Semantic Languages…
The evolution of Semiotic languages and tools for Semantic Abstraction
abstraction
/əbˈstrakʃ(ə)n/
a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal, real or concrete signifiers, first principles, or other methods
semantics
/sɪˈmantɪk/
the study of meaning
general semantics
the meaning or relationship of meanings of a sign or set of signs, especially: connotative meaning
“Logic and mathematics are nothing but specialised linguistic structures”…
- Jean Piaget
Linguistics [1] is the scientific study of language and its structure. Semantics (meaning), grammar, sounds, and social context.
Local and International Languages — natural & constructed — have the capacity to evolve [4] as new meaning emerges through the plasticity of the spatial structures of thought — The Geometric Mind — to respond and adapt to an ever-changing fitness landscape.
A capacity to bring a Sense of Coherence to complexity.
Natural languages are the primary means by which humans communicate using signs and symbols. Language is a system of signs that are used to convey meaning.
Mathematics is a universal language [6] for uncovering patterns of thought [8] and relationships in our Material World — Verstand.
Patterns [9] enable us to understand by rules and compress & simplify the complexity of the Material World.
Calculus is the language of change.
Calculus comprises two functions that are the inverse of each other (i.e. differentiation and integration).
To interpret, simplify and understand by rules complexity, differentiation is the process of finding the rate (a rule) at which a function changes with respect to its input variables. It is the process of calculating the derivative of a function. It is a language that enables us to zoom in and break down complexity into smaller parts.
Integration (the inverse — the anti-derivative) allows us to recover the original function from its derivative. It is a language that enables us to zoom out and look at the sum of the parts.
Calculus (a form of Semiotics) is an example of how humans use semiotic signs to derive meaning and bring a sense of coherence to complexity.
Signs simplify complexity and enable us to abstract the World. Comparisons then can be made between these spatial structures of thought — representations — and states of transformation in meaning.
Computation is a suite of global languages — software — and — machines (hardware)– mechanical, electronic, & quantum — that can assist with the abstraction [10] of our Material World and mechanise the comparison of representations & states of transformation of semiotic signs.
Automating Verstand — a fundamental form of human thinking and reasoning — to create, represent, arrange, and manipulate abstract ideas through rules of understanding.
Classical Computation [10] is anchored in the language of the Symbolic, Algorithmic and Deduction.
Machine & Deep Learning is anchored in the language of the Structural, Statistics, and Induction.
The High Dimensional mechanisation of Rules of Abstraction ( Verstand) – Generalisations – Patterns of Thought.
Semiotic Sign Machines that apply Syntax – Reasoning Engines.
Deductive and Inductive Reasoning are abstract (i.e. Mental World) forms of Inference.
Abduction is the process of forming an explanatory hypothesis for observed & experienced phenomena (observer & observed — semiotics). It is the only logical operation that introduces a new idea by using inference-based or incomplete information to draw a conclusion (Material World).
Induction is the process of generalisation (reductionism), which is based on a sufficient number of specific observations or examples to determine a value. It is a combination of logical processes but is also dependent on intuition and a hypothesis (combines Material World + Mental World).
It is probabilistic in nature, given it is confronted by the complexity, uncertainty and emergent qualities of our Material World. The limits of observation (i.e. finite phenomena) simply cannot entirely eliminate all uncertainty (e.g. Knightian Uncertainty). It, therefore, remains a probabilistic-based explanation based on the available evidence.
Deduction is a form of logical reasoning (i.e. Formal semiotics of Abstraction) that involves drawing conclusions from premises or assumptions (axioms) that are assumed to be true (Mental World).
It involves a process of logical inference that moves from general principles or axioms to specific conclusions, which are capable of generating certain knowledge or truths.
The conclusion is necessarily implied by the premises or assumptions
Geometric Deep Learning [11b] enables us to uncover higher-dimensional representations and states of transformation in semiotic signs (meaning), thereby compressing & simplifying Complexity.
Graphs [12a] are anchored in the language of relationships of meaning and changes in meaning (states of transformation).
Computation enables us to shift our perspective of reality —from digital to analog — from discrete to continuous — from mathematics to computation [10] and processes of transformation.
Physics is the universal language of symmetries.
Symmetries – Invariants in Mathematics – in our Material World enables us to uncover Ground Truths.
Through relationships – they compress and simplify complexity — (algorithms, heuristics) — inference & abstraction as forms of reason – and are at the core of logic.
Emergence is breaking those Symmetries [13b].
Logic is the language of Rules of Inference [13] in our search for certainty [14] and order — Inductive (Statistical, Probabilistic and High Dimensional ) and Deductive (Symbolic — Deterministic — Axiomatic — Low Dimensional).
According to US 20th Century Philosopher Charles Sanders Peirce:
“Logic will here be defined as formal semiotic”
– forms of signs & symbols
All our thoughts are in Signs, and Inquiry is an inference process to make sense of and derive meaning from these signs that exist throughout the World.
“Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry[16]”…
- Charles Sanders Peirce
In the 21st Century, we now have a portfolio of Languages — Linguistics — Logic – Physics — Mathematics — Computation — that can assist with the Semantic Abstraction of an emergent complex Material World.
“The limits of my language mean the limits of my world”…
- Ludwig Wittgenstein
Footnotes:
[1] — The key to language is universal psychology, not universal grammar — https://theconversation.com/the-key-to-language-is-universal-psychology-not-universal-grammar-144220
[2] — The blind spot — It’s tempting to think science gives a God’s-eye view of reality. But we forget the place of human experience at our peril — https://aeon-co.cdn.ampproject.org/c/s/aeon.co/amp/essays/the-blind-spot-of-science-is-the-neglect-of-lived-experience
[3] — Economics in Nouns & Verbs — https://arxiv.org/abs/2104.01868v2
[4] — The end of Ambiguity — LogLan — Logical Language — https://podcasts.apple.com/au/podcast/lexicon-valley-no-33-the-end-of-ambiguity/id500673866?i=1000204773588
[5] — Same Action, Different Meaning: Neural substrates of Semantic Goal Representation — 2021.04.18.440307v1
[6] — How natural is numeracy? — Where does our number sense come from? Is it a neural capacity we are born with — or is it a product of our culture… — https://aeon-co.cdn.ampproject.org/c/s/aeon.co/amp/essays/why-do-humans-have-numbers-are-they-cultural-or-innate
[7] — Consciousness and the Philosophy of Signs: How Peircean Semiotics Combines Phenomenal Qualia and Practical Effects — https://ndpr.nd.edu/reviews/consciousness-and-the-philosophy-of-signs-how-peircean-semiotics-combines-phenomenal-qualia-and-practical-effects/
[8] — Mathematics as the Science of Patterns — Mathematics as the Science of Patterns — https://www.maa.org/book/export/html/116188
[9] — The Power of Patterns — https://richardschutte.medium.com/the-power-of-patterns-e1dc4c2352aa
[10] — Foundations of Computer Science — http://infolab.stanford.edu/~ullman/focs.html — Computer Science: The Mechanisation of Abstraction — http://infolab.stanford.edu/~ullman/focs/ch01.pdf — and — How Aristotle Created the Computer — by Chris Dixon — https://a16z.com/2017/08/01/how-aristotle-created-the-computer-atlantic/-and — Geometrical Thinking Offers a Window Into Computation — https://www.simonsfoundation.org/2021/04/07/geometrical-thinking-offers-a-window-into-computation/--and--Abel Prize celebrates union of mathematics and computer science — The work of winners László Lovász and Avi Wigderson underpins applications from Internet security to the study of networks — https://www.nature.com/articles/d41586-021-00694-9
[11] — Geometric Deep Learning — https://geometricdeeplearning.com
[12a] — Exploring complex graphs using three-dimensional quantum walks of correlated photons — eabc5266
[12b] — Peirce’s Theory of Signs — https://plato.stanford.edu/entries/peirce-semiotics/
[13] — Inference, Truth & Validity — https://users.cecs.anu.edu.au/~jks/LogicNotes/inference-truth-and-validity.html
[13b] – https://www.sciencemag.org/news/2020/03/philip-anderson-legendary-theorist-whose-ideas-shaped-modern-physics-dies#:~:text=In%20essence%2C%20the%20symmetry%20of,zero%E2%80%94expels%20a%20magnetic%20field.
[14] — In Search of Ground Truths — https://richardschutte.medium.com/in-search-of-ground-truths-3817ce821572
[15] — The Complexity Void — https://richardschutte.medium.com/unbundling-complexity-503c77f0b261
[16] — Charles Sanders Peirce — Theory of Inquiry — truth-pragmatic..
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