Showing posts with label Mathesis Universalis. Show all posts
Showing posts with label Mathesis Universalis. Show all posts

Wednesday, 13 December 2017

Is using an heuristic to make a decision logically sound?

By its very definition it is logical - even if that logic may be abstract or incomplete.

Whether it is sound (logically) or not, is determined by what is called a validity test.



Here is a diagram based upon traditional logic. Looking these in a more detailed way:


With an heuristic, its ‘validity’ is solely determined by its usefulness to a purpose. The measure or nature of that usefulness is how effective it is.

Answer on Quora

Sunday, 17 September 2017

Does Division By Zero Have Meaning?



Yes, in knowledge representation, the answer is the interior of a holon.

Ontologies go ‘out of scope’ when entering interiority. The common ontological representation via mathematical expression is 1/0.

When we ‘leave’ the exterior ontology of current mathematics by replacing number with relation, we enter the realm of interiority.

In the interior of relation, we access the epistemological aspects of any relation.

As an aide to understanding - Ontology answers questions like: ‘What?’, ‘Who?’, ‘Where?’, and ‘When?’. Epistemology answers questions like: ‘Why?’ and ‘How do we know?’

In vortex mathematics 1/0 is known as ‘entering the vortex’.

There are other connections to some new developments in mathematics involving what is called ‘inversive geometry’.


Saturday, 9 September 2017

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

Actually, 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

Thursday, 11 May 2017

Is Real World Knowledge More Valuable Than Fictional Knowledge?

No.

Here an excerpt from a short summary of a paper I am writing that provides some context to answer this question:

What Knowledge is not:

Knowledge is not very well understood so I'll briefly point out some of the reasons why we've been unable to precisely define what knowledge is thus far. Humanity has made numerous attempts at defining knowledge. Plato taught that justified truth and belief are required for something to be considered knowledge.

Throughout the history of the theory of knowledge (epistemology), others have done their best to add to Plato's work or create new or more comprehensive definitions in their attempts to 'contain' the meaning of meaning (knowledge). All of these efforts have failed for one reason or another.

Using truth value and 'justification’ as a basis for knowledge or introducing broader definitions or finer classifications can only fail.

I will now provide a small set of examples of why this is so.

Truth value is only a value that knowledge may attend.

Knowledge can be true or false, justified or unjustified, because

knowledge is the meaning of meaning

What about false or fictitious knowledge? [Here’s the reason why I say no.]

Their perfectly valid structure and dynamics are ignored by classifying them as something else than what they are. Differences in culture or language even make no difference, because the objects being referred to have meaning that transcends language barriers.

Another problem is that knowledge is often thought to be primarily semantics or even ontology based. Both of these cannot be true for many reasons. In the first case (semantics):

There already exists knowledge structure and dynamics for objects we cannot or will not yet know.

The same is true for objects to which meaning has not yet been assigned, such as ideas, connections and perspectives that we're not yet aware of or have forgotten. Their meaning is never clear until we've become aware of or remember them.

In the second case (ontology): collations that are fed ontological framing are necessarily bound to memory, initial conditions of some kind and/or association in terms of space, time, order, context, relation,... We build whole catalogues, dictionaries and theories about them: Triads, diads, quints, ontology charts, neural networks, semiotics and even the current research in linguistics are examples.

Even if an ontology or set of them attempts to represent intrinsic meaning, it can only do so in a descriptive ‘extrinsic’ way. An ontology, no matter how sophisticated, is incapable of generating the purpose of even its own inception, not to mention the purpose of the objects to which it corresponds.

The knowledge is not coming from the data itself, it is always coming from the observer of the data, even if that observer is an algorithm.

Therefore ontology-based semantic analysis can only produce the artefacts of knowledge, such as search results, association to other objects, 'knowledge graphs' like Cayley,…

Real knowledge precedes, transcends and includes our conceptions, cognitive processes, perception, communication, reasoning and is more than simply related to our capacity of acknowledgement.

In fact knowledge cannot even be completely systematised; it can only be interacted with using ever increasing precision.

[For those interested, my summary is found at: A Precise Definition of Knowledge - Knowledge Representation as a Means to Define the Meaning of Meaning Precisely: http://bit.ly/2pA8Y8Y

Wednesday, 10 May 2017

Does Knowledge Become More Accurate Over Time?


Change lies deeper in the knowledge substrate than time.

Knowledge is not necessarily coupled with time, but it can be influenced by it. It can be influenced by change of any kind: not only time.

Knowledge may exist in a moment and vanish. The incipient perspective(s) it contains may change. Or the perspective(s) that it comprises may resist change.

Also, knowledge changes with reality and vice versa.

Time requires events to influence this relationship between knowledge and reality.

Knowledge cannot be relied upon to be a more accurate expression of reality, whether time is involved or not, because the relationship between knowledge and reality is not necessarily dependent upon time, nor is there necessarily a coupling of the relationship between knowledge and reality. The relationships of 'more’ and ‘accurate' are also not necessarily coupled with time.

Example: Eratosthenes calculated the circumference of the Earth long before Copernicus published. The ‘common knowledge’ of the time (Copernicus knew about Eratosthenes, but the culture did not) was that the Earth was flat.