GRAMMARS OF DECIDABILITY
The Geometry of Our Grammars
Now that we have completed our journey through creating Dimensions of Decidability using Deflation, Operationalization, Serialization, and Competition, we can:
- Discover and enumerate the Dimensions extant in our Language.
- Discover how those dimensions can be combined into Grammars of Decidability.
- Discover how those grammars can be organized into a spectrum that covers every niche of human communication from physical, perceptual, emotional, intellectual, and imaginary – as well as deception.
- Discover that our set of grammars illustrate a hierarchy of patterns in the physical universe – and that our understanding of that pattern and our grammars are very nearly complete.
- Discover that our Language consists of :
- Continuous Recursive Disambiguation in Real Time (Serial Speech)
- Using Some Set of Analogies to Experience (Words)
- Resulting in Transactions (Sentences)
- That produce Contracts for Meaning (Stories)
- Within some Set of Dimensions (Physical, Experiential, Imaginary)
- And that opportunity for Deception (Frauds, Fictions, Fictionalisms) is ever-present.
- But by limiting our speech (prose) to Operational Grammar ( using constant relations between reality, perceptions, cognition, actions, and consequences), or what we traditionally call “Testimony”, all statements are both objectively and subjectively testable, thereby providing extremely limited opportunity for error, bias, and deceit.
- And by performing Due Diligence, for consistency, correspondence, existential possibility, rationality of choice, reciprocity, completeness and coherence;
- We force a Competition for Coherence by which we expose our ignorance and can Warranty our speech is as free of error, bias, and deceit as is possible given our current language knowledge.
Geometry of Decidability
(the via negativa pzzle pcs)
Dimensions Present in our Vocabulary
Next, we can examine our vocabulary and organize the terms into a series of categories.
|WORD| > Name(Noun) > Action(Verb) > Relations > Agreements > Noise Words > Code Words.
And within each category of word we find multiple dimensions.
|Name(Noun)| : Proper(Person > Thing > Place > Idea > Perception(sense) > Emotion(value)) > Common (categorical) > Compound > Pronoun > Clarifier (Determiner/Measure) > Property(adjective) >
|State| State > Event > Action > Experience > Thought
|Person| First > Second > Third > Abstract
|Gender| Female < Young Female < Neutral > Young Male > Male.
|Possession|- Possession (‘s – “apostrophe s” in English) (“Can Own”) > (“Can be owned”) > (Cannot be owned”)
|Number|- Unique > Countable > Collection/Mass(not worth counting) > Uncountable.
|Perception|- Concrete(observable 5 Senses) > Emotions(Feelings) > Ideas(Abstr.)
Or: |Experience| Perceivable > Experience-able > Imaginable
|Action(Verb)| > Action Property(adverb) > Action Clarifier(Phrasal Verbs) >
|Knowledge| Unknown > Believed > Known > Undeniable > Tautological
|Ownership| Undiscovered > Unconvertible > Unconverted > “Homesteaded”(Worked) > Possessed(Fact) > Consensual Property (Agreement) > Normative Property (Habit) > Property Right (Insured by third party) > inalienable(life, memory, imagination, Emotion)
|Possibility| Impossibility > Contingency(Might) > Possibility(Can) > Necessity(Shall).
|Permissibility| Impermissible > Permissible(May) > Obligatory(Must).
|Temporality| Always Been > Has been > is Currently > Will Be > Will Always Be.
|Gain or Loss| Gain < Neutral > Loss
|Decidability| Incommensurable > Undecidable > Preferable > Good > True.
|Relations| Relation (Preposition/Postposition) > Link (Conjunction > Copula ) >
|Agreements| Agreement(yes-no) >
|Noise Words| Noise Words(Expletives etc.) >
|Code Words| code-words(acronyms etc.)
What Can We Learn From Those Dimensions?
A great deal:
- Limited Scales Measurement: We tend to consider only a scale of five, in any dimension which mirrors the accuracy of survey responses: a 1-5 scale is about as accurate as one can get, with 1-3 1-5, 1-7 appearing frequently and with a 1-10 scale ratings always reducible to a 1-5 scale with finer graduation to the high end and lower granulation to the low end. This 3,5,7 scale shows up in nearly all aspects of cognition, such as the number of objects we can independently visualize or numbers one can recall. Usually in the seven plus or minus two range.
- Limited Dimensions To Describe References: There are about as many dimensions in both nouns and verbs: seven. While there are about fourteen dimensions between nouns and verbs, the only complex relationships are:
- Perception (Experience)
But these three sets provide a large set of sensory dimensions for describing our references.
- State, Perception, and Relation function as Weights and Measures:
( … )
- Dimensions of Negotiation: Other than Perception and Relations, the number of dimensions is surprisingly small. And nearly all can be categorized as necessities of
- Negotiation and
- Possession, and
- Weights and Measures.
- Dimensions of Possession: Our language contains an extraordinary dedication of dimensions to possession. Given the dimensions above, please note the following:
- Person, Gender, and Possession are dimensions in our Nouns.
- Ownership, Permissibility, and Gain or Loss are dimensions in our Verbs.
- The degree of Warranty of our meaning is implied not stated.
As we will see later, this emphasis on possession, ownership, and property is necessary for both cooperation and ‘calculation’, and function as the basis of ethics and morality, and our valuation of changes in state of possessions (or interests) the origin of our emotional responses. We are, whether we like it or not, acquisition machines, using language to negotiate cooperation because of the far higher returns on a division of labor than are possibly by individual action.
A Change In Paradigm (Ontology)
Justification an self and knowledge
Contract and others and trade and consent.
Note: For those who have experience with Taxonomies of vocabulary, this categorization is significantly different from Roget’s – and somewhat dehumanizing.
Words: Measurements and Collections of Measurements (Weights and Measures)
The Contractual Constitution of Meaning (Words, Phrases, Sentences)
The Experiential: The Dimensions of Perception (Experience)
|EXPERIENCE| Physical(external intermaterial) > Perceptual (external-internal) > Emotional(internal) > Mental(imaginary) > Social(external interpersonal)
( … )
The Real: Dimensions of Reality
Now, how can we DESCRIBE the universe? With dimensions consisting of constant relations.
Now, we are going to make frequent use of these terms ‘dimension’ and ‘dimensions’. And the most simple constant relation we know of is mathematics: the study of positional relations:
0-Point (Referent)(Identity, anchor referent)(quantity)
3-Object (Ideal Object) (Space)
4-Time (Velocity) (Change)
5 – N – Pure Relations (Concepts/Categories)
6 – N vs. N’ Relations, (Forces) (Equilibria)
7 – N vs. N’ Intermediate Relations, (Symmetries)
8 – N vs N’ relations between symmetries (Paradigms)
9 – (N vs N’)’ recursive hierarchies of symmetries ad infinitum. (Reality)
And we have mathematical techniques for such dimensions.
0 – Correspondence (referents, identity)
1 – Positional names, Arithmetic, Accounting. (counting)
2 – Mathematics and algebra (Ratios)
3 – Geometry (Space)
4 – Calculus, Finance, Economics. (Change)
5 – Algebraic Geometry (Math of sets of constant relations)
6 – Physics (equilibration)
7 – Lie Groups, (Symmetries, Externalities, Future of Economics)
(8 – Grammars)
(9 – Paradigms) (stories) (Semantics)
(10 – Fictions)
(11 – Ideals )
(12 – Dreams)
And that we have discovered mathematical techniques for the preservation of constant relations in increasing layers of complexity ….
The Dimensions of Relations
Dimensions of Meaning: Geometry of Thought, Speech, and Argument
(try to explain)
(how the mathematical dimensions and the verbal dimension and paradigms and stories…. It’s all dimensions)
From any given point, there are an infinite number of vectors.
All thoughts can be represented geometrically.
But like Mandelbrot’s Fractals, they are not calculable by man, only computable by machines.
However, the underlying symmetries (shapes) will be consistent across contexts, for the simple reason that grammars are consistent across contexts (paradigms).
THE DIMENSIONAL GRAMMARS
The Periodic Table Of Speech
|GRAMMARS| Deflationary Grammars < Ordinary Grammars > Inflationary Grammars.
Grammars: Overcoming the Problem of Human Scale (necessary because of computational limitations)
Use of external resources to render commensurable that which is beyond our abilities.
Deflationary Grammars (decidable)
- Logic of Differences (identity)
- The Logic of Continuous Relations, Logic of Sets (categories)
- The Logic of Counting: Counting, Arithmetic, Accounting.
- The Logic of Positional Relations (measurement): Mathematics (all of it), Equilibrium mathematics (constant relations)
- The Logic of Algorithms – Computers, simulations (automation)
- The Logic of Transformations: Physics, chemistry, biology, sentience, reason (transformations)
- The Logic of Reciprocity, Law, Contract (cooperation) and Economics
- The Logic of Science: Science, Reporting, Testimony (testimony)
Ordinary Grammars (practical)
So we can at least include these Ordinary Language grammars.
- Formal or Written
- Ordinary Conversational (in the commons)
- Idiomatic Varies by Region, class, discipline, and occupation.
Inflationary Grammars (meaningful)
- Story (grammar of stories)
- Fiction (grammar of fiction)
Deception Grammars (Under, over, and false loading)
- Intentional avoidance of due diligence
- Bias and Wishful thinking,
Conflationary (Fraud) Grammars (overloading, frauds)
- Pseudoscience ( conflation of magic and technology)
- Psuedo-rationalism (Pilpul and Critique), (Justificationism en Closure)
- Pseudo-mythology (conflation of history and myth as well as wisdom and law, as well as real and supernatural)
- Occult (experiential Fiction)
The Periodic Table of Grammars
Figure 1 The Periodic Table of Grammars
Note: The table is too large for inclusion in this book, in any readable form,
but is available online at https://naturallawinstitute.com/grammars where you can download a PDF version, or order a poster online.
Reorganizing Our Categories of Language
Semantics Are Limited by and Subordinate To Grammars
Now Let’s Look at the Rest of Communication
Now, Just as mathematics consists in the study of constant relations, at increasing numbers of dimensions, we can perform the same analysis for all other forms of communication. And we will see how all our grammars are organized by the very same means – the organization of constant relations. And then how some deflate relations, so me preserve relations, some inflate relations, some conflate relations. And as such we will see how we use these various grammars to communicate the entire spectrum of reality from the existential to the imaginary.
Language – all same enough that they reflect a common set of abilities and limits of the human brain. SVO, SOV, VSO, but in all cases we describe states of subjects or changes in states of subjects, and we combine this little stories into ever increasingly complex sentences, paragraphs and stories, and we weave these stories into paradigms and then into networks of paradigms, and those networks of paradigms and stories provide us with context, and that content lessens the computational cost of composing stories, paragraphs, sentences, phrases, and sub-stories consisting of descriptions of state or changes in state – and attach to those stories some value or other. And therefore assist us in making decisions from the most casual and unconscious to the most deliberative and calculative.
Context and Precision: Ordinary language varies from formal, meaning low context and high precision, to common to idiomatic, meaning high context low precision. The lower the precision the higher the context the more suggestion is created by the speaker and the more substitution is required of the audience.
Dialects. Within languages we create Dialects – regional, class, and occupational. These vary in paradigms, vocabulary, values, morphology and phonology, but most often preserve the same syntax: rules of sentence construction.
Across these dialects, and across all languages and dialects, we have produced various technological variations in grammar (paradigm?), meaning rules of word and sentence construction, which in turn limit the vocabulary, the paradigm, the logic within the paradigm, and the grammar and syntax of statements, sentences, paragraphs, arguments, stories and ever increasing stories within the paradigm.
And Speech itself consists of a hierarchical repetition of increasing complexity:
|Speech| Word > Phrase > Clause > Sentence(Subject + Predicate=Story) > Paragraph(story) > Grammar of Science > Grammar of Narrative > Grammar of Stories(Story) > Grammar of Story > Story, “all the way up”.
So we can organize (or rather we have no choice but to organize) something like a hierarchy such as:
1 – Universal Grammar: recursively limited differences, similarities in all available dimensions.
2 – Dimensional Grammars (Dimensional Semantics?):
Deflationary (real) < Ordinary (experiential) > Inflationary (Ideal) > Conflationary (supernatural)
3 – Languages
4 – Ordinary Language Grammars
5 – Semantics (Paradigms)
6 – Dialects
7 – Idioms and expletives etc.
Anglo Analytic deflationary and scientific as a reformation of law versus continental conflationary and philosophical as a reformation of religion.
Deflationary Literature Markets versus Conflationary Literature Monopolies
( … )
Meaning (Grammars of Meaning?)
THE ART OF SUGGESTION
The Two Faces of Suggestion
( … )
The transfer of knowledge is dependent upon at least ten “supply demand” curves. Such that the contract (exchange) of knowledge is a function of the costs involved in an exchange. In other words, some communication is low cost and some is worthwhile, and some is very costly, and some is prohibitively costly, and some is simply impossible no matter what is done. So transfer of knowledge is one of the most complex human endeavors in no small part because of high causal density with diverse means of increasing costs.
|METHOD| Suggest > Communicate(illustrate) > Explain > Teach > Train(Repetition) > Saturate(Immersion)
|LEARNING| Learns through inference (145+) < Learns through Suggestion(135+) < Learns through Illustration (125+) < Learns through Explanation (115+) < Learns through Teaching (105+) < Learns through Training (95+) < Learns through Immersion (85+) < Learning challenged (85-)
|ABILITY| Same Sigma > .5 Sigma > 1 Sigma(helpful) > 1.5 Sigma > 2 Sigma (Difficult)> 2.5 Sigma > 3 Sigma(~Impossible) > 3.5 Sigma > 4 Sigma(~Inconceivable)
|CONTEXT| Enemies(resisting cooperation) > Negotiation (exploring cooperation) > Discovery (cooperation) > Pedagogy (education) > Court/Jury(dispute resolution)
ie: Cost (Consequence) —>+
|MODEL| Impulsive(emotive) > Intuitionistic(sympathetic) > Reasonable(verbal)* > Logical-Rational(internally consistent)* > Scientific(Externally consistent) > Ratio-Scientific (Internal and external) > Testimonial (Complete)
|PRIORS| Prior Technical Knowledge < Prior Specific Knowledge* < Prior General Knowledge < Limited General Knowledge
|CONTENT| Identical < Near Identical < Analogistic < Novel < Counter Intuitive < Counter Investment < Counter Status(signal) Investment
|TRUST| Suggestibility(False Positive) > Honest-Reasonable(Exchange Positive) > “Dunning Kruger(False Negative)”
|STRATEGY| Seeking to Understand > Seeking to Disagree > Seeking to Falsify > Seeking to Deny* > Denial.
|HONESTY| Intellectual honesty > Intellectual skepticism > Intellectual Dishonesty*.
This (large) set of causal relations, illustrates the difficulty in the range of communication problems Suggesting > Communicating(illustrate) > Explaining > Teaching > Training(Repetition). And illustrates why it’s simply false to say that if one cannot understand it, one cannot explain it. Instead, it is, that all other causal axis being equal, one should be able to explain a phenomenon to a peer. But as the difference in peerage increases the problem of communication even if all participants are intellectually honest
We use different words for pretentious purposes – largely we don’t know better. So let’s clear up the difference between a religion, an ideology, a philosophy, a logic and a science.
(STORY/CHANGE IN STATE/TRANSACTION)
|NARRATIVE(Story)| Name > Change in State > Description > History (Recipe) > Idealism(Substitution) > Fiction(suggestion) > Myth > Supernatural > Occult > Free Association.
War is a scientific not emotional process. It is only the men at the bottom who need inspiration. And it is the foot-soldier at the bottom whose tenacity most determines a battle. So the relationship between the top and the bottom is necessary, and this is why non-martial polities cannot compete with martial polities – we fight together even if we conceptualize differently.
A Religion provides mindfulness – which is increasingly necessary outside of the simplicity of tribal life of hunter gatherers. Mindfulness increases trust and our ability to cooperate peacefully in larger and larger numbers. A religion provides not only decidability on social interactions, but mindfulness so that we can cope with stresses of all kinds in an increasingly uncertain world. A religion relies on an internally coherent set of rules, myths, rituals, and festivals, but its neither logical nor empirical.
( … )
( … )
( … )
( … )
( … )
( … )
– A RELIGION consists of any set of ideas of justification which require belief in, testimony to, or action according to, one or more falsehoods as a cost of inclusion and use.
1) A religion consists of a set of myths and rules the purpose of which is to resist outsiders, and to set limits on behavior or to be treated as an outsider and deprived of opportunity and insurance of the in-group. Hence most religions evolve with the weak, who have no means of competition except resistance and exclusion.
A Belief, or a Set of Beliefs provides an individual or group with a strategy for achieving personal objectives, a set of methods of decidability, and a moral defense (rationalization ) for our behavior if we are criticized.
(…) Myth – (INTERTEMPORAL) Wisdom Literature (in my opinion the proper forum for teaching wisdom) – Inflationary vocabulary, grammar, and reality.
An Ideology provides an emotional incentive to act in favor of political change under democracy. An ideology provides political decidability for interest groups. An ideology relies upon correspondence with a prejudice, shared by a group with self-perceived common interests. It need not be either rational nor empirical, since the purpose of ideology, like religion, is to make logical and empirical criticism impossible – or at least too costly to prosecute.
– AN IDEOLOGY consist of any set of ideas that agitate, motivate, or inspire achievement of political ends under majoritarian (monopoly) democracy. An ideology need not be internally consistent externally correspondent, or existentially possible. It need only motivate individuals to act in furtherance of policy.
2) An ideology consists of a set of ideas the purpose of which is to excite subclasses to act under democracy to obtain political power. Ideologies are used to obtain followers. Likewise followers, follow ideologies. Hence most ideologies if not all ideologies are lower and working class ideologies, and most followers from the lower and working classes.
3) A philosophical system provides criteria for making judgments in the pursuit of preferences. Philosophies are used to obtain peers. Likewise peers seek philosophies with which to pursue preferences together with their peers. hence all philosophies are class philosophies, and most philosophies are middle class philosophies.
A Philosophy provides a coherent JUSTIFICATIONARY system of decidability within a domain of interest. Philosophy relies upon tests of internal consistency we call logical grammars. A Philosophy need be internally consistent, non contradictory, coherent, even if only marginally correspondent to reality. A philosophy answers the questions of preference and good.
In practice it is very hard to claim that philosophy has practiced the pursuit of truth. (more harm appears to have been done by novelists, philosophers an prophets than good, and more good by historians and scientists than harm. We can easily claim that philosophy has practiced the pursuit of choice and decidability. But if we claim philosophy has sought to produce truth we would have a harder time demarcating between science and philosophy. And my understanding of the point of demarcation between science and philosophy is the difference between choice and decidability – or rather the preferable and the good versus the true.
And as you will discover, my understanding is that the velocity of human existential transcendence – meaning the development of human agency both physical, emotional, and intellectual, and both individual and cooperative – is dependent upon the difference between the decidable truth and the practiced falsehoods.
As such I separate the grammars, from the operations, from the testimonies, from the fictions. Meaning that I separate logical grammars of testimony, from operational recipes such as the sciences, from wisdom literature such as histories, from the literature of persuasion and conflict we call philosophies, fictions, and religions.
In this sense while I have combined philosophy, law, science, logic, and grammar into a single commensurable language, you will find that I frequently criticize those who have done all the damage to this world, with little contribution to the good of it. And in that sense I will come across as an anti-philosopher of sorts who has appropriated some of the content of philosophy while excoriating vast categories of it, as dishonest, manipulative, and harmful to man.
– A PHILOSOPHY consists of any set of internally consistent ideas of decidability which justify pursuit of personal preferences or group goods.
If we define philosophy (positive and literary) as the search for methods of decidability within a domain of preference, and
If we define truth (negative and descriptive) as the search for methods of decidability across all domains regardless of preference.
We find that positive or literary philosophy(fiction or philosophy) informs, suggests opportunities, and justifies preferences for the purpose of forming cooperation and alliances between individuals and groups.
We find that negative or juridical philosophy(truth or law) decides, states limits, and discounts preferences, for the purpose of resolving conflicts between individuals and groups.
The Natural Law of Reciprocity, is a negative, descriptive, juridical science, not a fictional literature.
A Fiction (Story)
Now, you wouldn’t assume that there exists a formal grammar to the structure of narratives but there is. And it consists of just ‘changes in state, all the way up.’ Just as reality consists of changes in state of dimensions.
And if we look at Fiction (Stories) we see many permutations of changes in state: nothing more than sequences of changes in state. (re: Vonnegut). And only three endings: Happy, Unhappy, and Tragedy.
|ENDINGS| Happy > Unhappy > Tragedy
And only six paths to combine to achieve those endings:
1) “Rags to Riches” (rise – a rise in happiness),
2) “Tragedy”, or “riches to rags” (fall – a fall in happiness),
3) “Man in a hole” (fall–rise),
4) “Icarus” (rise–fall),
5) “Cinderella” (rise–fall–rise)
6) “Oedipus” (fall–rise–fall)
|PLOTS | Fall-Rise-Fall < Fall-Rise < Fall < |STATE| > Rise > Rise-Fall > Rise-Fall-Rise.
And a number of ( … )
So our language consists of not much more than the names (references) and changes in state of some set of marginally indifferent constant relations, using some combination of physical, emotional, and intellectual senses.
And we can create increasingly complex words that themselves constitute micro-paradigms. And in doing so weave together extraordinarily complex sets of categories, relations, changes in state – where one of those changes in state is our ‘value’ – generally expressed as an emotional response.
- A Story
- A Chapter
- A Sentence
- A Phrase
- A Word
- A Sound
- A Narrative (Story, Recipe)
- A Description (Story) Present
- A Testimony (story) past.
( … )
( … )
A Testimony provides a warranty of due diligence against ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit. A testimony answers questions of liability against falsehood.
- Only sentient beings can make truth claims because only sentient beings can give testimony.
- All truth claims can and must exist as testimony.
- A truth claim can be false (disagreeable)
Testimonial or Complete Science – operationalism.
( … )
A Traditional Order of Habits (or group evolutionary strategy) provides a group with an evolutionary strategy necessary for survival and in the world and competition against others with different strategies. They consist at least, in a portfolio of metaphysical value judgments and carriers (users) of these habits rarely if ever understand or are even aware of, alternatives to these prejudices.
A Normative Order of Habits provides a group with means of preserving the traditional order within the current demographic, social, economic, political, and military context. This set of habits need not be understood, coherent, rationally articulated but merely practiced. They consist, at least, in manners, ethics, morals, and laws.
– MARKET, TRADITION, NORM, HABIT consist of … (Demonstrated results…)
Laws: Commands, Legislations
5) A legal system provides a means of resolving differences so that a group can cooperate in the production of generations, goods and services. Legal systems are used to rule others. But require strength to enforce. Hence most legal systems are the product of the upper classes that rule by force, and make use of scientific, philosophical, ideological, and religious systems to speak to classes while ruling them with law and violence.
( … )
(Record of conflicts settled…)
– NATURAL LAW of RECIPROCITY (Tort), was produced scientifically (empirically) by trial and error, through the resolution of disputes across personal preferences, group goods, norms, traditions, and intuitions, cumulating always and everywhere that decidability is provided by property, and property consists in the demonstrated investment of human action or inaction anything whether genetic, material, behavioral, or informational.
A Discipline or Field of Study (Network of Paradigms)
4) A scientific system provides for making truthful (true) statements for the description of operations (transformations instate). Scientific systems are used to decide, create, invent, and to provide power over nature and man. Hence, science . Hence science is a largely professional or upper middle class philosophy.
A specialization in the division of labor in the market for the production of knowledge. (usually a difference in operations and scale)
- A Demonstration (reality)
- A Recipe (protocol…)
- An Action
- An Input, Output
- A Paradigm in Science or ‘-ism’ in Philosophy, provides a system of decidability in an area of exploration, investigation, and research. Either a network of theories or justifications that are used to make decisions in pursuit of research. Wherever possible I choose the scientific term because it is less likely to have been inflated and conflated. And I have chosen the term paradigm for that reason.
- An Hypothesis
- A Theory(Story, Opportunity, Search Algorithm) – A Test (Warranty) against Impossibility
- A theory of possibility by falsification
- A Law
Science, Physical Science, or Empiricism (deflation) of imagination, but absent operations.
(Search for Laws(avgs) and Operations(causes))
A Science provides a CRITICAL means of decidability across all domains regardless of convention, interest or preference (Philosophy, Norm, Religion, or Ideology). A Science relies in the very least, upon tests of:
- Categorical consistency, i.e. all differences
- Internal (logical) consistency, i.e. all logics (Deflationary Grammars)
- External (empirical) consistency, and (Correlative)
- Existential (operational) consistency,
Under Propertarianism (Testimonialism) it must also include tests of
- Rational consistency (rational choice), and
- Reciprocal consistency (reciprocity of rational choice).
And we require limits.
- Scope consistency (full accounting),
- Parsimony (Deflation), and
- Commensurable Consistency(Coherence).
– A SCIENCE consists of any set of ideas that provide decidability independent of personal preference or group goods, by the systematic elimination of ignorance, error, bias, wishful thinking, suggestion, obscurantism, Fictionalism, and deceit, by the use of measurement and record of actions – demonstrations versus words.
Physics, Engineering, Chemistry, Biology, Medicine, Protocols
Algorithms, Accounting, Mathematics, and Logic
- A Simulation (program)
- An Algorithm (Procedure)
- A Calculation (transformation of inputs into outputs) but with deduction.
- A Balance Sheet
- An Income Statement
- A General Ledger
- A Ledger
- A Journal
- An Entry
- An inventory item.
- A Model (mathematic)
- A Computation (lacking deduction) (information is closed)
- A Formula
– MATHEMATICS consists of a deflationary grammar of decidability consisting purely of competition between positional names under the preservation of ratios providing a single axis of decidability: position, but in N dimensions, providing commensurability between any set of positional relations of any number of dimensions.
The Logics (words)
- A Proposition
- An Axiom
- A Statement
- A Proof (Operations, Cost, Recipe) – A Test (Warranty) of Possibility
A proof of possibility by construction.
( … )
A proof of internal consistency
( … )
– A LOGIC consists of any deflationary grammar of decidability that assists in the falsification by competition of one or more constant relations between states. (Note that one proves nothing logically other than internal consistency, because all premises of external correspondence are forever contingent.)
The Logics. We use the word logic ‘loosely’, I have to get across the difference between the multiple uses of the term:
The Rationalisms (Justificationisms)
- A Justification
- A Statement
- An Argument
Rationalism is often contrasted with empiricism.
The empiricist view holds that all ideas come to us a posterior through experience; either through the external senses or through such inner sensations as pain and gratification. The empiricist essentially believes that knowledge is based on or derived directly from experience.
The rationalist believes we come to knowledge a priori – through the use of logic – and is thus independent of sensory experience.
Rationalism consists of adopting one of these three claims
- The Intuition/Deduction Thesis,
- The Innate Knowledge Thesis, or
- The Innate Concept Thesis.
In addition, rationalists can choose to adopt the claims of Indispensability of Reason and or the Superiority of Reason – although one can be a rationalist without adopting either thesis.
Logic (formal grammar of decidability)
Logic, via-positiva, consists of the use of deflation, organization, and competition to test the survivability of statements) which ( scientifically), consists in the preservation of constant relations in the differences in dimensions available to human action, perception, and experience.
Those constant relations are possible because of a deterministic (non-random) universe – at least at various scales. Conversely, via-negativa, we can say that the function of logic is to eliminate ignorance, error, bias, assumption of knowledge, wishful thinking, suggestion, obscurantism, and deceit from our free associations.
Which I’m sure is a mouthful.
A logic requires at least:
- The assumption of deterministic Universe (constant relations) within the scope(limits) of the context.
- Constant Referents (Names)
- A competition between the properties, relation and values two or more referents.
- Preservation of Constant relations by grammar
- Commensurability (or network of commensurability) of referents
- Transformation Operators
- Comparison operators
- At least ternary logic || Incomparable > Undecidable > Contingent > True(not false) > False (highest certainty is falsehood)
- For proofs, only Binary Logic: Unknown or False > True for purpose of deduction. Note that falsehood has greater certainty than truth.
Arbitrary(Normative) or Descriptive(Necessary)?
Is a logic – a means of preserving constant relations – Axiomatic and Arbitrary in a Meaningful Paradigm,? Or is it Natural Law and Correspondent in an Existential Paradigm?
If descriptive, what dimensions of reality can we identify?
- Logic of Differences (logic proper)
- Logic of Categories of Constant Relations (cumulative differences) (identity)
- Logic of Constant Positional Relations (mathematics)
- Logic of Physical (Natural) Operations (changes in state/time)
- Logic (Operations) of Physical Human Action
- Logic (Operations) of Incentives using Property in Toto
- Logic (Operations) of Cooperation using Reciprocity
- Logic (Operations) of Contingent Relations(Language)
- Logic (Operations) Of Testimony given all of the above. (coherence, scope, limits, parsimony)
A Formal Logic. (I’m going to define formal logic as a dimensionally limited grammar – a grammar which limits vocabulary by limiting semantics).
Formal logic consists of the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property.
In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.
We can identify at least two uses of formal logic:
- The construction of discursive proof (or possibility of construction) or disproof about the world using the logic of internal consistency through exclusive reliance on argumentative closure. Mathematics, Law, and Norms rely upon justificationary reasoning. (Science, like evolution, does not. It relies on survivability whether we can explain the causes or not).
- Philosophical Logic, Rationalism or Justificationism: The use of Textualism (interpretation) for the interpretation of scripture and law (Pilpul, Interpretation). Generally the attempt at closure rather than appeal to the next higher dimension where there is more information. Non contradiction can be seen as a variation of the liar’s paradox.
To interpret legal precedent or legislation without return to the legislature or judge of record – in which case, again, the construction of said sentences constituted a failure of the authors to produce grammatically complete sentences – or the attempt by prosecutor, defense, and judge to create new law.
To interpret Scripture or other Wisdom Literature under the pretext that it consists of law, history, or science, or any kind of truth – in which case, like interpreting the law, we see only a failure of the authors to produce grammatically complete sentences, open to current knowledge, and we seek to create what is not there.
To construct deceptions by appeals to authority by making use of the ignorance of the audience, the malice of the interpreter, and, once again, the failure of the authors to produce grammatically complete sentences (and paragraphs).
Much of our time will be spent falsifying and replacing the ….
Symbolic logic consists of the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two main branches: propositional logic and predicate logic. We can think of modal and propositional logic as …..
Mathematical logic consists in of extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.”—
A Turing, Programmatic, or Algorithmic Logic: The addition of control structure differentiates programmatic logic from mathematical logic. As a consequence the problem of closure increases by the addition of the halting problem.
Logic of Language: The study of the rules of language, the rules of logic and the rules of grammar, and how grammar and syntax function to produce logical statements for the simple reason that what we think of as logic – differences, within a sentence – is reasonably intuitive to us, even if that logic fails us in the comprehension of arguments (and deceits).
Syntax is the study of sentences and their structure, and the constructions within sentences. Syntax tells us what goes where in a sentence. Grammar is the general term referring to the set of rules in a given language including syntax , morphology, phonology, while syntax studies sentence structures.
My preference would be to improve clarity, by redefining grammar as phonology(sounds) and morphology (words), and Syntax for Sentences. So that I could speak of Vocabulary and Syntax. (hmmm….) Because a language consists of vocabulary consisting of morphology and phonology, organized into sentences through syntax. (hmmm….)
Modal Logic – we can think of as the symbolic logic of grammar – qualification or refinement. I think of it as the logic of verb properties.
To discover the operations and therefore universal grammar of human beings through analysis of language. In this sense, the study of such grammars constitutes an investigatory cognitive science.
I rely on cognitive science, (neural networks and the structure of the brain) for most of my work. And so I see logic as nothing more than our ability to determine differences. But when those differences are organized into a language we develop this wonderful thing called grammar: the organization of the flow of information between individuals according to predictable rules.
Language is an interesting problem because it’s serialized and very parsimonious and informationally dense, even if it can easily informationally imprecise, ranging from burdensome low context and high precision, to lazy high context and low precision. Yet our minds produce a continuous stream of possibilities that we must transform into that which can be communicated serially in speech.
Investigation of the brain: The use of language to study of cognitive ability of the human brain – and perhaps all brains, given the vocabulary, and the grammatical and syntactical rules the speaker is capable of.
Investigation of reality: The use of language, including semantics (meaning), vocabulary , grammar, phonology, morphology and syntax to investigate reality. This is the ‘verbal’ and primacy of reason strategy. And it is in contrast with the scientific and engineering investigation of reality, by investigation of actions.
As we will see later on when we discuss the table of grammars, the various disciplines all have produced deflated vocabularies, deflationary grammar, and syntax that identifiably if not predictably reflect reality. Conversely, there exist some disciplines that reflect only fictions. And not surprisingly, those fictions exist largely in the pseudosciences we refer to as social science. So as an empirical judgment it is very hard to suggest that these grammars are fictional or arbitrary, and very difficult to deny that our language – at least Germanic languages – reflect and therefore allow us to represent the various dimensions of reality.
As a side note, I was fairly hostile to the philosophy of language producing any result until I’d read kripke. And I have found that language does reflect reality – because cognitive science, analysis of language, and physical science have shown me so. But because I am principally concerned with the elimination of error, bias, and especially deceit, leaving us only truthful voluntary cooperation and exchange, I remain hostile to it for empirical reasons. Which is the next topic (empirical differences).
Empirical difference between the two …..
Informal Logic: The use of Vocabulary, Grammar, Logic(Logic Cognitive Bias, and Fallacy), Correspondence, Ethics, Morality and Rhetoric for the production and falsification of arguments.
–“Informal logic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive – on some conceptions of logic, informal logic is not logic at all.”—
|Type||Situation||Arguers’ Goal||Dialogue Goal|
|Discovery||Need for Explanation||Find a Hypothesis||Test a Hypo-
|Information||Need Information||Acquire Info||Exchange Info|
|Education||Transfer Info||Shared Understanding|
|Justification||Need to Have Proof||Verify Evidence||Prove Hypothesis|
|Deliberation||Practical Choice||Fit Goals and Actions||Decide Action|
|Persuasion||Conflict of Opinion||Persuade Other Party||Resolve Issue|
|Negotiation||Search for common Interests||Secure Interests||Settle Issue|
|Prosecution||Conflict in Fact||Expose the other Party||Cessation, Punishment or restitution|
|Testimony||Warranty of Due Diligence against conflict||Obtain and preserve unearned premium or discount||Elimination of retaliation, punishment, restitution via truth|
|Deception||Reciprocity, Conflict, Punishment Avoidance||Fraud||Deceive via falsehood|
|Distribution||Undermine Opponents interests||Poisoning the well||Opportunity for increase in conflict|
|Eristic||Avoid argument||Attack an Opponent, or interests||Preserve Conflict|
Table 1 Table of Dialog Conditions and Goals
The Problem of Closure: There Isn’t Any.
Closure. Close or Not Closed (Open). The question of closure. Given a set S, grammar G, and set of operations O, all operations O in that grammar G, upon that set S, will produce a member of that set S in grammar G. In formal logic, it refers to that output set that can be deduced from the given input set. For reasons I won’t go into here, very few systems of operations and values are closed. In fact, only the most reductive (simple) systems can be.
Closure is important for at least these six reasons.
- that arguments or proofs in any simple system (sets, grammar, and operations) must be solved by appeal to a containing system (sets, grammar, and operations) – or rather system using more information than available in the current system. You will see me use the problem of closure to explain testimonial truth, and to undermine philosophical rationalism, just as we have undermined theological rationalism.
- That closure creates one form of symmetry (shape), but that all sets of operations on all sets produce symmetries because of the variations in the sets, and variations in the possible combinations of operations.
- Language is not closed. I hate this non operational term, but “discrete infinity” refers to the property of such things as language to produce an infinite set of discrete sound combinations – at least within sets of paradigmatic assumptions about the world.
- That the mind is able to identify symmetries, and produce paradigms, of ever increasing scales, as long as those scales are reducible – even if thru training – to an analogy to experience that are commensurable within our senses, and where we can compare differences and therefore make decisions with.
- As such while the set of operations possible within the physical universe is limited, there is no limit to what man can understand through the creating of disciplines (paradigms) of commensurability.
- And the principle problem in our development is limiting the difference between our cognitive biases and the state of our knowledge, and those symmetry’s for which we can produce paradigms that are possible and or useful within the universe. But otherwise our ability to understand and manipulate the universe is limited only by our ability to develop means of harnessing the energy to take actions that produce transformations.
Knowledge is never closed because of the cognitive window of action at any given scale of knowledge. As such, Language is never closed. It may be true that we can know the full set of operations possible in the existing universe at each cumulative scale. But, assuming we possess the ability to harness increasing scales of energy, then what we might be able to construct in this universe through though physical, intuitionistic, rational, calculative, and computational means is …. As far as I can tell, not closed.
What is closed, and what is measurable, is the information necessary to cause change in state in the human mind. I am not quite sure, but Nassim Taleb seems to have been struggling to discover this value, although, like me, he has finally come around to warranty rather than measurement – and I think the search is futile at any scale other than the one he has already produced (meaning, logarithmic or big, and therefore economically impossible) if for no other reason than the information sets available to us are not sufficient. Yet when we develop general artificial intelligence we will develop some measure or other of that information. If I had another life to live I might work on that problem. It’s interesting.
So while the volume of information necessary for humans to identify opportunities for changes in state may remain constant, the use of increasingly complex concepts preserves that ability regardless of scale. More on this later.
As such, it is not clear that we will experience any ‘limit’ to cognition as long as – like every other scale of the universe – new symmetries (meaning objects of consideration) never cease to emerge.
Fields, Symmetries, and Generations
Given a six sided die, and the single operation “roll the die”, we can produce a noisy distribution of :
1(x1), 2(x1), 3(x1), 4(x1), 5(x1), 6(x1).
Given two six sided dice, and the single operation “roll the dice and sum the results”, we can produce a noisy distribution of:
2(x1), 3(x2), 4(x3), 5(x4), 6(x5), 7(x6), 8(x5), 9(x4),
10(x3), 11(x2), 12(x1).
The difference between the one-die and two-die distributions is that while the results of rolling one die are equidistributed between 1 and 6, with two dice the results of rolling can produce more combinations that sum to 7 than there are that sum to 2 and 12, and therefor the results are normally distributed: in a bell curve.
We can produce the same results with logic instead of numbers: For example, we can take the two words “Even” and “Odd”, and define two operations: “addition” and “multiplication”. Then apply the operations to all pairs:
Even + Even = Even,
Even + Odd = Odd + Even = Odd,
Odd + Odd = Even,
Even x Even = Even x Odd = Odd x Even = Even,
Odd x Odd = Odd.
(… geometric, scalar vectors … from every point, infinite points….)
And we can produce the same set of results with any grammatically correct operations on a set, given the operations possible on the set; including the set of Ordinary Language using ordinary language grammar. Although, unlike our simple examples using dice, the set of combinations of ordinary language is not closed, and so the number of combinations is infinite.
So any grammar applied to a set, allows us to produce a distribution of results, and a density (frequency) of results.
In mathematics this result set is called a ‘field’. A field consists of all the possible results of a set of operations on a set’s members, that are selected from the range of possible operations on those set members.
So in any set of results there will be a range of very dense, less dense, sparse, and empty spaces in the set’s distribution.
Now those ‘holes’ in the distribution are not constructible with the set and operations available to us. So, not everything can be described using the set with the available operations in every grammar. Conversely, we can create a set of operations describing those symmetries (patterns), whether we are referring to holes or densities.
There are things we cannot say then. But by and large, nearly anything we can say that consists of constant relations between existence, perception, cognition, and action, is possible to say – if we possess the knowledge. And conversely: that which does not consist of constant relations between existence, perception, cognition, and action can be said but not said constructively: meaning operationally. So that is why people resort to those terms that are not operational: to compensate for your lack of knowledge, to compensate for their lack of knowledge, to levy pretense of knowledge when they do not possess it, or to deceive despite possessing that knowledge.
|Estimating| Description > Deduction > Induction > Abduction > Guessing > Free Association.
In fact, the virtue of fields is that they assist us in finding those symmetries – albeit with a lot of work. That’s because some results are neither constructible or deducible from a construction, except by via-negativa trial and error.
(Limits of Deduction)
Symmetries as Externalities
In most if not all of these sets, we will discover symmetries (patterns), including patterns of density and patterns of emptiness, and then patterns of relations between those patterns.
These holes and densities consist of the consequences of the operations we performed on the set of references we’ve chosen. So, for example, when we make purchases with money, and observe the resulting financial and economic data, there are patterns within the consequences of the operation we call ‘exchange’ of the set ‘goods and services’. Those consequences appear as patterns in the financial and economic data – as a pattern of holes, distributions, and densities, that we call price, volume, profit, and loss.
And so for the sake of discussion, I’m going to adopt the term externalities from the discipline of economics to describe those unintended or accidental patterns that emerge from the operations we call ‘transactions’ on the set of ‘goods, services and information’. Meaning that Externalities consist of Symmetries produced by our economic cooperation.
It’s these externalities (for example, losses, and profits) that as a consequence determine the behavior of businesses, then industries, then markets – not the individual transactions.
The Natural World: Generations of Operations
At this moment we do not yet understand the fundamental Forces of the universe. But we have discovered a set of the fundamental Particles that those forces produce. And, of those particles that have mass, we have a fairly deep understanding of the Elements (Matter) in the periodic table of elements, that those particles that have mass produce. We have at least scratched the surface of the Molecules that those elements can combine produce. We have barely scratched the surface of the Organic Molecules that those elements can produce. We have only recently begun to understand how those molecules construct organs of Life. We increasingly understand how RNA and DNA construct life forms, although the complexity of that process is so vast that we can spot only correlations not yet operations. It is questionable how much we understand of sentience and consciousness or speech processing, but an understanding of reason, calculation and computation are available through introspection.
Universe > Forces > Particles > Elements > Molecules > Organic Molecules > Life(cells) > Sentience > Consciousness > Speech > Reason > Calculation > Computation
Assumptions (Metaphysics) > Psychology (Acquisition) > Sociology(Cooperation) > ( Norms > Traditions > Laws) > Markets > Informal Institutions > Politics(formal institutions) > Education(Religion) > Group Strategy(War)
At each stage of complexity, some set of possible operations produces potentials (densities) for yet another set of possible operations, as well as weaker distributions and holes that do not provide opportunities for yet another set of operations. So for the sake of our discussion we’re going to refer to each stage as an Operational Generation.
Operational Generations as Disciplines
The various Sciences (disciplines) mirror these Operational Generations. Each discipline seeks to discover the operations and sets (objects, states) that complete the grammar of the discipline. (Categories, properties, relations, values, and Operations, and Externalities (Symmetries)).
Commensurability Across Grammars
Unfortunately, some of these disciplines are very old – like mathematics – and some are quite new – like genetics. Some are fairly scientific (chemistry most of all) and some are merely storytelling if not outright deceits (psychology and sociology). In mathematics we find archaic (supernatural) terms left over from Mathematical Platonism. In the sciences we use awkward non-operational names for phenomenon and processes – often peoples names. In economics we use the term ‘rents and rent-seeking’ for what is a form of parasitism or corruption. In psychology and sociology the terms are by and large no better than fairy tale fictions with no basis in science whatsoever.
By converting the terminology in each discipline to purely operational prose, we create commensurability across disciplines. And with that commensurability we can rapidly improve the ease of learning them. We can identify that which they claim to understand but do not. And identify what they claim that is outright false.
Operational grammar leaves holes.
Continuous recursive disambiguation resulting in a series of transactions, culminating in a contract for meaning.
In this era, as in prior eras, the world has been converging on common weights and measures: the common languages of science, of technology, of business, of contract of accounting rules, a common trade law – at least at the international level of cooperation. The current financial system of fiat money, central banks, and reserves, allows relative commensurability of worldwide trade.
However, those convergences tend to occur both within and across commercial and legal fields, but only within fields – thereby preserving incommensurability of language across all fields. And within fields they converge on old habits that preserve obscurant language.
SOME OF OUR MODELS ARE WRONG:
THEY ARE DISCONTIGUOUS WITH REALITY
Law (Natural law of reciprocity)
Politics (the production of commons)
Strategy (group competitive strategy)
Religion ( production of commensurability)
Current knowledge ….. my understanding…..
Constant vs contingent vs inconsistent vs non-relations.
Recursive Continuous Disambiguation vs Scale of Set of Constant Relations(density)
Cumulation of association vs falsification of associations
State Persistence vs breadth search, vs depth search
We cannot know the intelligence of distant ancestors.
Planning a series of steps in sequence must emerge – which requires recursion.
Consciousness must emerge, meaning, the ability to compare states.
Cooperation must emerge, meaning, the ability to empathize with intent.
At some point we must develop sufficient computational ability to manipulate our bodies in some way that allows for unambiguous communication, or a means of continuous disambiguation, that is fast enough for one another to make use of in real time, and easy enough for one another to retain.
And at some point, given sufficient computational ability, memory, and state persistence independent of recursion, language must emerge.
At some point the value of such communication much be such that the cost of it is offset by the rewards of it.
And we should see a cliff in history where there is a dramatic change when we did develop those abilities. And we do see it – rather recently.
But language requires a system of measurement. The system of measurement is limited by our senses. And as such meaning refers to a set of measurements, eventually reducible to analogies to human experience.
So while semantic content (measurements) must vary from species to species, grammar (continuous recursive disambiguation) should be universal in the sense that it varies predictably with computational abilities.
We can understand a child, a person with 60IQ, 70IQ and so on, up to 200+ IQ. But as far as I can tell the set of measurements (basis of semantics) remain the same, and all that changes is the scope of the state persisted, the depth of recursion, and the density and distance of relations, and the ability to model (forecast). In other words, simple people are in fact simply ‘more simple’ in the density of content of their semantics, use of grammar, and models (Stories) that they can construct with them.
So universal grammar as a set of computational minimums and efficiencies, should always exist, and human universal grammar as universal grammar limited to human measurements (semantics), does exist. And any organism with sufficient computational (neural) capacity, should develop some means of communication using some variation of universal grammar, and some sense-perception – action dependent semantics.