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gustav Wrote: ------------------------------------------------------- > 汪純瑩 > > 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