Logic as a dynamical system?

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This thread is a shoot-off from this thread.

Assuming some relation between human language and logical reasoning, how would this relate, let's say, to the arrival and evolution of logic in human and animal psychology?

I would presume that some logic, for example classical logic, can be more or less 'in harmony' with some particular aspect of human neural wiring, viewed for simplicity as as a neural network.

From such a vantage point, it would seem natural to assume that a neural network (or the human) could preferentially choose to 'select'/utilize the logic that generally runs the smoothest on his/her particular wiring, in the largest number or most important kinds of instances of usage.

The 'final' neural wiring in a human being clearly results from a balance between genetics and developmental processes early in childhood/life, meaning it would probably be really different between humans; this could be seen as different basins of attraction in the state space.

Is anyone here familiar with such lines of research or any other similar 'applied mathematics' approaches to using mathematical modelling to study (human) logic as a naturally evolved phenomena?
 
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  • #2
BillTre
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I would think that evolution would have selected for brains that are in sync with the events in the world around them.
This should result in the evolved brains having the ability to use logic to deal with those events in world in which they exist, if the logic is in sync with that world.

Can't say I know of any research on this.
I Googled "modelling evolved cognitive logic" and got some hits, but I know nothing of this field.
 
  • #3
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I would think that evolution would have selected for brains that are in sync with the events in the world around them.
Agreed.
This should result in the evolved brains having the ability to use logic to deal with those events in world in which they exist, if the logic is in sync with that world.
Disagreed. The major function of the brain is hardly to carry out logical reasoning, but instead seems to be to create a model of the experienced world: this modelling process seems to be capable of being done in a large variety of ways, logic just being one way which might be useful in particular circumstances for particular tasks.

This can be backed up empirically seeing that neither animals nor humans in general act or think logically in the large majority of the time, certainly not without social conventions limiting their baser instincts; any strict adherence to logical reasoning is very much a learned behaviour.

If animals are just able to respond to stimuli according to randomly programmed responses, the correct response-program combinations will survive and the others won't; programs and responses can probably also be in competition with each other within single animals.

This means that the most important programs will overrule most other responses and/or most or all responses even end up being stimulus-intensity-dependent. In either case, surviving programs will get made more efficient over time, becoming more accurate and probably more automated i.e. intuition.

Almost all truly essential procedural knowledge for survival is automated by some physiological function (e.g. autonomous nervous system, hunger mechanism, sex drive, etc); this possibly happened completely outside of rational cognition.

Cognitively speaking, adherence to logic in practice for survival of any social animal such as a primate among other primates is actually only partially necessary, namely in order to adhere to group norms, i.e. rote memorization and imitation tend to be sufficient forms of reasoning in order to function in a group.

Nothing described so far has required proper logical reasoning yet. If an animal models some (aspect of some) phenomena in such a manner that he can do something of great benefit directly obvious to onlookers, it could become a new form of group behaviour through imitation.

If an animal however just models some (aspect of some) phenomena abstractly for himself such that it can be reduced to some non-obvious logical rule which applies generally, in a group setting he might have to convince the others of the idea and/or its utility; depending on the temperament of the rest of the group and the perceived audacity of the idea they might just end up killing him.
 
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I would presume that some logic, for example classical logic, can be more or less 'in harmony' with some particular aspect of human neural wiring, viewed for simplicity as as a neural network.
The fact that we have no idea how are the subjects of logic reasoning represented on our neural network makes this part entirely speculative.

a large variety of ways, logic just being one way
In regards of NN functions you (somebody) has to prove that this distinction is not baseless.
Honestly, I think this distinction IS baseless (in regards of NN functions). My opinion is, that what makes the difference is the social functionality, not the underlying neural networks. Without the need to transfer/communicate there is no logic, but only ... complex impulses? A bit hard to describe something what is exactly the 'non-described'.
People often 'communicates' with themselves too. But often not.
 
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  • #5
Klystron
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Consider the forms of human speech mentioned in this thread. Putting aside the original assumption for the moment which speech mode can be modeled by dynamical systems [definition required]:

Spoken language: collection of physical processes, measurable, reproducible, dynamic yet well documented. Can be artificially generated.

Written text: even larger space, defined symbol sets, reproducible, documented almost by definition. Easy artificial generation.

Sign language: contains most of spoken language attributes minus sound, reproducible, dynamic, visual recording. Artificial generation.

Mental language (Thought): despite research into so-called "thought controlled systems" and considerable abstract modelling, classification into reproducible physical processes at early stage. Not artificially generated. Inferential data available such as recording eye movements, micro-tremors and other measurable variations in recorded spoken language, kinematics and so-called body language.

Strong relationship indicated between spoken language and mental and sub-verbal [needs citation!]. How to prove or falsify that human subject "thinks in natural language", "thinks in mother tongue"? [Inference: computational-linguistics offers physical inroads to thought process. Reproducible TBD.]
 
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The fact that we have no idea how are the subjects of logic reasoning represented on our neural network makes this part entirely speculative.
There are multiple ideas, the strongest seeming to be the so called X-bar structure from in biolinguistics; there are by now even experimental searches for biological/neural correlates of X-bar underway.

Here is a recent dynamical systems based biolinguistic theory by one of the leaders of the field: Piatelli-Palmarini et al. 2015, Linguistics and some aspects of its underlying dynamics
Abstract said:
In recent years, central components of a new approach to linguistics, the Minimalist Program (MP) have come closer to physics. Features of the Minimalist Program, such as the unconstrained nature of recursive Merge, the operation of the Labeling Algorithm that only operates at the interface of Narrow Syntax with the Conceptual-Intentional and the Sensory-Motor interfaces, the difference between pronounced and un-pronounced copies of elements in a sentence and the build-up of the Fibonacci sequence in the syntactic derivation of sentence structures, are directly accessible to representation in terms of algebraic formalism. Although in our scheme linguistic structures are classical ones, we find that an interesting and productive isomorphism can be established between the MP structure, algebraic structures and many-body field theory opening new avenues of inquiry on the dynamics underlying some central aspects of linguistics.
Here is a decade old review by Chomsky of the field of biolinguistics: Chomsky 2007, Of Minds and Language
Abstract said:
This article reviews, and rethinks, a few leading themes of the biolinguistic program since its inception in the early 1950s, at each stage influenced by developments in the biological sciences. The following also discusses how the questions now entering the research agenda develop in a natural way from some of the earliest concerns of these inquiries.
As @Klystron makes clear, there is much more data available than many would like to admit.
In regards of NN functions you (somebody) has to prove that this distinction is not baseless.
Honestly, I think this distinction IS baseless (in regards of NN functions).
There is clear empirical evidence for a large degree of human reasoning to consist of deductively invalid reasoning forms such as pure guesswork, mimicry, deception, etc. The relation between human reasoning and some biological faculty of language seems obvious; this should also admit some relationship to logic.

It's actually only a small step from identifying a biological correlate of X-bar to directly linking this correlate/substrate to network theoretic proporties of the human NN such as weights, clustering, etc. (literally mountains of empirical data available which needs to be fitted). Theoretically this might then be directly related via a dimensionless group identification to parameters in the differential equations of the NN.
My opinion is, that what makes the difference is the social functionality, not the underlying neural networks.
You need both: social functionality is a/the function of the machine, not the machine itself; without the machine there is no social functionality.
Without the need to transfer/communicate there is no logic, but only ... complex impulses? A bit hard to describe something what is exactly the 'non-described'.
People often 'communicates' with themselves too. But often not.
Elaborate.
 
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  • #7
Klystron
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Thanks for the texts. I'm bogged down around page 8 in 'Pia-Pal' which I noticed is referenced by Chomsky. I need to read both texts again when I'm fresh. The level seems to jump to the quantum scale then up into X-Bar faster than I can keep track. As usual I argue in my mind with Chomsky but enjoy his writing, insights and ideas.
 
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To come back to this point:
I would think that evolution would have selected for brains that are in sync with the events in the world around them.
From a control theory perspective there are two options, namely open-loop controllers and closed-loop controllers.

Processors are built top-down by engineers based on an open loop design, i.e. their logical processing is independent of their output: in other words, the output does not need to be checked by the processor regardless of the question whether or not their output is correct. This means three things: a) the processors needs to be engineered to function extremely precise in order to function error free, b) the engineer handpicks/selects those produced processors that do not produce errors and c) that machine learning is impossible for such a system.

Brains in contrast seem to have been built bottom-up by nature based on a close loop design, with multiple feedback loops, i.e. their "processing" is very much dependent upon what they output, i.e. behavior, since there are consequences and reciprocal actions to behavior which are directly fed back into the system, i.e. the organism learns. This also implies three things: d) such a design based on feedback would not need to be highly precise in order to function accurately, e) be able to reliably respond to its environment even when there large variations and uncertainty, f) above two properties mean such a design would be selected for by nature.

It goes without saying that feedback from this closed-loop design is exactly why NN are able to adjust their own parameters and engage in machine learning.
 
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  • #9
BillTre
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Brains in contrast seem to have been built bottom-up by nature based on a close loop design, with multiple feedback loops, i.e. their "processing" is very much dependent upon what they output, i.e. behavior, since there are consequences and reciprocal actions to behavior which are directly fed back into the system, i.e. the organism learns. This also implies three things: d) such a design based on feedback would not need to be highly precise in order to function accurately, e) be able to reliably respond to its environment even when there large variations and uncertainty, f) above two properties mean such a design would be selected for by nature.
Feedback loops like this are rampant through biology at all levels.
Similar feedback loops can be found in molecular interactions, in cells and cellular components, in the simple neural circuits found in many invertebrate nervous systems and well as in other kinds of biological control systems like hormones and parts of the nervous system that interact with them.
 
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Feedback loops like this are rampant through biology at all levels.
Similar feedback loops can be found in molecular interactions, in cells and cellular components, in the simple neural circuits found in many invertebrate nervous systems and well as in other kinds of biological control systems like hormones and parts of the nervous system that interact with them.
Exactly my point. Regulation in physiology, immunology and neurophysiology is all about achieving a dynamic balance between positive and negative feedback loops. These feedback loops do not merely occur at one organizational level but also work across domains, from molecular to organ level.

It also seems pretty clear that not all feedback loops lead to conscious awareness, since most of these systems obviously do not seem to be conscious. Even stronger, the entire peripheral nervous system, which even has direct reflex loops between sensor and effector systems, and a large part of the central nervous system, namely the cerebellum, do not seem to be conscious at all.

Therefore the real question seems to be: how do feedback loops lead to conscious awareness? A researcher over at the Max-Planck Institute for Brain Research, prof. dr. @Danko Nikolic, seems to have actually found an answer. Nikolić has as far as I can tell a very solid mathematically grounded theory called practopoiesis. Here is an open access link explaining it:

Nikolić 2015, Practopoiesis: Or how life fosters a mind
Abstract said:
The mind is a biological phenomenon. Thus, biological principles of organization should also be the principles underlying mental operations. Practopoiesis states that the key for achieving intelligence through adaptation is an arrangement in which mechanisms laying at a lower level of organization, by their operations and interaction with the environment, enable creation of mechanisms laying at a higher level of organization. When such an organizational advance of a system occurs, it is called a traverse. A case of traverse is when plasticity mechanisms (at a lower level of organization), by their operations, create a neural network anatomy (at a higher level of organization). Another case is the actual production of behavior by that network, whereby the mechanisms of neuronal activity operate to create motor actions. Practopoietic theory explains why the adaptability of a system increases with each increase in the number of traverses. With a larger number of traverses, a system can be relatively small and yet, produce a higher degree of adaptive/intelligent behavior than a system with a lower number of traverses. The present analyses indicate that the two well-known traverses – neural plasticity and neural activity – are not sufficient to explain human mental capabilities. At least one additional traverse is needed, which is named anapoiesis for its contribution in reconstructing knowledge e.g., from long-term memory into working memory. The conclusions bear implications for brain theory, the mind–body explanatory gap, and developments of artificial intelligence technologies.
 
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Thanks Buzz, fixed it.
 
  • #13
Klystron
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Located another human speech mode to consider: tactile.

Consider the Braille alphabet and applications. This device appears in a thread concerned with teaching visually impaired science students.
3D-print a spacetime diagram

See also
http://sahyun.net/projects/3Dprint/index.php
This device raises metal cylinders in coded sequences read by touch. Other devices show or transmit graphs and figures. Consider HTML or any tactile code designed to be touch (or pointer) activated.
 

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