筆記20081209: Cross-textual explanation

1

First notice, we have to keep in mind that the following modeling is based mainly upon the ground of the first two moments of the logical function of judgment, the quantity and the quality, i.e., the mathematical functions. That is to say, the modeling is not complete yet, i.e., is to be completed. But an extra notice is, although the modeling is not complete yet, the modeling is based upon the complete logical function of judgment and this is why its completion can be anticipated. -- Mathematical function and philosophical function of the logical function of judgment are organic!

Following the previous notice, added is that the concern here is in binary, i.e., only vector spaces, i.e., dimensions, are here in concern, i.e., not enough care about degree (of quality) is cared yet, i.e., the concern is mathematically categorial. That is to say, only the taxonomy without real cases is here concerned.

Second notice, The modeling is modified from the classical vector space model of information retrieval, computer science, with algebraic as well as topological understanding.

1.1

Modeling Display

Let's define:

a. our experience of something =Vmi

b. our awareness of the experience of something = Vki

c. something understood as an idea/a concept = ki

d. given the fact that the amount of all possible k's is t, i.e, i = {1, 2, 3, ...., t}

e. and the interested serial number as j.

Where V indicates vector space (dimension), m indicates minterm, k indicates key term.

1.1.1

When every k expands a vector space of k,

then the form of Vki is notated as

Vkj = (0, 0, 0, ... 1, 0, 0,..., 0) ,

where the digit in which 1 appears is the digit number j, while the last digit is the digit number t.

Then,

Vk1 = (1, 0, 0, ..., 0, 0)

Vk2 = (0, 1, 0, ..., 0, 0)

Vk3 = (0, 0, 1, ..., 0, 0)

...

Vkt = (0, 0, 0, ..., 0, 1)

I.e, the amount of Vki is t.

1.1.2

Based upon Vkj , we believe that there are knowledge such as ki, and we believe:

k1 = (1, 0, 0, ..., 0, 0)

k2 = (0, 1, 0, ..., 0, 0)

k3 = (0, 0, 1, ..., 0, 0)

...

kt = (0, 0, 0, ..., 0, 1)

and that the amount of ki is t.

1.1.3

But in reflection, the indetermiate state, we find that there should be some relation among some of the kj's,

i.e., we find that beside the vector spaces of the kj's themselves,

there are also the vector spaces of the relation of kj's.

E.g, the vector space in the relation of k1 and k2 is notated as:

Vm1,2 = (1, 1, 0, ..., 0, 0)

E.g. the vector space in the reltaion of k1, k3 and kt is

Vm1,3, t = (1, 0, 1, ..., 0, 1)

Thus the dispaly of Vmi is:

Vm0 = (0, 0, 0, ..., 0, 0)

Vm1 = (1, 0, 0, ..., 0, 0)

Vm2 = (0, 1, 0, ..., 0, 0)

Vm3 = (0, 0, 1, ..., 0, 0)

...

Vm(2^t-1) = (1, 1, 1, ..., 1, 1)

I.e, the amount of Vm's is 2^t.

And upto now, we know that on the basis of VM, there is never any Vkj, but Vmj. We just take kj for Vmj, so we are allowed to believe there Vkj is! But actually, there only Vmj, or more precisely, VM can exist.

VM exists (ontically, existentiel),

Vmj is (in awareness) because we understand Vkj with kj. That is, to us,

Vkj = kj = Vmj

(where now the j can be both the singular interested key term or the plural cluster of interested key terms-- yet the cluster is still meaningless, unless the last two moments are introduced in.)

1.1.4

In order to step into the present step, I need to take the degree in concern now.

The Vmi is so far just for the toxonomical classification form. Any Vmi in such sense is an idea.

However, when there are cases in the vector space, i.e., there's content varies in degree within the vector space, then the key term kj of the vector space Vkj is a concept which can be applied to all the cases of kj distributed within the vector space Vkj.

Now let's fix our focus on VM, and there's a given singular existence of case Kj in VM,

if you make a determined judgment of Kj, you do the following:

a. you find Kj only within Vkj, while

b. you locate Vkj upon the VM understood as Vmj.

If you make an indeterminate judgment of Kj, you do the following:

a. you find Kj within all the possible Vmj insofar as Kj can appear in the vector spaces, (and it is indeed that with the power of judgment Kj can appear in every vector space,)

b. you locate Vkj upon VM and the VM is the sole ground.

1.2

Example

Given a kind of being whose

a. possible experience of something is either something or nothing Vm1 and Vm2

b. whose awareness is either Vk1 or Vk2

c. who has only the ideas/concepts of k1 or k2

1.2.1

Now their awareness situation is:

Vki = (something-dimension, nothing-dimension)

Vk1 = (1, 0)

Vk2 = (0, 1)

1.2.2

Based upon Vkj , this kind of being believes that there are knowledge such as ki, and they believe:

k1 = (1, 0)

k2 = (0, 1)

1.2.3

But in reflection, the indetermiate state, they find that there should be some relation between the kj's,

i.e., they find that beside the vector spaces of the kj's themselves,

there are also the vector spaces of the relation of kj's.

Thus the dispaly of Vmi is:

Vm1 = (1, 0) : somthing is

Vm2 = (0, 1): nothing is

Vm3 = (0, 0): nullity

Vm4 = (1, 1): existence betwen being (生) and not being （滅）

Upto now, this kind of being can realize that there's a basis such as VM which includes Vm1, Vm2, Vm3, Vm4.

Vmj is (in their awareness) because they understand Vkj with kj. That is, to them,

Any instance of Vk1 = k1 = Vm1

Any instance of Vk2 = k2 = Vm2

1.2.4

If one of them makes a determined judgment, i.e., experience something, he does the following: he

a. finds K1 (1, 0) only within Vk1 (1, 0), while

b. locates Vk1 (1,0) upon the VM understood as Vm1. (1, 0) as of the possiblities

Vm1 = (1, 0) : somthing is

Vm2 = (0, 1): nothing is

Vm3 = (0, 0): nullity

Vm4 = (1, 1): existence betwen being (生) and not being （滅）

If one of them makes an indetermiate judgment, i.e., experience an K1 against the basis of VM, he does the following:

a. he finds K1 within all the possible Vmj insofar as K1 can appear in the vector spaces, (and it is indeed that with the power of judgment K1 can appear in every vector space,)

b. you locate Vk1 upon VM and the VM is the sole ground.

1.3

Kantian Understanding of the Display

1.3.1

cognition

1.3.2

coordination of the categories

1.3.3

purposiveness between understanding and imagination

1.3.4

determined judgment and indeterminate judgment

1.4

Hua-yan's Understading of the Display

1.4.1

事法界

1.4.2

理法界

1.4.3

理事無礙法界

1.4.4

事事無礙法界]]>