Just because mathematics is constructed for scale independence, does not mean any theory that corresponds to reality can be true without limit. Mathematics is only scale independent in measurement, there is nothing we can find in the universe that is scale independent for mathematics to measure.
Source date (UTC): 2017-10-10 12:41:00 UTC
—“My question concerns technical and scientific language rather than colloquial language: I would like to ask if there is any inclination in English to give the words class and category more or less different meanings or shades of meaning, or are they completely interchangeable in all kinds of use?”— From Elsewhere You CLASSIFY things that exist (Science – referents that exist into a hierarchy) whose organization doesn’t change, and you CATEGORIZE ideas (Philosophy – referents that have meaning into a list) because they can change. So classify(things, hierarchy or order, relatively invariant), vs. categorize(concepts, terms, that might be categorized differently in different contexts). So just as english words have origins in german(commoners, farmers, craftsmen), french(nobility, ruling class, wealthy), Latin and Greek(scholarly or educated classes), English (like all european languages) uses specialized vocabulary for mathematical, philosophical, political/Legal, and scientific classes of vocabulary. English is very ‘precise’ in its use of sets of terms the same way that german is precise in its precisely descriptive terms. Now, do uneducated people conflate terms? All the time. In fact educated people do all the time as well. My favorite examples being the conflation of mathematic (axiomatic), philosophical(rational), and scientific (theoretic), terminology. It’s not uncommon to hear someone make an argument with terms from math, philosophy, and science without having the faintest idea that the terms in each limit the possible properties of argument. For example, True in math and logic is binary(Deductive and Necessary). In philosophy it can be binary(non contradictory), in law it’s ternary(True false and undecidable), in and in science it’s multivalued with False being the only certainty, and truth being little more than an ordinality by triangulation). If someone disagrees with you on usage you can correct them. 😉
—“What do believe is the qualitative difference between human and animal language?”—Bob Robertson As far as I know animals do not possess language, it only exists within humans. All other creatures merely manage to communicate. Charles Hockett (1967) introduced a generally accepted check list for language, a set of features that all human languages possess. His seven key properties are: 1 – productivity (the ability to create and understand new utterances): system which makes it possible to construct an unlimited number of sentences from a limited set of rules. 2 – arbitrariness (when signs/words do not resemble the things they represent), 3 – displacement (the ability to refer to the past and to things not present), and 4 – duality of pattern (the combination of a phonological system and a grammatical system), 5 – interchangeability (the ability to transmit and to receive messages by exchanging roles), 6 – specialization (when the only function of speech is communication and the speaker does not act out his message), 7 – cultural transmission (the ability to teach/learn from other individuals, e.g. by imitation). As far as I know the reason humans can speak is simply brain size and complexity (long chains). But I won’t go into all of it here. But the ability to imagine futures, imagine stories, ‘self-observe’ and describe those stories in a series of symbols, using a series of rules’ takes a great deal of processing power. While we can see elements of these patterns in parrots, corvids, dolphins, and the apes, we must teach them, and they say very simple things – because they only think very simple things. Assuming we selected and trained enough chimpanzees to use sign language to build a self sustaining community of them, and assuming we could leave them on an island for a few centuries, it’s possible that sign language would persist. I suspect the problem is that it’s hard to produce a community of chimps with the intelligence necessary for perpetuation.
—“What do believe is the qualitative difference between human and animal language?”—Bob Robertson As far as I know animals do not possess language, it only exists within humans. All other creatures merely manage to communicate. Charles Hockett (1967) introduced a generally accepted check list for language, a set of features that all human languages possess. His seven key properties are: 1 – productivity (the ability to create and understand new utterances): system which makes it possible to construct an unlimited number of sentences from a limited set of rules. 2 – arbitrariness (when signs/words do not resemble the things they represent), 3 – displacement (the ability to refer to the past and to things not present), and 4 – duality of pattern (the combination of a phonological system and a grammatical system), 5 – interchangeability (the ability to transmit and to receive messages by exchanging roles), 6 – specialization (when the only function of speech is communication and the speaker does not act out his message), 7 – cultural transmission (the ability to teach/learn from other individuals, e.g. by imitation). As far as I know the reason humans can speak is simply brain size and complexity (long chains). But I won’t go into all of it here. But the ability to imagine futures, imagine stories, ‘self-observe’ and describe those stories in a series of symbols, using a series of rules’ takes a great deal of processing power. While we can see elements of these patterns in parrots, corvids, dolphins, and the apes, we must teach them, and they say very simple things – because they only think very simple things. Assuming we selected and trained enough chimpanzees to use sign language to build a self sustaining community of them, and assuming we could leave them on an island for a few centuries, it’s possible that sign language would persist. I suspect the problem is that it’s hard to produce a community of chimps with the intelligence necessary for perpetuation.
So it’s correct to call apriorism an ideal grammar, but not a formal grammar. Thankfully I finally know how to talk about the grammars of each incremental dimension… sigh.
Grammar A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of productions, and S is an element of N. The set T of terminal symbols is L’s alphabet. Nonterminals are symbols representing language constructs. The sets N and T should not intersect. S is called the start symbol. Productions are rules of the form: alpha->beta, where both alpha and beta are strings of terminals and nonterminals, alpha contains at least one nonterminal. Sentential forms for grammar G=(N,T,R,S) are defined by the following rules: S is a sentential form and if alphabetagamma is a sentential form and production beta->delta belongs to R, then alphadeltagamma is a sentential form as well. L is the set of all strings which are sentential forms consisting entirely of terminal symbols. For a language defined by a grammar, recognition whether a given string (expression) belongs to that language is, in general, a non-trivial task. All languages defined by grammars are recursively enumerable sets. 1. A grammar G is called right linear if all its productions have the form A->alphaB or A->alpha, where A,B in N and alpha is a string of terminal symbols. 2. A grammar G is called context-free if all its productions have the form A->alpha, where A in N and alpha is a string of terminal and nonterminal symbols. 3. A grammar G is called context-sensitive if all its productions have the form alpha->beta, where both alpha and beta are strings of terminal and nonterminal symbols and the length of alpha is not more than the length of beta. 4. A grammar G is called unrestricted if it does not belong to categories 1 through 3. This hierarchy of grammars was introduced by N. Chomsky. The set of languages defined by grammars of every category is a proper superset of that for the previous category. The languages defined by grammars of categories 1 through 3 are recursive sets. A language can be defined by a grammar of category 1 iff it is defined by a regular expression.
So it’s correct to call apriorism an ideal grammar, but not a formal grammar. Thankfully I finally know how to talk about the grammars of each incremental dimension… sigh.
Grammar A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of productions, and S is an element of N. The set T of terminal symbols is L’s alphabet. Nonterminals are symbols representing language constructs. The sets N and T should not intersect. S is called the start symbol. Productions are rules of the form: alpha->beta, where both alpha and beta are strings of terminals and nonterminals, alpha contains at least one nonterminal. Sentential forms for grammar G=(N,T,R,S) are defined by the following rules: S is a sentential form and if alphabetagamma is a sentential form and production beta->delta belongs to R, then alphadeltagamma is a sentential form as well. L is the set of all strings which are sentential forms consisting entirely of terminal symbols. For a language defined by a grammar, recognition whether a given string (expression) belongs to that language is, in general, a non-trivial task. All languages defined by grammars are recursively enumerable sets. 1. A grammar G is called right linear if all its productions have the form A->alphaB or A->alpha, where A,B in N and alpha is a string of terminal symbols. 2. A grammar G is called context-free if all its productions have the form A->alpha, where A in N and alpha is a string of terminal and nonterminal symbols. 3. A grammar G is called context-sensitive if all its productions have the form alpha->beta, where both alpha and beta are strings of terminal and nonterminal symbols and the length of alpha is not more than the length of beta. 4. A grammar G is called unrestricted if it does not belong to categories 1 through 3. This hierarchy of grammars was introduced by N. Chomsky. The set of languages defined by grammars of every category is a proper superset of that for the previous category. The languages defined by grammars of categories 1 through 3 are recursive sets. A language can be defined by a grammar of category 1 iff it is defined by a regular expression.
DOOLITTLE’S LAW OF MARKET LIMITS The limit to the evolutionary value markets, is measurable by changes in genetic capital, and genetic capital is measureable by differences in total number of population and distribution(superiority) of traits. Likewise, the limit to genetic capital is competitive speciation (transcendence). Again, if you cannot state the limit to a theory(‘good’) then you do not understand of what you speak.
DOOLITTLE’S LAW OF MARKET LIMITS The limit to the evolutionary value markets, is measurable by changes in genetic capital, and genetic capital is measureable by differences in total number of population and distribution(superiority) of traits. Likewise, the limit to genetic capital is competitive speciation (transcendence). Again, if you cannot state the limit to a theory(‘good’) then you do not understand of what you speak.
Four years of art criticism. The primary rule of which was ‘no empty words’. One had to make thoughtful compliments and thoughtful criticisms. It sticks with you. DIMENSIONS: 1) Craft Scale (Craftsmanship(presence of resources)) 2) Design Scale (Aesthetics (presence of resources)) 3) Content (“Meaning” (presence of resources)) Scale (Population) 4) Monument Scale (Capital (Presence of resources))
Four years of art criticism. The primary rule of which was ‘no empty words’. One had to make thoughtful compliments and thoughtful criticisms. It sticks with you. DIMENSIONS: 1) Craft Scale (Craftsmanship(presence of resources)) 2) Design Scale (Aesthetics (presence of resources)) 3) Content (“Meaning” (presence of resources)) Scale (Population) 4) Monument Scale (Capital (Presence of resources))