Sociopath Community

AliceInWonderland said: 

MartinLooterKing said: 

AliceInWonderland said: 

 I am glad you said something given my mind works mostly in terms of maths as apposed to CS, I would have not made the connection outright. 

 I am math ignorant myself, but CS aware through sheer passion and years of learning, slowly breaking into math through CS. hardcore programming challenges teach me math concepts alot of time. Would you believe that I struggled with fibonacci last year? It was that bad. Now im starting to break into calculus thanks to Haskell and R which allowed me to jump into it.

If you took a homeless retard who never really went to school, where would you start him on math with?

 You just want a stronger foundation for CS applications? 

 yes

MartinLooterKing said: 

AliceInWonderland said: 

MartinLooterKing said: 

AliceInWonderland said: 

 I am glad you said something given my mind works mostly in terms of maths as apposed to CS, I would have not made the connection outright. 

 I am math ignorant myself, but CS aware through sheer passion and years of learning, slowly breaking into math through CS. hardcore programming challenges teach me math concepts alot of time. Would you believe that I struggled with fibonacci last year? It was that bad. Now im starting to break into calculus thanks to Haskell and R which allowed me to jump into it.

If you took a homeless retard who never really went to school, where would you start him on math with?

 You just want a stronger foundation for CS applications? 

 yes

Algebraic Progression: Precalculus, Linear Algebra, Abstract Algebra, Matrix Theory

Logical Progression: Discrete Mathematics, Propositional Logic, Symbolic Logic

It's hard to say what the thing in itself is, it seems the answer is dependent on whether you are a realist or idealist and the strength of your position. But it seems even in the best case scenario from a realist our perception is an excellent approximation of the real world outside of ourselves. All things would still be an approximation however and as such are not purely what the thing is they are still representations. The representation is never a thing in itself and everything we say about things are mere descriptions of our representations, that is list of attributes derived observations that are in some way empirical. Hence, even our best material descriptions are descriptions of our representations and it is those representations that we consider material. Is the thing in itself a material? It could be and a Bayesian approach would dictate that it is but in the end, especially in the Bayesian sense, all that is and can be stated is a reflection of our own epistemic condition.

If we are talking about a material in a space, once again that space is a representation and its reality beyond the representation is questionable. What is space when there are no things in it that hold relation? How dependent is space on the objects is subjugates? By that idea one can question whether a object is in space or space is in objects, or if one were to accept the material nature of things in themselves, in the relations of objects.

We always accept our representations as the reality and when we say a material object has said attributes we are talking about some object that we'd like to think is detached from us and as such all observations are too detached. But as stated what is being described is always the representation and that representation is then what we call material. Do you think what is outside us is immaterial? In some sense this is a valid view as to make something material is to objectify it and give it attribute, hence materialism and its application could be said to be idealistic. Meaning only something that makes sense only when an object is in relation to a human being. Attributes and more broadly lists of attributes are not things in themselves, they are epistemic statements about representations and a thing being given the category of matter is to giving it attribute. In that specific case of matter that attribute is to merely a epistemic statement about the relation representations hold. Physically that relation is some quantifiable unit called mass that is the quantity of matter. Matter can only be quantified when in relation to other matter, this being because the quantification of matter is to relate inertial coordinate systems - which is wholly idealistic as all parent systems are treated as absolute space.

   What I find particularly fantastic about Fikhtengolts in his 'The Foundations of Mathematical Analysis' is commitment to proof of the real numbers. This is hardly seen in a text, even ones on Real Analysis, as it is typical to suggest mere familiarity with the Reals. The only Analysis texts I know that actually commit themselves to the rigor of self-containment is Spivak and Rudin whom have a complete proof in the appendix of their texts.

   Fikhtengolts does not take the appendix approach however, he makes the primary concern from page.1 until sections on functions about the validity of the real numbers as not only a set of genuine numbers but most importantly a continuous set of numbers. His method is that of Dedekinds in which he cuts the rationals in half via a division where all rationals belong to one of the sets or the other (not both). The cut itself can be said to be made on a space for which no rational exists (this is done via analytical inequalities) and as such a proof for gaps in the rationals has been achieved.

   Fikhtengolts then turns his analysis to the notion of infinite fractional decimal quantities where he proves that a number can exist through an infinite number of fractional processes (limiting process) that shrink an interval around a value. He then does this fraction process around the cut between the two sets of rationals and in doing so proves the existence of an infinitely varying fractional decimal in the gap, hence he proves the existence of irrationals in this gap and in so doing constructs the ideal of a set of real numbers. All that is left to do is prove the continuity of this new set across be generalizing the two described processes for any gap that exists in a rational set.

I feel stupid almost constantly and fear that in the end I really know nothing. Every time I think I've broken through a wall another one is thrown up and I run straight into it and sometime the foundations of what I previously thought was sustainable falls apart beneath me. I have a hard time believing anything as a result and sometimes it makes me sad. 

AliceInWonderland said: 

I feel stupid almost constantly and fear that in the end I really know nothing. Every time I think I've broken through a wall another one is thrown up and I run straight into it and sometime the foundations of what I previously thought was sustainable falls apart beneath me. I have a hard time believing anything as a result and sometimes it makes me sad. 

 That's why you should never compete with me.

Jk. I couldn't resist. 

Don't be afraid of not knowing. It's natural and we really won't learn 1% of all there is to discover.

The notion of transcendental object is quite difficult to discern as it relates to the work of Kant. Kant describes it in terms of appearance and as a thing in itself, as such the term has no definition. In the case of appearance where Kant describes it as something within cognition (hence it is appearance) he says the only notion one can have of the transcendental object is through the declaration ‘general = X’. For the object’s treatment as a thing in itself, or close to it, it is said to be the unknown thing that acts as source for all sensory data.

What is of particular interest to me is that he acknowledges the difficulty of defining transcendental object when stating “What kind of constitution does the transcendental object have? One cannot give an answer saying what it is, but one can answer that the question itself is nothing because no object for the concept is given”. By this phrasing I think it is again appropriate to view the transcendental object as general = X as is typical, but it also seems valid to go a step further and say in all practical purposes the transcendental object is a null set as no object can be said to be an element of it.

 I mean this in the sense that we can never leave the bounds of our representations. Given either interpretation of the transcendental object it is at least not a representation and a such all that a human being stuck in the realm of representation could ever place in the set of transcendental objects is a representation which would invalidate the idea in the first place. As such, the transcendental object is neither plural nor singular, in all purposes to the human being it is empty.

I have not read Kant but here we'll seminar.

Here's what I get from you

 Transcendental object

¶ 1. Appearance of object defined as identity term (ie "itself" or more formally, general=x) 

    since Object is itself source of sensory data

¶ 2 Further, transcendental object as  "hard to define' like "null set" (i.e. an empty set without elements)

¶3 Alice's interpretation. You speak of humans bound by 'representation' which is distinct and problematic from 'object' based on point 1 Thus, you wish to invalidate Kant

Coming to Kant from your notes only, I am interested in why he may have used the term transcendental for object and if that holds any other clues. Transcendent means above the range of human experience thus, hard to define.
Though outside of the scope of Kant I am struck by corollary in first principles' Heisenberg Uncertainty Principle, the theorem that it is impossible to simultaneously know the position and velocity of a particle unperturbed. Could we not say that general=x and null set factors would also apply to first principles, namely Heisenberg.

-Med

Med said: 

I have not read Kant but here we'll seminar.

Here's what I get from you

 Transcendental object

¶ 1. Appearance of object defined as identity term (ie "itself" or more formally, general=x) 

    since Object is itself source of sensory data

No.

The transcendental object is defined under two opposing contexts, one within the realm of cognition as an appearance which is something that comes before representation and understand and the other as a thing in itself which is source of all sensory data. These contexts are oppose one another because the former exists within cognition and the latter exists outside cognition.

The statement general = X implies alludes to the indeterminate nature of the transcendental object as something beyond representation. 

¶ 2 Further, transcendental object as  "hard to define' like "null set" (i.e. an empty set without elements)

No. 

The null set is not hard to define as it is merely an empty set, that which has know elements or that set whose only element is symbolic null. The transcendental object is hard to define given but the null set is not, yet they represent similarities when thinking in terms on object inclusion. Under the pretense of thinking in terms of objectification and inclusion you can treat the transcendental object as a null set. 

¶3 Alice's interpretation. You speak of humans bound by 'representation' which is distinct and problematic from 'object' based on point 1 Thus, you wish to invalidate Kant

No. 

Kant agrees with the difficulty of definition and alludes to process of definition, that is asking the question of constitution, as nothingness which alludes to it being a none-sensical process. Instead, given the multiplicity of interpretation he presents it seems he advocates for a multi-perspective view on the topic. 

I am merely adding the idea of empty set as one of the possibilities. 

Coming to Kant from your notes only, I am interested in why he may have used the term transcendental for object and if that holds any other clues. Transcendent means above the range of human experience thus, hard to define.
Though outside of the scope of Kant I am struck by corollary in first principles' Heisenberg Uncertainty Principle, the theorem that it is impossible to simultaneously know the position and velocity of a particle unperturbed. Could we not say that general=x and null set factors would also apply to first principles, namely Heisenberg.

-Med

In the confines of transcendental philosophy transcendent is the limit of all human knowledge and experience while transcendental are all things that are beyond that limit. 

Hence, the transcendental object is an object whose reality is beyond the limit of human experience and knowledge. The study of such an object is an attempt to understand what dictates that transcendent limit in order to understand what can be known and why. 

Another conversation on discord I am enjoying

Bob said:

because it makes a fundamental law of classical logic (principle of excluded middle) - albeit axiomatic - appear to be a mere mindless convention/tradition rather than an inductively obtained conclusion with various justifications for it.

 I do not think the general view of logicians is that to be a convention is to make a logic mindless. Classical Logic is seen is not mindless but, I will speak in the neokantian sense of the Logical Positivists, as a language that allows us to make and explore factual statements derived from sensibility and intuition. Given it has the capacity Classical Logic is deemed factual in opinion but not necessarily the only factual language as it relates to the project of logic and mathematics (however you may view them).
The conventionalist project seems to be to find the set of factual languages.

Bob said:

Secondly, intuitionistic logic in praxis, by rejecting this fundamental law, ends up failing to provide sufficient tools to regularly produce actual proofs and deductions, ultimately taking away our ability to reason properly for any given point.

 Rejecting excluded middle was an early idea within the intuitionist tradition but it has been made sense of, as in LEM makes sense within the intuitionist logic and can even be used. Furthermore, in so far as constraining a language and its results, intuitionist logic does not have this problem as all results are fully translatable between the it and classical by Glivenko translation (and there are others). There is no real constraining of results but rather a question of a fundamentalist nature. Is a system a sub system of any other? This debate is an interesting one but in the end the results do not change given its answer.

Intutionistic logic is valuable imo as it opened the door to a more constructive and rigorous discussion of Computability.

Bob said:

And lastly, ambiguity in language is a vital part of communication. It allows to express the inexpressible, hence why words like "thing" are this common in virtually any language. Even mathematically, we express ambiguity and variability with symbols such as "x".

First, I agree completely that ambiguity is useful and vital.

Second, I am not so sure that variability is necessarily ambiguous in the context of mathematics given that variability is necessarily well defined – if it is not it is not logical nor mathematical. The concept within language proper may be ambiguous in general or until defined and it may be sensible to say that ambiguity is inherent and unavoidable in any language construct or system. However, that does not necessarily mean that ambiguity is not reducible. Reducibility seems to be the project of logic which again deems it necessary that we reduce ambiguity to deal with factualness. Does it achieve that goal and is that goal reasonable?  I am not really sure seems to have been fruitful and as such the goal seems justified.