a woman is an actor too. But if the term "man"
expressly refers to the male, it should be taken to be so.

There are some who believe that a woman cannot own property; but she
can do so; only she is second to man; but what belongs specially to
her is the power to bless and to remain chaste.

A further discussion on the subject maybe read at:

http://www.narachphilosophy.com/the_problem_of_action.htm

(You may click on the link above or type the complete URL address into
your browser)

Let us call an object M in a category C a "proper class object" if for
every object N in C there is a monic arrow f:N->M.

A topos cannot have a proper class object (since objects in a topos
are required to have power objects), but given a topos T, we can
extend it into a category which does include a proper class object. To
be precise, we can find a category which has a subcategory equivalent
to T and in which any object not in this subcategory is a proper class
object.

For example, we can extend the topos FinSets into a category which we
may call FinSets* which in addition to finite sets includes a natural
numbers object, but which does not include anything besides this.