What do all things have in common?

Posts tagged “Philosophy

Getting Hypertension About Hyperreals

HyperReals(Links below)

This system is quite interesting if we allow ourselves to talk about the qualities of infinite sets as if we can know their character completely. The problem is, any discussion of an infinite set includes their definition which MAY NOT be the same as any characterisation which they may actually have.

Also, and more importantly, interiority as well as exteriority are accessible without the use of this system. These ‘Hyperreals’ are an ontological approach to epistemology via characteristics/properties we cannot really know. There can be no both true and verifiable validity claim in this system.

https://www.youtube.com/watch?v=rJWe1BunlXI (Part1)
https://www.youtube.com/watch?v=jBmJWEQTl1w (Part2)


Knowledge Representation – Holographic Heart Torus

Holographic Heart Torus

Holographic Heart Torus by Ryan Cameron on YouTube


Which questions does Category Theory help us answer?

Category 02

Another chapter in my attempt to help break the ‘spell’ of the category theoretical ‘ontologicisation’ of our world.

This may seem to many as a purely academic question, but we all need to realise that all of what we consider a modern way of thinking rests upon ‘mental technologies’ such as Category Theory.

Academics are literally taking the ‘heart’ out of how our world is being defined!
If we don’t pay attention, humanity will continue losing its way.

Category theory is a wonderful and powerful tool; nevertheless category theory, with all of its utility, is purely ontological. It can masterfully answer questions such as ‘Who?’, ‘What?’, and ‘How?’.

Category 01

However; it is regretfully inadequate to form a comprehensive representation of knowledge, for it lacks expression of epistemological value, which are the very reasons for is use. Epistemology is about answering the questions of ‘Why?’, ‘What does it mean?’, ‘What is my purpose?’,…
Answers to questions of this kind are implicitly supplied by us during our consumption of the utility afforded by category theory. We often are so beguiled by this power of categorical expression that we don’t realise that is we ourselves who bring the ‘missing elements’ to what it offers as an expression of knowledge.
It does a wonderful job with exteriority (ontology), but cannot sufficiently describe nor comprehensively access interiority (epistemology). Therefore, it has limited metaphysical value with respect to philosophy in general.

Interiority 08

Philosophies of mind, of language, or of learning are not comprehensive using only category theoretical tools.
Categorical structures are highly portable, but they can describe/express only part of what is there. There are structures, dynamics, and resonance that the ontology and functionalism in category theory completely turns a blind eye to.
More general than category theory is knowledge representation. It includes and surpasses category theory in many areas, both in scope and depth, but in particular: knowledge representation includes not just the ontological aspects of what we know, it goes further to describe the epistemological as well.
The qualities of Truth, Goodness, Beauty, Clarity,… can be defined and identified within a knowledge representation if the representation is not restricted to ontology. When category theory is used for the purpose of defining qualia, the objects must first be ontologised and functionally reduced. Trying to grasp them with tools restricted to category theory (or even semiotics) is like grasping into thin air.

 

Category theory, although very powerful, is no match for the challenge of a complete representation of knowledge. Category theory will tell you how to tie your shoes, but it can’t tell you why you are motivated to do so.


Strictly Speaking Can’t! Natural Language Won’t?

Werner Heisenberg - on Language of Mathematics

Physics is only complex, because it’s in someone’s interest to have it that way. The way to understanding, even if you don’t understand science, was paved with words. Even if those words led only to a symbolic form of understanding.

Common ordinary language is quite capable of explaining physics. Mathematics is simply more precise than common language. Modern Mathematics pays the price for that precision by being overly complex and subservient to causal and compositional relations. These are limitations that metaphysics and philosophy do not have.

Words in language have a structure that mathematics alone will never see as it looks for their structure and dynamics in the wrong places and in the wrong ways. Modern pure mathematics lacks an underlying expression of inherent purpose in its ‘tool set’.

With natural language we are even able to cross the ‘event horizon’ into interiority (where unity makes its journey through the non-dual into the causal realm). It is a place where mathematics may also ‘visit’ and investigate, but only with some metaphysical foundation to navigate with. The ‘landscape’ is very different there… where even time and space ‘behave’ (manifest) differently. Yet common language can take us there! Why? It’s made of the ‘right stuff’!

The mono-logical gaze with its incipient ontological foundation, as found in (modern) pure mathematics, is too myopic. That’s why languages such as Category Theory, although subtle and general in nature, even lose their way. They can tell us how we got there, but none can tell us why we wanted to get there in the first place!

It’s easy to expose modern corporate science’s (mainstream) limitations with this limited tool set – you need simply ask questions like: “What in my methodology inherently expresses why am I looking in here?” (what purpose) or “What assumptions am I making that I’m not even aware of?” or “Why does it choose to do that? and you’re already there where ontology falls flat on its face.

Even questions like these are met with disdain, intolerance and ridicule (the shadow knows it can’t see them and wills to banish what it cannot)! And that’s where science begins to resemble religion (psyence).

Those are also some of the reasons why philosophers and philosophy have almost disappeared from the mainstream. I’ll give you a few philosophical hints to pique your interest.

Why do they call it Chaos Theory and not Cosmos Theory?
Why coincidence and not synchronicity?
Why entropy and not centropy?

Why particle and not field?
(many more examples…)


Are sets, in an abstract sense, one of the most fundamental objects in contemporary mathematics?

Equivalence Relation

Yes and no.

The equivalence relation lies deeper within the knowledge representation and it’s foundation.

There are other knowledge prerequisites which lie even deeper within the knowledge substrate than the equivalence relation.

The concepts of a boundary, of quantity, membership, reflexivity, symmetry, transitivity, and relation are some examples.

http://bit.ly/2wPV7RN


Limits of Category Theory and Semiotics

Category Theory 01

They are wonderful tools to explain much of our world, but lack ‘The Right Stuff’ to handle the metaphysical underpinnings of anything near a Philosophy of Mind, Philosophy of Language , or a Philosophy of Learning.

This is, because Category Theory specialises on roughly half of the Noosphere. It does a wonderful job on exteriority, but cannot sufficiently describe nor comprehensively access interiority.

Interiority Exteriority

Therefore, as is the case with Semiotics, has limited metaphysical value with respect to philosophy in general.

Semiotics 2

Semiotics

For example: philosophies of mind, language, or learning are not possible using only category theoretical tools and/or semiotics.

Here is an example of one attempt which fails in this regard: http://nickrossiter.org.uk/proce…

(and here: VisualizationFoundationsIEEE)

Here are two problems (of many) in the paper:

4.4.2 Knowledge is the Terminal Object of Visualisation states:

“The ultimate purpose of the visualisation process is to gain Knowledge of the original System. When this succeeds (when the diagram commutes) then the result is a ‘truth’ relationship between the Knowledge and the System. When this process breaks down and we fail to deduce correct conclusions then the diagram does not commute.”

I want to also comment on Figure 3 (which also exposes missing or false premises in the paper), but I will wait until I have discussed the assertions in the quote above which the authors of this paper reference, accept, and wish to justify/confirm.

1) The purpose of a representation is NOT to gain knowledge; rather, to express knowledge. Also, truth has nothing to do with knowledge except when that value is imposed upon it for some purpose. Truth value is a value that knowledge may or not ‘attend’ (participate in).

1a) The ‘truth value’ of the System (‘system’ is a false paradigm [later, perhaps] and a term that I also vehemently disagree with) does not always enter into the ‘dialogue’ between any knowledge that is represented and the observer interpreting that knowledge.

2) The interpretation of a representation is not to “deduce correct conclusions”; rather, to understand the meaning (semantics and epistemology) of what is represented. ‘Correct’ understanding is not exclusive to understanding nor is it necessary or sufficient for understanding a representation, because that understanding finds expression in the observer.

2a) ‘Correct’, as used in this paragraph, is coming from the outside (via the choice of which data [see Fig. 3] is represented to the observer) and may have no correspondence (hence may never ever commute) whatever to what that term means for the observer.

The authors are only talking about ontologies. That is a contrived and provincial look at the subject they are supposing to examine.

There may (and usually are) artefacts inherent in any collection and collation of data. The observer is forced to make ‘right’ (‘correct’) conclusions from that data which those who collected it have ‘seeded’ (tainted) with their own volition.

‘System’ (systematising) anything is Reductionism. This disqualifies the procedure at its outset.

They are proving essentially that manipulation leads to a ‘correct’ (their chosen version) representation of a ‘truth’ value.

I could tie my shoelaces into some kind of knot and think it were a ‘correct’ way to do so if the arrows indicate this. This is why paying too much attention to a navigation system can have one finding themselves at the bottom of a river!

The paper contains assumptions that are overlooked and terms that are never adequately defined! How can you name variables without defining their meaning? They then serve no purpose and must be removed from domain of discourse.

Categorical structures are highly portable, but they can describe/express only part of what is there. There are structure, dynamics, and resonance that ontology and functionalism completely turns a blind eye to.

The qualities of Truth, Goodness, Beauty, Clarity,… (even Falsehood, Badness, Ugliness, Obscurity,…) can be defined and identified within a knowledge representation if the representation is not restricted to ontology alone.

In order to express these qualities in semiotics and category theory, they must first be ontologised funtionally (reduced). Trying to grasp them with tools restricted to semiotics and category theory is like grasping into thin air.

That is actually the point I’m trying to make. Category Theory, and even Semiotics, each have their utility, but they are no match for the challenge of a complete representation of knowledge.


Universal Constants, Variations, and Identities #19 (Inverse Awareness)

Inverse Square
Universal Constants, Variations, and Identities
#19 The Inverse Awareness Relation

The Inverse Awareness Relation establishes a fundamental relationship in our universe:

Micro Awareness = \dfrac{1}{scope}

and

Macro Awareness = \dfrac{1}{depth}
or

\dfrac {Micro Awareness}{Macro Awareness} = \dfrac{depth}{scope}

Which essentially state:

The closer awareness is in some way to an entity, the more depth and the less scope it discerns.

The farther awareness is in some way to an entity, the more scope and the less depth it discerns.

(Be careful, this idea of closeness is not the same as distance.)