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KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
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Joined: Sat Aug 16, 2014 3:50 pm
Posts: 49
Post KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
(I think that the present text can change the course of history, if it gets to be understood enough. Until then, it should not be forgotten. The original text, in Spanish, can be obtained in http://vixra.org/author/fernando_sanchez-escribano.)

I intend to definitely bring out the concept confusions which prevent, in the current official foundations of mathematics and physics, the logical explanation of reality, and induce to posit some principles implying contradiction with the dictates of intuition, ignoring necessary compatibility of this with reason. Certainly, these confusions are caused by a deficient perception of primitive concepts that should be possessed with absolute clarity, if wanted to get the purported evidence: who come to have them clear will immediately be able to notice the falsity of such principles, without any major reasoning. So, I will try to first expose the primitive concepts in question –their perception does not require greater knowledge, but natural intelligence– and then indicate committed confusions, whose elimination will leave free the road of logical explanation.
(Now I have dealt more or less lightly with this subject in earlier texts, which I hope this time to improve enough to produce the desired effect. However, the definitive treatment is left for a future Theory of the Entes, which will require the introduction of a certain natural idiom, giving just a different and perfectly determined meaning (in a natural, non-arbitrary form, within the reach of anyone of sufficient intelligence) to each noun (finite sequence of letters of an infinite arbitrary set, ordered as that of natural numbers, which may be: 0,1,2...9,X,Y,Z,B,C,D,F,G,H,J...) of the own dictionary. We agree to say –it will be very important to keep this in mind– that nouns denote concepts, and that each only designates the individuals of the concept denoted.)

The most general concept of all existing (and certainly one of the most primitive) is the one of ens (being), which represents all entes (beings) as individuals of its own, and by whose perception (intuition) is obtained the most abstract (the least, in a certain sense) knowledge of them. Saving the unique ens (The-I) which is not a thing, other entes have an infinite number of copies or entes essentially equal to anyone, distinguishable only by their relations with other entes, i.e. by intuition not of primary concepts (characteristic of pure knowledge or evidence), to call entemas, but of concepts, called recepts, relative to other concepts (and, therefore, directly or indirectly to entemas). Of course, all essentially equal concepts are equivalent (have the same individuals) each other, and everyone, to call form, which represents all entes essentially equal to any individual of its own is void (with no individual) or equivalent to an entema. In addition, it can posited that equivalent entemas are also essentially equal each other, and that every concept have forms (and therefore, entemas, if not void) that comprise it minimally (representing all and only all entes equal in essence to its individuals).
(About the mentioned natural idiom, I inform in advance that its nouns designate things only (never The-I, though it can easily be enhanced to allow this possibility), as well as they denote entemas only. According to this, the natural noun (belonging to the natural idiom) with more general meaning is that equivalent to the vulgar one of thing: it consists of only one letter, the first ("0") of the natural alphabet, and designates all the entes that are not The-I, included all the concepts –I say all this to prevent possible misinterpretation of certain expressions to use here and to procure mental exercise– counting this singular ens as an individual of its own and having no natural noun denoting them (despise their having nouns designating them, as things they are). Note that normally, by language license, you can speak of the entes equal in essence, and even of equivalent concepts, as if they were identical, i.e. the same one, although there is an infinite number of them (as things they are): the context must determine the use sense. As an illustration, and to indicate that a given (belonging to the language) vulgar noun (possibly neologism) is used with a perfectly determined primitive sense, I may postpone in parentheses the corresponding natural noun, which (in my current opinion) denotes the entema equivalent to the concept denoted by the vulgar first.)

The simplest entemas, called ideas, are those representing all entes essentially equal to the same one (and which should not be confused with atomic concepts, each of them representing only one thing, and being necessarily a recept, as all those with a finite number of such individuals). Strictly, it will be said that an ens is understood only if an idea of its own (representing it and their equals in essence) is perceived (or intuited), and understanding of an ens should be distinguished from understanding of its idea (supposing the perception of the idea of its idea, normally less frequent) to interpret correctly some texts of mine: the obvious relationship between both ideas leads to talk about them, in lax sense, as if they were equal, and to confuse them, if they are not sufficiently clear. (In the natural idiom, ideas are just those entemas denoted by minimal sequences, consistent of single letters, other than the first letter: 1, 2, 3.... Note that when speaking of the idea denoted by a certain noun which designates entes distinct in essence, it is normally wanted to speak –in the strict sense adopted here, such an idea cannot exist, as it should represent such distinct entes– of the idea of the entema denoted by the noun: the obvious possibility of confusion leading to a contradiction –we will see later– is what justifies this clarification of concepts.)
The most intuitive ideas, after that of The-I (the only absolutely atomic entema, with just a single individual), are the one of state (1), which represents the states of The-I (in which this can be), and the other of space (2), whose individuals are the spaces or extensive things not contained in (which are not part of) other such. Who possess (i.e. can easily intuit) these ideas may recognize that the entema of thing (0) comprises two complementary (also easy to intuit): those of aente (20) and of uente (21), respectively equivalent to the total concepts of things that can be called discrete (in an obvious sense, quite simple or decomposable in other such), and be states (1) or deeds (120), the former, or extensive (not simple, decomposable only in other such), and be spaces (2) or sites (202), the latter.
Likewise, who possess all these entemas may recognize the existence of certain natural relations among them, which determine the devenir, the obvious ordering of the totality of states, equal to that of integers (without first and last), and also the natural coordinations of the former with the totality of the spaces, and the other one of the totality of increasing pairs of states (initial, final) with that of realized deeds, as well as the totality of parts, or own sites, of each space (by means of the its own relations of continence and of contact), the common spatial structure and the relationship of motion: all this allows –you will see– to distinguish each thing from its copies, or entes of its same essence.
The entema of aente (20) –sorry, need to continue distinguishing concepts– consists of the complementary (with respect to the former) entemas of state or action (200) and of act (210), which represent those deeds whose initial and final states are consecutive (in the devenir of their own), the latter, and the states (1) and the other deeds, to call actions (1200), which are not acts, the former. On its turn, the entema of act (210) is composed of the complementary entemas of eact (2010) and of sensu (2110), which represent the volitive acts (equal in essence, all of them), to call volits (3), and the cognitive percepts, to call notes (20103) (logues, in previous texts), the former, and the sensitive percepts (called sensus by me), the latter. (In an obvious sense, it can said that every deed is formed by one or more acts consecutive in the (derived from the) devenir order –it will be called volition, notion or sensation, respectively, every action formed only by volits, notes or sensus– and can be analysed in terms of them, being normal (at least in human stages of the devenir) that many essentially equal acts of each of these types occur consecutively, forming actions of the respective types: that's why both vulgar nouns of notion and cognitive deed can be used as synonyms.)
It is still necessary to distinguish between the entemas of eracto (20010) –neologisms are introduced in the vulgar language in order to facilitate the interpretation of natural idiom– and of entema (21010) –equal vulgar nouns are being used in different ways– as respective representatives of the volits (3) and those notes to call relates (200103), relative –the essence of notes allows this possibility– to other notes, the former, and of the primary notes, non-relative to others, the second, both complementary each other in the entema of eacto (2010); item, between the entemas of fact (200010) and of recept (210010), complementary in the entema of eracto (20010) and respective representatives of the volits (3) and the relates relating to themselves (as notes they are), to call reflects (2000103), the former, and of relates not relating to themselves (those already mentioned, receptos), the second; item more, between the entemas (complementary in that of note) of concept (21001021010), representative of the entemas (21010) and the recepts (210010), and of reflect (2000103), representative of the notes called reflects.

Some notions, denoted in an ambiguous form in vulgar language, whose confusion produces those paradoxes which gave rise to the erroneous axiomatic of current official set theory have already been distinguished: mainly, those of entema (21010), of note (20103), of recept (210010), of reflect (2000103) and of concept (21001021010) (cited in the natural order of their nouns (that of appearance in the dictionary of natural idiom), as much primitive, the former, as much short, the latter). Of the five, that of note is the most general, by comprising the other four; of these, those of entema, reflect and recept are disjoint and compose that of note, while that of concept is (product of) the union of those of entema and of recept. The key to undo the confusion is in the recognition that certain reflexos (unlike concepts) can, at the same time, be equal in essence and not be equivalent (i.e. failing to have the same own individuals), although it is also to be clarified the notion of set, key in mathematics (although much less primitive than those earlier mentioned). However, before attempting this final point, it is advisable to ensure the correct interpretation of the used terminology:
- As already mentioned, every vulgar noun with a natural equivalent shown here denotes a perfectly determined entema (except for equality in essence). So there are the entemas denoted by natural names: 0, 1, 00, 01, 10, 11, 2, 02, 12, 20, 21, 22, 000, 001... (cited in its own order), some of whom have been here mentioned. In addition to these entemas, to call cosemas (211010), there are the idea to call iema (Y), which represents The-I (as a single individual), as well as the entemas, called ientemas (201010), whose individuals are The-I and those own of a same cosema. (Note that both the iema and the other ientemas are things and may be designated by natural names, despite the fact that one of their represented individuals (The-I) cannot be, and so none of them can be denoted (as concepts they are) by such nouns. Nevertheless, if a special letter is added to the natural alphabet –be "I"– which designates The-I, or, alternatively, another such –be "E"– which designates all entes (including The-I), just to put in the first place, we can agree these special nouns with one of such initial letters denote the less ientema comprising either the cosema denoted by the reduced noun (without the special letter), or its complementary: so, the special names "I" and "E0" are equivalent, as well as "E" and "I0", denoting the respective absolutely atomic or total ientema (without a doubt, the most primitive concepts), and designating The-I or all the entes; on the other hand, the ideas of such ientemas have natural names denoting each of them (as cosemas they are) and designate their respective individuals (such ientemas), and happing to be composed (if I am not wrong) by just one letter: the 12th ("Y") or the 44th of the alphabet, respectively.)
– Every recept is directly relative to other two concepts, called objects (in other texts, arguments), and, if these are also receptos, indirectly to their own objects: all of them (main recept and direct and indirect objects) have to occur successively (according to certain devenir laws, not to deal with now) in a minimal action (relation) (to call, of course, reception). Certainly, every entema has an infinity of different receptos (forms) equivalent to it (with an infinite number of possible entemas as objects), and every form without equivalent entemas is void (without no own individual), some of which former may be easier to intuit, for humans, than the equivalent entemas, if these (for any reason) are less than the objects of their own: thus, the cosema of thing is obviously much easier to intuit that the recept of ens designated by the first noun in dictionary of natural idiom (equivalent to the former, and relative to the ientema of ens and the cosemas of noun, of dictionary and of natural idiom), while the recept of thing designated by third name in natural dictionary ("00") –this example can serve to appreciate the immensity of the theory of the entes– it is more than the equivalent entema (out of the reach of human, despite being a primary, not relative to any other concepts).
– Every reflect, in contrast to the recept, is directly relative only to a concept and a reflect, which may be the same reflect or other having this, directly or indirectly, as an object: reflect and objects have to occur successively in the same action (relation), called reflection. To see that essential equality of reflects, unlike the concepts, does not imply representative equivalence, even unless essential equality of individuals, consider the reflect of present deed, that representing those deeds with initial and final states respectively before and after those own of itself: each of such equal reflects has itself as the only own individual which is an act (none more equal to or different from it), and the infinity of essentially distinct deeds of any number of own acts, prevents the devenir from being periodic, and each two such reflects from fulfilling the equivalence conditions (inclusive, except for essential equality).

Although it can be posited that every concept has an infinity of reflects equivalent to it (with the same individuals), and that every reflect has equivalent concepts, it happens that the human being cannot intuit concepts, but only reflects, whose number of individuals is finite, if not void or equivalent to the iema: obviously, the existence of an infinity of things essentially equal to any one requires a higher power (divine) for its determination (to be necessarily performed by means of their different relations with deeds occurring in the devenir, each with an infinite number of equal in essence, successive and alternating with others different, in a way depending on the devenir present stage). Thus, for example, they are easily realizable by man those reflects of present act, of next following act and of next preceding act, whose respective unique individuals are the same first reflect, the next following act (in the devenir) to the same second and the next preceding act to the same third, but it is completely out of huma reach the intuition of a concept whose only element is a state, or an act or anything else: taking the first case as an example, it can be seen that the determination of a state requires something like the intuition of the entema whose individuals are the deeds essentially equal to those (infinitely many and, one of each two, component of the other) having it as own initial state (or final) in the devenir, so that it is obviously needed an infinite power.
Although man is born with the power to easily intuit certain entemas and relates (recepts or reflects) more or less primitive or simple, ordinary language acquisition allows it to greatly increase the complexity of those second, first, by reflection (i.e. perceiving reflects relative to the current language (in the present deed) in which they are expressed –normally, a reflect is defined by means of a nominal expression containing the noun of a concept comprising it and a proposition which individuals of the concept must comply with to be also individuals of its own– without the need for understanding (by intuition of the idea) or precise knowledge (through concepts) of such a language, or of the own individuals of the perceived reflects) and, then, by intuition of concepts (if possible, entemas) equivalent to certain utilized reflects. However, it is obvious this involves the possibility that the concepts of a purported theory be empty and do not provide knowledge at all: though ambiguity of the vulgar language normally allows to alter meanings, attributing secondary senses to nouns or nominal expressions, to denote only nonempty concepts (including entemas, which never are void), concepts obtained in that case will not most likely have the value intended with the primary senses (normally, more primitive), and, of course, their alleged existence should not be accepted if it is incompatible with the evidence of understood entemas.
Note that the existence of equivalent concepts and reflects postulate does not imply that there is always the note (concept or reflect) whose individuals are all own of reflects essentially equal to the same one (i.e. the product of the union of all the concepts that are equivalent to any copy of that same reflect), while the (equality of) essence of a reflect must allow to determine if any ens either is , or not, an individual of any of its copies, that is, if it can, or cannot, be designated with the noun or nominal expression denoting the reflect (and each of its copies). There is the key point of confusion leading to the error: although it can always be (in more or less lax sense) said that such a noun, or nominal expression, denoting (all copies of) a reflect designates every individual of (at least) one of its copies, it is not true that such a noun always have an equivalent denoting (all copies of) a concept whose individuals are those designated by it (because there may exist no such a concept).

Can be already recognized that the confusion between the concepts of recept and of reflect is the sought after cause of the paradoxes that upset the mathematical foundations: said with the terminology introduced here, the note of concept that is not individual of itself is not a concept –it cannot: it should be and not be, at the same time, an individual of itself– but necessarily a reflect (doubly relative to the entema of concept: directly and indirectly, through the note itself), so that one can say it is not an individual of such a note, without incurring in contradiction.
Likely, the note of reflect that is not an individual of itself also is a reflect, and neither can be an individual of itself: the obvious existence of the entema of reflect (2000103) –it is very primitive, within easy reach of the human intuition– allows us to infer that entema comprises (infinity of) certain increasing others (one of each two, comprised by the other), to call (reflective) grades, such that the note of reflect that is an individual of any same grade, but not of itself, is an individual of a superior grade, and that such a note of grade is a reflect. Indeed, the entema of reflect (2000103) is composed of the entemas of ordinary reflect (20000103) and of not ordinary reflect (2100010), respective representatives of those reflects with grades of their own and of those called entelechies, with no own grade (as such a note of grade).
Of course, you also may wonder what happens with the note of entelechy that is not an individual of itself, but there is a response: such a note is not an entelechy but a recept (relative to the entema of entelechy (2100010) twice, both times –the difference between both entemas of concept and of entelechy makes it possible– directly, without passing through the note itself), which is not of those here called forms (empty or equivalent to entemas), but of those recepts which can well be called ultralogical, out of human reach, which is not enough to intuit them (but enough to intuit the entema of ultralogical recept –I have not recognized its natural noun yet– and to understand (or intuit the idea of) any of them: if not, I could not be speaking of such a recept).
Unfortunately, ambiguity and licenses of vulgar language allow very different uses of certain equal expressions, which can lead to confusion, if it is not known how to recognize the used sense. Thus, when speaking (using the terminology introduced here) of the note of grade, you may be speaking of the reflect of grade, in absolute primary sense, i.e. of the entelechy of grade, but also –this example can serve to check your capacity of discernment– of the entema of (reflect of) grade (parentheses possibly implicit), which is an idea (as all the reflects of grade are notes equal in essence, although non-equivalent), in a secondary sense, and, therefore, of a concept, not of a reflect; likewise, in less likely senses, you may be speaking of the idea of entema of grade, of the idea of idea of entema of grade..., all of which are mutually determined in obvious way (so it is justified the multiple use of the initial expression, provided that there is no likelihood of confusion). Of course, confusions that must be avoided are those of an idea with their (equal in essence) individuals, these together (especially if they are reflects), of a reflect with concepts equivalent to its copies, of these together..., all of them, source of serious errors.
(I insist that vulgar language licenses allow to try things essentially equal as if they were identical or the same, when really each one has an infinite number of copies with its very essence. Of course, the entema of essence has been supposed primitive, and can be identified as the minimal entema (i.e. comprised by any else fulfilling the condition) which represents all copies and (all) ideas of each own individual, i.e. which comprises all ideas of its own individuals. It is obvious –it can be posited– that every ens determines (except for essential equality) its own essence, and is (likely) determined by this: naturally, essences, as entes they are, have their own ideas and essences, and the jump (transfinite step) from any ens, to call first initial, to its essence, to call second initial, passing through all the successive previous ideas, can be reiterated in an obvious way, taking every second initial as the first of the new process and increasing unceasingly the complexity of possible jumps, i.e. without ever realizing the absolutely total concept of them, which cannot exist (in the primary or principal sense), as the note of jump is an entelechy. Nevertheless, nothing prevents the existence of the minimal entemas not only comprising all the essences of own individuals, but also representing all successive initial, first and second, individuals of them: in fact, the idea of such an entema, which has The-I as the single absolute initial individual (i.e. which is not second in any other such) is easy to intuit, almost as much as the idea of essence of The-I, both (this and that) denoted by the natural nouns composed of two unique letters, 74th, and 204th, of the alphabet (if I am not wrong in some hasty decisions taken for the occasion, perfectly correctable if wrong).

If the notion of set was introduced in mathematics, it was not only because each set is determined by its elements, but also (and especially) because any concept has an equivalent set (whose elements are the individuals of the former). Obviously, determination of sets is only possible for the human being in a reflective way, i.e. treating the notion of set as a reflect; nevertheless, this does not prevent from defining sets as uniquely determined concepts by (the inclusion of) its elements (since all reflects have equivalent concepts), or from requiring the existence of the set equivalent to any concept: although human power is not sufficient to understand such a concept of set (i.e. the one whose individuals are all actually established sets), it allows the very intuition of the entema of concept of set and, therefore, knowing the existence of such concepts (and so its compatibility with the existence of the most obvious concepts).
Certainly, the official set theory (or any other, as far as I know, prior to proposed mine) does not meet this essential requirement, so it cannot be satisfactory; much less, if there is known one that is able not only to comply with it (and thus, richer), but also to admit the enumeration of every infinite set, and to explain the inexistence of the absolutely total set of ordinal numbers (despite admitting every initial segment of them as a set): the note of ordinal number (or logical order) is not a concept or an ordinary reflect, but an entelechy.
Of course, the enumeration of the universal set (of all entes) implies the possibility (out of human reach) of assigning, to each ordinal number (as an ens) the natural number assigned in the coordination of the universal set with the one of natural numbers, but this is not repugnant to intuition: the note of number assigned in such coordination also is an entelechy, and, even though this assignment can be altered by replacing each successive natural number assigned to an ordinal number by the following next to the respective previously assigned (so as to obtain the coordination between natural and ordinal numbers), the new coordination (whatever is defined the concept of coordination) would happen to be an entelechy. Thus, the notion of cardinal number greater than that of any infinite set is void.

I know what I am attempting to communicate is complex and delicate matter, and that my texts require time to be interpreted correctly. It has taken me all life to clear up all of that, and yet, when reviewing some of those texts I may need some work –my memory is rather deplorable– to find the correct interpretation, and sometimes I find confusions in them that I should censure in other`s texts: no matter, the pertinent correction always allows me to improve the previous valuation of the theory, so as confirming that, in essence, it is correct (though, as all human work, it need to be criticized, never admitted as a dogma). Nevertheless, I don't think required a complete security in the success of the new theory to be able to recognize the falsity of the old official one, up to leave worthless the big artifice built in the last century on the void notion of uncountable infinite set, and to force a thorough revision of those numerous mathematical branches affected by (which, as it could not be otherwise, has only brought complication, no practical advantage).

(The next post will be dedicated to clarify the concepts confused by the official physical theory).


Mon Feb 08, 2016 6:14 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
(I think that the present text can change the course of history, if it gets to be understood enough. Until then, it should not be forgotten. The original text, in Spanish, can be obtained in http://vixra.org/author/fernando_sanchez-escribano.)

To discover the conceptual confusions having led official Physics to alter the established scale of values and support principles contrary to the dictates of intuition in order to supposedly explain certain experimental results, we must continue the initiated distinction of primitive concepts, now between those comprised by the entema of uente (21), representative of the extensive things (divisible into also extensive parts only), which can be or spaces (2), all equal in essence and not contained in others, or sites (212), each one contained in a space, as a part of its own, and fulfilling, with each other of the own space, natural relations of contact (which allow to determine the individuals represented by concepts to treat).
The entema of uens (21) consists of the (complementary in it) entemas of 2-uens (201) and of site′1 (211), the first of which represents all spaces (2) and the sites of dimension not less than 2, to call sites′′2 (2012), and the second the dimension 1 sites, which may be (exclusively) of one piece (connected component), to call sites'1'1, boloides'1 or dihedrons (2011), or of more than one pieces, to call sites'1'2 (2111). On its turn, the entema of 2-uens (201) consists of the entemas of 3-uens (2001) and of site'2 (2101), respective representatives of spaces (2) and of the sites of dimension not less than 3, to call sites"3 (20012), one, and of the sites"2 (2012) of dimension 2, the other; these, sites'2 (2101), can be or sites'2'1 (20101), also called boloids'2 and cercoids, if of the same topo (primitive entema of the topologically equal sites) as circles, or sites'2"2 (21101), if of a distinct topo; similarly, the sites'2"2 (21101) may be or sites'2'2 (201101), or sites'2"3 (211101), if formed, or not, by two sites'2'1 (20101), respectively, as well as those first (201101), or sites'2'2'1 (2001101), or sites'2'2"2 (2101101), according to their respective complements (in space) are sites'2'1 (20101), or sites'2"2 (21101), and the latter ones (211101), or sites'2'3 (2011101), or sites'2"4 (2111101), according to whether they are composed of three sites'2'1 (20101), or not, respectively. Likewise, the entema of 3-uens (2001) consists of the disjoint entemas of 4-uens (20001) and of site'3 (21001), the first representing the spaces (2) and not less than 4 dimension sites, to call sites"4 (200012), and the second representing the sites"3 (20012) of ordinary dimension, 3, only; these latter (21001) may be or sites'3'1 (201001) (also called boloids'3 and ordinary boloids), or sites'3''2 (211001), according to whether of the same topo, or not, as balls, respectively; item, these latter (211001), or sites'3'2 (2011001) or sites3''3 (2111001), according to whether or not composed of two boloides'3, respectively; item, the new first (2011001), or sites'3'2'2 (20011001) or sites'3'2"3 (21011001), according to the respective complements are sites'3'2 (201001) (and sites'3'2'2) or sites'3"3, and the second ones (2111001), or sites'3'3 (20111001) or sites'3''4 (21111001), whether composed or not of three boloides'3; item, the new first (20111001), or sites'3'3'1 (200111001) or sites'3'3''2 (210111001), according to whether or not the respective complementary sites are boloides'3, and, the others second (21111001), or sites'3'4 or sites'3"5, if composed or not of four boloides....
You may want to know which are, according to the natural dictionary, in my current opinion, the following ideas of uentes after the first one, of space (2): the second, of dihedron (2011) essentially equal to its complement, and volume (or length) half of that own of the space (2), to call medihedron (4); the third, of site'2'1 (20101) of the greatest symmetry (ordinary circle (200101)) and greatest volume contained in a medihedron, to call medicircle (6); the fourth, of site'1"2 of two pieces (so to call site'1'2 (20111), according to the obvious followed guidelines) essentially equal (dihedral of volume 1/4 of the total) to those of its complement, essentially equal to it (8); the fifth, of boloid'3 (201001) of the greatest symmetry (ordinary ball (2001001)) and volume contained in medihedron (4), to call ordinary mediball (X); the sixth, of site'2'2'1 (2001101) (which could well be called annuloid) complement of medicircle (6), to call mediannulus (Z); the seventh, of dihedron of volume not obtainable by analytical means (to treat another time), to call infinital (21011), and infinitesimal value (smaller than any rational non-null, and equal in essence to any other such, greater or smaller), to call transfinitesimal dihedron (C); the eighth, the site'1''2 (2111) that is not site'1'2 (to call, according to guidelines, site'1''3 (21111)), but composed of three dihedrons (so to be called site'1'3 (201111)) equal in essence to those own of its complement (and, therefore, each of volume 1/6 of the total), also equal to it (F). Skipping a few successive ideas, it is wanted to cite those of site'3'2'2 (20011001) (cylindroid) of the greatest symmetry (cylinder) and equal in essence to its complement, to call medicylinder (R), and of site'3'3'1 (200111001) (or coboloid'3) complementary to ordinary medibola (X), to be called medicoball'3 (with the 59th natural alphabet letter). (Not much more I will continue along this path: just wanted to start to show the method used in Theory of the Entes –remember that natural nouns denote entemas or primary concepts (easy to intuit and recognize with the help of the vulgar name, the appeared so far) and perfectly determined– and clarify certain concepts to use. Who has understood, will be able to easily realize –this enables us to form certain images of the space in successive dimensions– that the total space is composed of n boloids'n (whatever the natural value of the dimension n), eligible such (n-parahedrons regular, of 2n faces, analogous to the hexahedron, of 6) that all sites composed by as many of them are equal in essence.)

Every site complementary (in the space) to a dihedron (2011) is also a dihedron –in general, each two absolute complementary sites are of equal dimension– and every dihedron equal (in essence) to its own complementary is also equal to any other such (so called mediedro (4)); every dihedron can be divided into as many (finite number) others equal (without common parts) as wanted; the largest of each two distinct dihedrons can be divided into two, one of these equal to the smallest of those, and every dihedron divided into two distinct can also be divided into other two, each equal to one of both previous, the minor of each pair being contained in the major of the other. In the obvious sense, it can be posited that the essence of a dihedron is determined by its volume (or length). (Although I will not now discuss the matter –it would take me too far– I must warn that the reciprocal of this assumption is not true: all transfinitesimal dihedrons (C) are equal in essence, as well as all infinital (21011) complementary to any transfinitesimal in a same finital dihedron (20011, always obtainable by actual geometric means, from those of rational volume, as you can see later). Note that the dihedrons here called complementary are not identifiable with those normally so called, but with the others called supplementary.)
Calling every set of dihedrons of the same space dihedran, a cut is defined as the maximal dihedran (the one containing any other satisfying the conditions to impose) such that: first, every dihedron is the common element of only two cuts, called the sides of its own; second, each two cuts (of the same space) include only two dihedrons as their common elements, absolute complementary each other; third, each one of every two dihedrons composing another belongs to a different side of the latter. Also, calling two cuts perpendicular (each other) only if they are sides of a same medihedron (4), it is defined: first, a vertex as the total set of dihedrons whose sides are perpendicular (both) to a same cut, the own cut of the vertex; second, an arris as the total set of common dihedrons of two same vertices, through which passes the arris (common perpendicular to the own cuts of the vertices), on which they are; third, a co-arris as the total set of diedros whose (both) sides have own vertices (which are) on a same arris (and so all of them are perpendicular to all the sides of dihedrons of the arris), both called perdual of each other; finally, a face that passes through certain vertices, whatever, which are on it, as the diedran product of the intersection of such vertices (as sets of dihedrons). In general, a face will be said to be on other, and this to pass through that, only if the former contains (as a set of dihedrons) the latter; on the other hand, it will be said that a cut passes through a face, and that this is on the cut, if the former is the side of (an infinity of) dihedrons of the latter’s own. Finally, a vertex not being on the sides of a dihedron will be called interior to this only if it is on a cut dividing the dihedron into two others (i.e., being the common side of both), and exterior to the same only if it is interior to the complementary dihedron.

Calling vertices 1-faces, arrises 2-faces, and, by induction, a face n-face (n, natural number, called degree of the face) only if it is the maximal face not containing (as a set of dihedrons) any face of lower degree, as well as calling co-arrises 2-cofaces, or (–2)-face, and, in general, faces n-coface, or (-n)-face (n, natural number, called co-degree of such a face, as well as the negative opposite integer, –n, is called degree) only if it is the minimal face (contained in any other fulfilling this condition) not contained in any face of higher degree (i.e. of lower co-degree), it can be recognized (or posited, if preferred) that each n-face (n greater than 1) has a perdual n-coface, mutually determined and such that all dihedral sides of (dihedrons included in) one are perpendicular to all dihedral sides of the other. (Note that the smaller the faces (as dihedron sets), the greater their degrees, if of the same sign, and the smaller their co-degrees, if negative degrees, and that all those of positive degree are greater (by containing them) than those of negative degree. Also, that, according to the followed guidelines, it would be proper to call the empty set co-vertex or 1-coface (since there is only one cut perpendicular to all passing through a same vertex (its own one), and every dihedron has two sides, the minimum number needed to split the space), but it could be changed the notion of dihedron and consider the space as an special dihedron of arbitrary identical sides, the single element of any co-vertex.)

Accordingly, it can be recognized (or posited) the determination of each co-arris by whatever element (a dihedron) of its own, and so of the perdual arris (the common perpendicular to both sides), also determined one by the other, and, consequently, the uniqueness of the ariss perpendicular to a cut, which passes through a given point that is not the own vertex of the cut, as well as the obvious two coordinations of the total set of vertices on an arris with the total set of cuts through the perdual coarista, associating each cut to its own vertex, the one, or to the single vertex on the arris which is also on the cut, to call foot of the (perpendicular) arris on the cut, the other.
It is not difficult to get convinced that every finite set of n+1 (natural number) cuts of a same space determines a partition of this into not less than n+1 and not more than 2↑n (2 raised to n) sites, called polyhedra, maximal parts common to one of both complementary dihedrons into which the space is divided by every two such cuts, reaching the minimum when all cuts pass through a same co-arris and all such parts are dihedrons, and the maximum, when the face of the lowest co-degree (highest degree) that is, at the same time, on all of them is an (n+1)-coface and the parts are (n+1)-hedrons (the simplest n-dimensional polyhedra: triangles, tetrahedra..., if dimension 2, 3...). Obviously, every site is determined by the total set of polyhedra that are parts of its own; also, by the total subset of (n+1)-hedrons, if of dimension n, and even by any maximal subset of such (n+1)-hedrons with no common parts of two of them (forming a partition), as well as by the total set of vertices interior to the site (i.e. to all dihedrons of each polyhedron in such determinant sets). (Note, on the other hand, that not every set of sites (without, or with common parts) of the same space to determine a site that can be identified as the product of their union (as the minimal site having all of them as parts of its own). A significant example is the total set of transfinitesimal dihedrons (C) belonging to a same coarris and having an interior vertex in common to all: there is no such transfinitesimal dihedron –the note of infinitesimality degree is an entelechy, in both, increasing and decreasing senses– that can be considered absolutely maximal, whose sides separate the sides of such transfinitesimal dihedrons and the other cuts through the coarris.

It is obvious the natural relationship between the mentioned concepts of cut, vertex, arris, co-arris, face, n-face..., whose individuals are special sets of dihedrons (2011), and certain algebraic and geometrical, somewhat more complex, concepts of the theory of space:
In fact, each own pair of cut and vertex determines a bijection (biunivocal correspondence) of the total dihedron set of a space into itself, which carries every dihedron of the cut to its opposite (the other dihedron with the same volume, pertaining to the cut and the same co-arriss), and it can be posited to be sufficient to determine the unique bijection, to call puntor, compatible with the relations of continence and contact of the total set of sites of the space itself which is restriction that. Naturally, the puntors of a same space generate a group, called tractón, of bijections, called tracts, of such a total dihedron set by the obvious operation of succession, which determines the geometrical structure of space. I’m not going to discuss this matter (of which there was given a draft in the text on the physical theory) here: suffice to say that any plane is identified with the set of puntors belonging to certain subgroup, called trácton (generated by them), of the tractón, and that points are the planes with only one puntor as its own element –the succession of a puntor by itself produces the null tract– and (straight) lines are the planes whose maximal subsets of commuting puntors have 2 as cardinal number (called degree of the plane), while the dual plane (co-point, co-line...) of another plane (point, straight...) is the total set of puntores that commute with all those of the other dual plane.
Although the correspondence between faces and planes respects equality of the respective degrees, allowing the definition of the operations of conjunction and intersection of faces, or planes, of the same space (whose products are the smallest and the largest face, or plane, respectively continent of or contained in the factors), so that the sum of the degrees of two such factors is equal to the sum of the degrees of the products of their conjunction and their intersection (identifying the space as the face, or plane, of zero degree), note that both orders established by the relationship of continence in one or other, according to the given definitions, are reversed.

Yet, despite the nature of this relationship, it is necessary to distinguish the mentioned concepts if it is wanted to avoid the kind of mistakes which I intend to expose. Note first of all that, though both individuals of the ones (cuts, vertices, arrises, co-arrises...) and of the others (copoints, points, lines, co-lines...) are defined as sets (which are aentes (20) certainly complexes), the elements of the formers are uentes (21) as simple as the dihedrons (2011), represented by entemas very primitive or easy to intuit (so that they do not require to be defined, but only shown, like all denoted here in natural language), while the elements of the latter ones are, themselves, also aentes (20), as complex as the so-called puntors (no natural name of which I have recognized so far): it is the primitive character of the entemas of space (2), site (212), dihedron (2011)..., not subject to postulates, which just allows to postulate rightly on the respective concepts of total set of points in the space (also called space), of points interior to the site (usually called region), of points interior to the dihedron (usually called segment)..., so that we can apply the usual mathematical methods, while maintaining the natural relationships (due to the perfect analogy (isomorphism) between the tractón and the group, also called tractón, of their inner automorphisms, to call tractions (each one, own of a tract), generated by the own tractions of puntors, to call punctions, each of which transforms an arbitrary puntor into the (puntor) product of its own puntor by the arbitrary puntor and (again) by the own puntor).
Certainly, the characteristic property of the uentes (21) (which I intend to suggest by calling them extensive, not discrete things) allows to define the distance between two vertices as the extension or volume of the dihedron whose sides are the own cuts of those, but such a definition has no corresponding analogous for the distance between points, not so directly related to uentes as vertices, but to sets, which, as aentes (20) or discrete things they are, have no such property (despite all the beliefs against –see my text on set theory– this assertion), so that the definition of their distance requires other methods of a more complex nature, such as the algebraic ones (which allow to relate rational valued distances between two points with the order (minimum number of the same factors that produce the null tract) of the (rector) product) and the others topological (which allow to discriminate the sizes of all rectors of a same order and get the total ordering of sizes).

I think that now it can be clearly seen the heart of the matter: the poor possession of the idea of extensive space (2) (despite being one of the most primitive) has not allowed official physics to discover the very geometrical structure of the mathematical space identifiable with the total set of its points, but its attempt to explain certain experimental results has led it to alter the scale of conceptual values, putting the complex notion of mathematical space (set of points) before the primitive idea of space (2) and failing in the choice of the intended real space. In effect:
– Euclidean space, adopted by the classical physics and normally considered the easiest one of possible candidates, cannot have the own geometry or the extensive space (2), because this can be divided into as many equal parts of dimension 1, or diedros (2011), as wanted, while the former can only do so in two equal of such a dimension, as both extreme segments of any other more numerous partition are always (infinitely) larger than the others: in fact, the structure of Euclidean space is the natural one of the total set of vertices which are at infinitesimal distances –the existence of such values is perfectly compatible with the essential geometric axioms (as you can see on another occasion, if we come to discuss my construction of projective geometry, posited just the own one of the physical space)– all each other (the largest infinitesimal neighbourhood), which (as it can already have been seen) does not determine any site (212) of the space (2). (This assessment is confirmed by the absence, within the theory of Euclidean spaces, of any rational explanations of the necessarily three-dimensional character of the ordinary physical space, or of the existence of the spin of particles, which are obvious in the projective space.)
– While the local character of physics equations, relating to the infinitesimal environment of each point in so-called space-time allows us to consider this as the Cartesian product of both sets, the one of static points (in space) and the other of instants (of the time), with respect to a reference system, endowed with the respective structures of three-dimensional and one-dimensional Euclidean spaces, compatible with the relativistic four-dimensional pseudo-Euclidean structure, that does not mean, at all, that the first two structures must be considered as the natural own of the respective planes in the total set of points of the extensive space (2) (nor, therefore, the third, the space-time itself), but only the respective infinitesimal neighbourhoods of each point. Of course, the possibility of faster or slower communication does not have why affecting the absolute nature of the extensive space (2) or of the time space (very previous, in the natural scale of values, to the space-time reference system), or the notion of speed, of obvious relative (to a such a system) character: in fact, the official theory itself supports so-called group and wave speeds of each particle, respectively above and below that of light, with product equal to the square of the third –the incongruity with the own postulates about the purported relative character of space and time is obvious– and no more theoretical limits (something the new theory assumes and allows to apply to photons also, making communication with them without any limit on speed –spatial geometry attributes them a formal mass of imaginary value, so that their group speed is as higher as smaller their frequency (or energy)– theoretically possible, though significant overcoming of the ordinary limit requires very different to conventional methods). Even more: the absolute nature of the space and the physical time, is confirmed by the theoretical possibility of existence of waves generated in anti-normal temporal sense (converging towards the generating point charge), which allows instant communication by using two different propagation temporal senses for going to and back messages (something the human being is capable of doing, although possession of certain key concepts is required to appreciate it).
– Also, equality and constancy of the ratio between inertial and gravitational masses of bodies formed with ordinary matter has no why to affect the concepts of space, or of spacetime, or of their own natural geometries (no doubt, very earlier than the formers in the scale of values): even if the motion of particles in a gravitational field could be described by mean of geodesics in a (pseudo)-local metrics of space-time, this could not be identified to the own natural geometry, which must have a previous global character, determining its *own local metric, and capable of supporting definitions of so many others of local character (superposed to that own) as wanted (one of which can be, of course, the associated to the movement of ordinary matter in the gravitational field). Certainly, the alleged principle of equivalence of the general relativity has no more value than that of a simple mathematical formalism whose applicability to certain simplified sketches of the universe does not mean denial of the absolute character of space and time, or the impossibility of other types of matter, with other values of gravitational constants, other associated local geometries and other methods of detection: its incompatibility with equality of natures of the gravitational and electromagnetic fields and the possibility of unifying both are obvious, and the mathematical theory in this regard (on varieties in a Euclidean of greater dimension and its relative local geometry space, certainly very interesting) has little to do with the nature of the first of such fields, as well as these with the local own geometry of the space or space-time (determined by that naturally own of the extensive space (2), with a global character, previous in the scale of values).
– Who possesses the entema of uens (21), i.e., the one of extensive space (2) or part of its own, called site (212), shall consider evident the fact that such an space is the only uens (except for essential equality) which cannot be a part of others, or have own dimension –the zero dimension could be admitted for it– and that every site has own finite dimension and parts of any dimension greater than its own. This supposes that the well-known theorem about the embedding of finite dimensional manifolds into Euclidean spaces of sufficient high dimension does not imply the primacy of these, or the equality of any other candidates, distinct from the very one, to be entitled to it: both the Euclidean spaces and its manifolds can be embedded into the infinitesimal neighbourhood of the authentic space, while this cannot be into them for being the total set of points (or vertices) of the extensive space (2) and containing manifolds of whatever dimension. (The finite nature of the dimension of a site is what allows this to be determined by the total set of interior points contained in its own plane of its same dimension, since the other interior points are those contained in the straight lines passing, each one, through a point in that plane and another in its perdual.)

Indeed, the mathematical theory on manifolds immersed in the total space of points (determined by the extensive space (2), as it was already explained) and local geometries relative has as main objective the determination of total sets of points (or vertices) interior to sites (212), through the study of their edges, common to their respective complementary, and its application to the physical field of wave propagation is obvious: Who possesses the (already cited) entemas of devenir simple event, called act (201) by me, of volitive act, called vólito (3), of cognitive act, called note (20103), and of sensitive act, called senso (2101), and be able to distinguish signs (sensos) from meanings (notes), normally realized, ones and others, in the same action (1200) of the preceptive type, with a multitude of equals in essence, will also be certainly able to recognize that, among all of them, only some sensos, to call images (21101), are local (in the sense of existence of some natural relationship between what can be called the image sensitive field and the two-dimensional sphere on which the three-dimensional physical space or natural plane is projected by intersection with the radial rays) and have obvious and direct relationship with the physical processes of detection and data transmission, those characteristic of living organisms by me called bodies, which allow to know the current state of the universe, through the realization of notes (20103), which have no such a local character and are directly related with physical processes, not of bodies, but of those living organisms called minds (if the notes are reflexos, 2000103), or souls (if concepts, 21001021010), not observable in the conventional way (which may well be formed with ordinary matter in a certain special state only possible at the time of the cosmic cycle in which all their ordinarily observable semiparticulas are concentrated in (perhaps two) extremely dense and cold cosmic nuclei, allowing significant interaction between the (normally unobservable) antiparticles, as well as communication in antinormal temporal sense, the minds, and with non-ordinary matter (with both semiparticle charges, gravonic and lecronic, very scattered throughout the space), capable to overcome the cosmic cycles and allow communication in both temporal senses), in such a way that images provide specific data of the three-dimensional appearance –the deeper positions of equal objects, the smaller their appearances in the image– of the universe, while detection of specific data of the dimensionally infinite aspect of the total space requires cognitive perception related to the physical processes of minds and souls (which hardly can be achieved in the stage of mainly sensitive lifes of bodies, whose communication with souls almost monopolize the attention of these latter).

May the text be strange and difficult to interpret in many of its expressions, but I wanted to take this opportunity to expose the keys of the main theory (whose pure abstract character, does not require reason, but only intuition or evidence, without which the reason has no value, although each one enhances the other), which have allowed me to discover those of the new theories, on physics and sets, and I must try to make them known as soon as possible, to avoid its loss. Anyone who can give the true sense of these lines will also be surely able to rectify their errors and continue their development, enjoying the immense beauty inherent in the new theory (of which a good example may be the projective space) as much as I do.
Nevertheless, one doesn't need a perfect understanding of the new theories to recognize they represent clear confirmation of the mistakes made by the official ones when positing against the dictates of intuition, altering the natural scale of values up to the very aberration and confusing genius with inability to explain, i.e., to reason on the basis of those dictates. Even less it is needed to recognize the real reasons which can lead prestigious institutions to betray their own reason of being, pretending to ignore them or refusing to pronounce openly about them, even violating their own written norms.
Not even a minimum knowledge is required to be able to compare the reasons given by one and other theories trying to explain the facts in question in vulgar terms: while the officcial ones have never been expressed in an intelligible form for non-experts –I would bet that even they convince the experts– in the matter, those new respond even to the deeper insights of the human being, giving meaning to the common fund of certain deep beliefs and myths in the history of man, which can be interpreted as the last remains of their cognitive memory, own of organisms called minds by me (whose life, according to the new physical theory, evolves in antinormal temporal sense, contrary to that own of the bodies), which infuse it with the desire to improve its knowledge, and whose successive acquisitions can be interpreted as partial recoveries –sensitive future corresponds with the cognitive past in the respective lives (at opposite times of the cosmic cycle) of body and mind, communicated each other through the soul– of lost memory.

I have already proposed a simple experiment (the Michelson-Morley, aboard the ISS) on whose outcome the official theory differs from mine: the fact that the institution capable to do it pretends unawareness of the proposal after having been informed, I think that it says enough. Still more it amazes me the lack of response to this question from these forums: Please help me get the expected response.
While making up your mind to intervene, you may consider this another prediction of the new physical theory, which no doubt will come to be confirmed, though it is still perhaps too soon: two sufficiently sensitive telescopes observing the universe limits in opposite directions will get two images of both opposing sides of a same galaxy.


Mon Mar 14, 2016 6:57 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
Fernando, I have tried to say it before. And excuse me for saying it too bluntly now.
I think there are 2 reasons why you don’t get a response.
1: I feel it is safe to say that your texts are completely incomprehensible. I honestly believe that there is only one person on this universe who is understands what you are writing and that is you.
2: The statement that all the smartest minds that ever lived on this planet got key concepts confused is extremely unbelievable and frankly very disrespectful to those people. With a title like that you basically ruined the chance that most people will even try to understand your texts.
Again, sorry if I am being too blunt, but I think it is in your best interest that I say it like this.


Mon Mar 14, 2016 11:20 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
Dear HarryT: I appreciate your sincerity. I wish that mine was also accepted with pleasure. Do you really think that all of my text is incomprehensible?. If so, I would have been too generous in my assessment of the talent of my opponents.


Tue Mar 15, 2016 4:00 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
I do not think that I am the problem here. For example let’s look at the first part of the first sentence of the second paragraph. There you write: “The most general concept of all existing (and certainly one of the most primitive) is the one of ens (being)”.
You cannot say “of all existing” in English without adding of what existing things. So it should have been for example “of all existing monkeys” . Then I would have known that an “ens” is a Monkey. Because this sentence is incorrect English I do not understand the sentence and I cannot continue reading. And this is just one example. I find this kind of confusing use of the English language in most of your sentences.
Now, since you also added the Spanish version I looked at that to see if I could maybe see there what you are trying to say. In the Spanish text I read: “El concepto más general que existe (y, desde luego, uno de los más primitivos) es el de ente”.
Although I don’t speak Spanish it turns out that the Spanish sentence actually is much better understandable to me than the English text. I think the correct translation from Spanish to English of the first part is: “The most general concept that exists”.
You could also have said: “The most general concept of all concepts” or “The most general concept of all existing concepts”. At least then I would have understood it the first time and could have continued reading.
Still, I wonder why you call these concepts “ens” and not “umpa lumpa” for example, but that is another matter.
I hope you now understand why the English version of your paper is incomprehensible to me.


Wed Mar 16, 2016 4:46 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
Harry, thank you for keeping in touch. I think it may be very useful.
Certainly my English must be very poor. Neither I have spoken it nor written, except in some letters to foreign people or institutions, and the texts sent to this forum. Indeed, it allowed me to read textbooks throughout my life, from which I have learnt a great part of all what I know.
Thus, I do not dare to argue with you about something that I do not master. I will only say that I try to supplement my lack of mastery of English grammar by applying certain rules that I believe can be of a common character in all languages. For example, in the case that your quotes: I use the word "all" as a pronoun, while "existing" is used as a present participle, i.e., as an adjective, so "all existing" turns out to be a nominal expression whose meaning I think it is well determined by the context, equal to that of "all existing concepts". What other meaning could it have?
I acknowledge that the introduction of many neologisms can be somewhat overwhelming. I do it to distinguish just one from the many other meanings that a same name may have in common use. The name "ens" has been taken from Latin, and preferred by me to the English word "being", for its obvious connection to the name used in Spanish. The introduction of a word, whatever, with its meaning is not a whim: it is essential to distinguish it from that of the word "thing".


Wed Mar 16, 2016 8:10 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
Fact is that I spent a lot of time looking at that sentence and I now only undestand the first part.
I still do not know what you mean with the rest of that sentence:
"which represents all entes (beings) as individuals of its own, and by whose perception (intuition) is obtained the most abstract (the least, in a certain sense) knowledge of them".


Thu Mar 17, 2016 4:56 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
As I have expressed in some other text, the underlining of a word indicates that the phrase is used to determine its meaning or usage (easily recognizable as the only one that gives an obvious sense to the phrase).
The notion of concept is more primitive than that of set: every concept has a lot of concepts equivalent to it, i.e. representing the same entes (i.e., having the same individuals); on the other hand, there is only a set that has just the same elements. In other words: a set is a concept perfectly determined by the totality of its individuals (to which I call elements, to indicate that I'm dealing with the mathematical notion of set.)
Intuition is the perception of concepts (cognitive perception), not the perception of sensus (sensitive perception).
Knowing an ens is the same that intuiting a concept representing it, or having it as an individual of its own. The more general is the concept (i.e., the many more individuals it has), the more abstract, or less concrete, is the knowledge provided by it (when intuited)): entes are distinguished from each other by intuiting concepts having some individuals and not others. Obviously, the concept of ens does not provide any distinction between any entes: it is common to all of them. To say that anything is an ens is the least that can be said of it.
Harry, please note that I do not intend to define the primitive notions, but that I take them to indicate the meaning I give to expressions that I use. I advise you to do a first fast reading throughout the text, though it may be unintelligible: you may find the answer to your questions in subsequent paragraphs.


Thu Mar 17, 2016 8:35 pm
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Post Re: KEY CONCEPTS CONFUSED BY OFFICIAL MATHS AND PHYSICS
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Mon Jul 18, 2016 6:43 am
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