[William of Ockham] Universaliën - Summa Logicae

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Arjen
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[William of Ockham] Universaliën - Summa Logicae

Bericht door Arjen » 11 apr 2008, 06:30


<<Warum willst du dich von uns Allen
Und unsrer Meinung entfernen? >>
- Ich schreibe nicht euch zu gefallen,
Ihr sollt was lernen.
~Goethe

breekhoornpikveer
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Bericht door breekhoornpikveer » 13 apr 2008, 13:46

elders geschreven, ockham

--

You seriously think I'm joking? Well, if you are I do not mind.
I would do the same if I understand you correctly. If true,
humourism taken and noted. Lets try to formulate it.

First to take asside all uncertainties

"http://www.ifom-ieo-campus.it/research/ ... entini.pdf"

Otherwise google: "Vagueness, Kant and Topology"

I do not know the relevant topology because I do not think there is any. Also that is not a relevant question to me in general, the question is, why would one want to measure? I think that our mind is best illustrated by Zeno or Cantor, I'll take Zeno because it is cute.

One can continue cutting a 'finitely measured stick' in halves, but that does not make the stick infinitely small, it makes us operate deeper and deeper.

I imagined that when cutting things in halves 'meters' and 'yards' are not always useful, I guess that 'cut in halve until biological level is seen' or 'certain complexities', the kind of complexities should be the reference point, not us. In this model that is.

I prefer 'continuities' over 'infinities'. To continue because of the propositions does not mean that the thing assumed being imagined is being imagined. One can walk endlessly on the proposition: 'walk straight ahead'. I call that N (natural numbers), so Z would be going up and down with 0 being the illusoir moment called inertia. The fault would be seeing Z in terms of N.

Thus, if one takes up another analogy. How can one distinguish between different infinities? Well, how can one cut? Ricci flow (as I understand it conceptually) does not do anything with the 'continuous' object, it only:
http://en.wikipedia.org/wiki/Solution_o ... conjecture

" Perelman and Hamilton proved the conjecture by deforming the manifold using something called the Ricci flow (which behaves similarly to the heat equation, which describes the diffusion of heat through some kind of body). The Ricci flow causes the manifold to deform towards a rounder shape, except for the possibility that it stretches apart from itself (like hot mozzarella) towards what are known as singularities. They then chop the manifold at the singularities (it is called "surgery") and watch all the separate pieces form into ball-like shapes. Major steps in the proof involved showing how manifolds behave when they are deformed by the Ricci flow, examining what sort of singularities develop, determining whether this surgery process can be completed and wondering whether the surgery might need to be repeated infinitely many times."

I do not know the proof or the mathematics. Also my online time creates habbits I do not like so as of Tomorrow (Sunday) 1600 (GMT+1) I am offline and my parents take my computer with them so I can silently enjoy the mathematics and music I love conceptually and enjoy for its rigour at the times when I am occupied with it. That will take a month. Then I'll check my mail etc and decide what todo from there. I'll react then if I get no reaction before tomorrow 16GMT+1.


Also things vague are things probable because a shape always is vague, one simply does not question it. Continuity cannot be different from vagueness from the knowledge I have. Do you have proof of it being different? I would highly appreciate that.

For the proofs one can refer to the document, it is also pretty redundant so I summarised only and changed some defintions for myself so that I can keep it more sharp for myself. And orient my concentration on the problem I see at hand.
--

Big letter: set
Small letter: element
Big letter within {}: subset
P(set):powerset
!P(set):no redundant subsets

Hypothesis: If {A} is a subset of A then {A} contains A. Russels paradox.
I here assume that all atoms (sets) are continuous and thus I need to deepen my rigour regarding this.

*-> = element or subset
Characteristics->C *->c
Concepts->D *->v
v *->c
Objects->O *->o, {S}, {P}

||- = binary/constitution relation

o ||- v -> a v or the v constituting o mentally.

Extension:
Ext(c)=all objects constituted by {c}
Thinking* is 'moving symbols'

Thus, when thinking* one cannot orient C, V and O at once. However, a concept like ordinal can be maintained by some group but not everyone knows the characteristics perse, in practice one can always refer to the ordinal and thus extend one's connotations under ordinal.

Objects for me are phenomena.
V# (V Sharp) *->model

If V# makes one not doubt an object it it neither belief nor ignorance, it is inertia as defined above I think. One has no reason to see a discontinuity between V# and O because it fits.

Naturally, if V# does hold in the mind it is a trueism and one can learn from it. It is however not productive to build institutions with big grands on this behaviour, one institution may fall. I always imagine an forgotmenot at moments of enthusiasm:

"http://www.catnip.co.uk/wallpaper/forge ... 24x768.jpg"

'forgetmyselfnot'. Powerful imagery which is better then words when one thinks verbally right?

Ext(−), a constitutive morphism, is consistent from a first order perspective. So philosophically one may start turning circles if one want to plaster with this.

V# in most cases is judged Ext(-) I guess.


--
Closed subset->{S},
the document says that at least one object in S is constituted by one v.
Open subset->{P},
equal to {S} but now constitution out of more concepts is possible.

Thus S & P can both be continuous cardinals (objects) or elements with cardinality.

Cl() ->Closure of a set of objects.
(1=>) ->at least one
I imagine the '#' here, namely because a system can be coherent and beautiful, even be perfectly consistent, counter examples are good in such cases!

Closure of sets does say nothing about the continuity of even a single element of it.

Dr. Angel : "Remember things vague are not things probable."
Does that hold for all kind of continuities (number systems)?

"Actually, a concept is vague when, together with objects which
are completely within its extension and objects which are completely outside
its extension, there are also objects which are neither completely inside nor
completely outside, that is, which are in the border of its extension. So, at this point, we have to give an explication of ‘border’."

1. if provable it is not vague
2. if unprovable it cannot be called vague
3. if inconsistent with other observations it is true
4. if one has a V# and 2 seemingly contradictory concepts that refer to distinct objects (which I normally call images) but both are consistent with V# then V# is not understood and thus V# is recognized as model.
5. Continuous continuities are not vague if one lives in continuities (one does not feel natural laws), but when one happens to observe it it worlds and thus vagueness indeed is the most authentic word one can use.
6. Since different models are used throughout life it is useful to keep certain vocabularies to certain models for autopedagogical reasons at times. Thus that also shows that a lot of concept hold 'differently' in different models.

Not formally proven here but I guess this can be easily proved by others or be disposed of with the same rigour, I see the open sets as cardinals and the closed ones as 'cardinality not known'.


(Side note, I do not know what an ordinal is in these terms, perhaps I'm tired.. I jot it down anyway.)

Bd() = Border --> Unknown cardinality definable as vague because some concept at least is not consistent and this a new V# undoes itself slowly (potentially).





http://en.wikipedia.org/wiki/Infinite_divisibility

Hi!

Thank you,

For me it is the question if a single number has planck length here, or is continous.

Qm:atoms as closed sets. Perhaps also only definable with more concepts or V#?

"According to the Standard Model of particle physics, the particles that make up an atom — quarks and electrons — are point particles: they do not take up space. What makes an
atom nevertheless take up space is not any spatially extended "stuff" that "occupies space", and that might be cut into smaller and smaller pieces, but the indeterminacy of its
internal spatial relations."

I guess that x can be represented by different iy yes. Some circles spiral, no chance in te latter.

"5.391 × 10−44 seconds, known as the Planck time) smaller than which meaningful measurement is impossible.", is why does one want to a priori?

Time and space in terms of Planck seem like continuities, do the line of numbers bend in other perspectives? What movement does one make when descending and ascending the

planck length in real life?

Hoped for critique however also. But this greatly complements the formerly sent concepts.

I am primarily interested in n-side continous numbers (http://en.wikipedia.org/wiki/Càdlàg), and what ordinals groups can be said to be like each other.

"The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3-dimensional space can be split into several non-overlapping pieces, which

can then be put back together in a different way to yield two identical copies of the original ball"
http://en.wikipedia.org/wiki/Banach&#82 ... ki_paradox

This seems pretty trivial also. -->In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S²,

the remainder can be divided into three subsets A, B and C such that A, B, C and B ∪ C are all congruent. In particular, it follows that on S² there is no "finitely additive

measure" defined on all subsets such that the measure of congruent sets is equal.

http://en.wikipedia.org/wiki/Hausdorff_paradox


"5.391 × 10−44 seconds, known as the Planck time)" ?

"Paradox" seems misleading.

http://en.wikipedia.org/wiki/Lebesgue's_density_theorem

'In mathematics, Lebesgue's density theorem states that for any Lebesgue measurable set A, the "density" of A is 1 at almost every point in A. Intuitively, this means that the

"edge" of A, the set of points in A whose "neighborhood" is partially in A and partially outside of A, is negligible.'

I like this fellow!

'In other words, for every measurable set A the density of A is 0 or 1 almost everywhere in Rn. However, it is a curious fact that if μ(A) > 0 and μ(Rn\A) > 0, then there are

always points of Rn where the density is neither 0 nor 1.

For example, given a square in the plane, the density at every point inside the square is 1, on the edges is 1/2, and at the corners is 1/4. The set of points in the plane at

which the density is neither 0 nor 1 is non-empty (the square boundary), but it is negligible.'

Lambda(0->5.391 × 10−44) =?
Lambda(5.391 × 10−44->inf] =?

If one asks circles, however Hausdorff paradox i guess does not hold if size should matter.

Dense or not, without size one keeps being
Hilbert.
Disclaimer:

Pleasuredom,
Neologism,
pleasure through wisdom,
Portmanteau without the port.

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Arjen
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Bericht door Arjen » 13 apr 2008, 14:37

Mag ik vragen hoe je dit aan ziet sluiten op Ockham's universalia? Ik heb het idee dat je inspeelt op een ontologie en middels paradoxen het onderscheid aan wilt geven. Klopt dat?
<<Warum willst du dich von uns Allen
Und unsrer Meinung entfernen? >>
- Ich schreibe nicht euch zu gefallen,
Ihr sollt was lernen.
~Goethe

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