What constitutes an explanation?

What should an artificial intelligence like A.s.a. be able to offer us in support of its conclusions or recommendations?  What can I offer students struggling to understand difficult subject matter? (Like quantum mechanics and relativity) What should we expect from Asa, what can students expect from us?

Explanations come in various kinds and at different levels of detail. There are formal-logical, ontological, pragmatic explanations, and explanations in terms of inheritance.

Formal-logical explanations might be in the form of covering-laws, be statistical, or unificationist in nature. For example, a logically valid deductive chain of propositions starting from a set of initial conditions may lead to (explain) a conclusion.

Ontological explanations may have an event explained by another event.  A fire may be the explanation for the presence of  a cloud of smoke.

A pragmatic explanation might explain a plane crash in terms of pilot error or a fist fight in terms of drunkenness.

Property inheritance may serve to explain something.  Socrates died because all human beings die and Socrates was a human being.

Level of detail is important.  We would explain a decline in the stock market in terms of recent national news events but not in terms of the interaction of quarks and gluons. We might be satisfied to know that smoking caused a case of lung cancer or we might want the detailed biochemical mechanisms involved.

Patterns of or patterns in

While considering the possibility of different degrees of nothingness Robert Lawrence Kuhn suggested that one might have no physical reality but still have a Platonic world of mathematical entities existing, things like numbers, equations, shapes, etc. (Closer to Truth, PBS, 24 May 2016) If mathematics is simply the science of patterns this doesn't seem likely. (Resnik, Mathematics as a Science of Patterns, OUP, 1997) You need to have something physical that you can then have patterns of. Patterns don't exist if the underlying fabric doesn't exist. (Synthetic or extrapolated patterns need not exist in the real world however.  See my blog of 18 Feb. 2016 for examples.)

Asa's knowledge of the world

"Knowledge is a particular way of being connected to the world, having a specific real factual connection to the world: tracking it." (Nozick, Philosophical Explanations, Harvard University Press, 1981) This is just what Asa H does.

AI education curriculum, output sequences

Asa H typically deals with far more inputs then outputs.  Typical output primitives are like those listed in my 1 April 2013 blog. A curriculum for learning more complex output sequences might then be:

1. learn to go fetch an object (perhaps identifiable by color or a beacon or gps location)
2. learn to grasp, lift, and carry an object (perhaps to some target location)
3. learn to group a number of objects together (at some location)
4. learn an orderly grouping of objects, one at a time, counting as you go
5. remove objects from a group, one at a time, counting as you go

In some cases odometry is useful. 1 through 3 have been done with Lego robots.  All 5 have been done in simulations.

You can't directly transfer what's been learned to new (significantly different) robots and environments.

Aristotle's 10 categories as Asa H concepts

In the Organon Aristotle claims to enumerate all of the possible kinds of things that can be the subject or predicate of a proposition.
1. Substance: This category would include as components all of the objects Asa learns to identify.
2. Quantity: This would include as vector components  distances, weights, and durations that Asa observes.
3. Quality: Asa's colors, tastes, temperature, etc.
4. Relative: knowledge, size, near, far
5 Where: gps and beacon locations
6. When: time, date
7. Attitude: rise, sit, lie
8. Having: a load for example
9. Doing: move, push, carry, lift
10 Being affected: to feel force, acceleration, damage

Asa's gestalt

"Gestalt psychology is a theory of sensation which suggests that we are primarily aware of organized wholes of our environment and not of the irreducible elements into which these wholes might in theory be analyzed." (The Blackwell Dictionary of Western Philosophy, Blackwell, 2004, pg 282)
Asa H 2.0 light, for instance, reacts to a group of NM input features at a time. (see my blogs of 10 Feb. 2011 and 14 May 2012) In the case of visual (image) input NM can be quite large.

More cognitive primitives

Lakoff and Nunez believe that human style reasoning requires:

prototypes, sets of common properties or examples

image schemas for spatial relations, things like an above concept, contact or touch concept, a support concept, a container concept with inside, outside, and boundary, a motion, path, goal schema, in, out, to, and from schemas

conceptual frames, the knowledge of sets of different steps/processes that achieve the same result

metaphor, perhaps as common correlations and polysemy

blends, the combining of several concepts

(see Where Mathematics Comes From, Basic Books, 2000, page 121)
I want to try to give my artificial intelligence A.s.a. H. these capabilities in order to allow it to do more humanlike reasoning. (Asa currently has a number of them of course.)

Mathematical platonism

While I agree with something like Cockshott, et. al. and Lakoff and Nunoz's accounts of the origins of mathematical concepts (see Computation and its Limits, Oxford University Press, 2012, chapter 2 and Where Mathematics Comes From, Basic Books, 2000)  I do believe that mathematical entities exist fully independent of the human mind or life.  I believe that mathematics is, among other things, a science of patterns, and patterns exist.  (see M. D. Resnik, Mathematics as a Science of Patterns, Oxford University Press, 1997) We can be talking about patterns of anything, patterns in our sensory inputs if nothing else. (Asa H builds concepts from these.) If anything exists then patterns may exist in it.

Mathematical pluralism

Scientific pluralism should apply to mathematics too. There is not one kind of geometry, there are many: Euclidean, non-Euclidean, projective, inversive, differential... There is not one set theory, there are many, each defined by different axioms.  There is not one formal logic, there are many: propositional logic, predicate logic, spatial logic, temporal logic, second order logic, ...  There is not one system of mathematics, there are many. (See Where Mathematics Comes From, Lakoff and Nunez, Basic Books, 2000 and Complementarity in Mathematics, Kuyk, Reidel Publishing, 1977)

Subitizing

I have added a subitizing neural network as a preprocessor for Asa H.

Asa H is sentient

My artificial intelligence A.s.a. H. is sentient according to the Merriam-Webster's definitions:
Able to feel, see, hear, smell, or taste
Responsive to or conscious of sense impressions
Aware
Finely sensitive in perception or feeling
Asa H does all of these when interfaced with Lego NXT/EV3 robots. It is also consistent with Clark's detailed theory of sentience (Austen Clark, A Theory of Sentience, Oxford University Press, 2000).

Asa H's concepts

Asa has occasionally formed concepts involving retrocausation and top-down causation.  I have experimented a bit with ways of blocking/discouraging these, or other concepts. Alternatively we can keep them, reconceptualizing reality.

Simple parallel computing again

Neural networks are especially hard/slow to train.  Rather than training a single network having m inputs and n outputs one can instead train, in parallel, on n computers, n networks each having the m inputs but each having only one of the outputs.

Asa clustering

Asa H consists of a hierarchical memory assembled out of clustering modules and feature detectors.  In typical Asa H light implementations (see my blogs of 10 Feb 2011 and 14 May 2012) clustering is performed on vectors having both input and output components.  One can add some discrimination by also clustering based on inputs alone and outputs alone. Usually there are far more inputs than outputs however.

Semantic engine

Floridi has proposed a two-machine metaprogramming architecture to solve the symbol grounding problem and give an artificial agent semantics.  (Luciano Floridi, The Philosophy of Information, Oxford University Press, 2011, pages 166-171) There looks to be some similarity to Asa H and to my older A.s.a. F. architecture. Floridi assumes a society of such agents inter communicating with each other, again as with Asa F and Asa H. I think I may code up a minimal implementation of his two-machine agent and try it out, in keeping with scientific pluralism. I want to see if it does anything that Asa H doesn't do.

Some history

In my "X files" I have a copy of Frank Tipler's book The Physics of Immortality (Doubleday, 1994).  On page 192 Tipler says "If the mathematics required to describe reality is sufficiently simple, then Gödel's Theorem will not apply..."  I had had this same idea in the late 1960s. Perhaps the ideal theoretical physics would not be subject to Gödel's limitations, something along the lines of Presburger arithmetic or propositional logic.  I had been accepted for graduate study at New York University (the Courant Institute in lower Manhattan) and had been assigned a faculty advisor.  I asked that I be allowed to take a math course on formal logic along with my physics courses. When this was refused I decided not to attend NYU and my career went off in a different direction.  The rest, as they say, is history.

Asa H learns/discovers sticky/tacky

With the added ability to measure pull as well as push forces Asa H has learned the concept:

sticky/tacky = (gripper motor close, feel push force, gripper motor open, feel pull force)

as contrasted with:

non stick = (gripper motor close, feel push force, gripper motor open)

The availability of sensors influences what concepts will be acquired/defined.

Asa H, being conscious of

Bertrand Russell said "Consciousness: a person is said to be conscious of a circumstance when he uses words, or images of words, to others or to himself, to assert the circumstance." (Collected Papers of Bertrand Russell, vol. IX)  My artificial intelligence Asa H did just that, for instance, when it suffered a collision and reported it to me in natural language, "collision." See chapter 1 of my book, Twelve Papers, www.robert-w-jones.com, Book.