Chapter 16 Volume Fourteen

Chapter One What we have said about such ontology should suffice.All philosophers regard opposites as first principles, whether in natural things or in things that do not change; A certain thing has its evolution; from this point of view, if "white" is the first principle, white should be regarded as white, and there is no more thing that is prior to white; but this white is presupposed as the evolution of another thing, and It is absurd that this underlying thing must precede "white". But all things derived from opposites arise from some substratum; then the opposites must contain this substratum somewhere.It is not only obvious that there is no antithesis to Being, but it can also be verified by intellectual considerations.Therefore all antithesis cannot be strictly called the first principle; the first principle should be distinguished from the antithesis.

These thinkers, however, took matter as one of the two opposites, and some took "inequity" (which they believed to be the nature of "many") as the antithesis of the one, while others took the many as the element. One against the other.The former refers to "unequal two", that is, "big and small" to make numbers, while the latter uses "public" to make numbers.When that philosopher said "unequal and unitary" as the elements, he took "unequal" as a "two" composed of "big and small", meaning "unequal" or "big and small" as the An element without stating that they are one by definition rather than one by number.They are quite confused about the principles of these so-called elements. Some people list "big" and "small" and "one" as the number of elements, two for matter and one for form; others list " More and less", because the nature of "big and small" can only be applied to measurement, not to counting; and some people list "exceeding and being exceeded"——

That is, the commonality of size and number.These different opinions are not different in some of the consequences they may give rise to; as the explanations they furnish are abstract, the consequences they produce are also abstract questions, and what each seeks to justify is also abstract. Just to avoid abstract difficulties,—the only difference is that if the principle is not big and small, but exceeding and being surpassed, such elements will be made into columns before 2; because " "Exceeded" and "exceeded" are more common than "big and small", and the number of columns is also more common than 2.But they only speak of one meaning and do not recognize the other.

Others regard "difference" and "different" as a pair, and only some people regard "all" as a (single) pair.However, according to what they said, "everything comes from opposites", "not equal" should be the opposite of "equal", "difference" should be the opposite of "same", and "different" should be the opposite of "original". , then it is still appropriate to regard "many" as opposed to "one", but the pairing of many as one cannot be completely free from criticism; because the opposite of many is less, and the many are many, then their corresponding is less, so "One" just turned into "less".

"One" is obviously a measure.In each instance there must be one, distinct, substantive things, such as music (scales) whose units are quarters, measurements whose units are a finger or a foot or the like, and rhythms whose units are one beat to one. syllable.Similarly, with respect to gravity the unit is a certain weight.All instances are measured qualitatively and quantitatively by the same method. (Measurement is indistinguishable. The former is based on category theory, while the latter is based on sensory theory.) "One" itself is not the ontology of anything.This is justified; the one is the measure of the many, and the number is the measured many, that is, the number of ones.So it is natural that one is not a number, nor is the unit of measure mixed with measures; for both the unit of measure and one are the starting point of calculation.The measurement must always be the same thing as everything it measures. For example, if the thing is a herd of horses, it must be measured as "horse", and if it is a crowd, it must also be measured as "human".If they were one man, one horse, and one god then the measure might be "living creatures", and their count would be three living creatures.If things are "people", "white", and "walking", these cannot be counted, because these belong to the same theme, and this theme is only one in number, but these (in terms of different types of predicates) are also Can calculate the number of its category, or the number of other names.

Those people regard "unequal" as one thing, and "two" as an undetermined combination of "big and small". It is impossible to make a statement, and it is not a probable fact.For (a) more and less are to number, and greatness and smallness are to measure, as odd and even, straight and curved, rough and smooth, are only the evolution and properties of number and measure and other things, and are not the substratum of those things.Again, (b) In addition to this error, "big and small" etc. must be related to certain things; but the category of relation comes after quality and quantity, and as reality or substance is only the last of them; we have said Here, however, it is not matter that is relevant, but only an attribute of quantity, for things must retain some manifest nature in order by which matter can be related to other things in general, or to parts of other things, or to their genus. .Those who establish a relationship with other things in a greater or lesser way, more or less, must themselves have the nature of being more or less, greater or lesser, or generally related to other things.Relation is the most subtle noumenon or reality, and its signs can be seen here, there is increase or decrease in quantity, change in quality, movement in place, birth and death in essence, but there is no birth and death in relation, no change.

There is no change in the relationship itself; if the things related to it change in quantity, although the thing itself does not change, its relationship will be "larger" one time, "smaller" another time, and then "smaller" again. Son "equal". (c) Every thing, that is to say, every substance, is necessarily potential in its matter in the respective categories involved; but the relation is neither potential nor actualized into a substance. It is strange, or rather impossible, then, to place the non-substance prior to the noumenon and to place it as an element within the noumenon; for all the categories are subsequent to the noumenon.And (D) element is not the cloud of the thing that itself is an element, but whether it is separated or combined, it is expressed as a number. Long and short are related to lines, and the same is true for width and narrowness.Now if there are many (quite a lot of numbers), among them the term "less" is included in the constant function, such as 2 (2 cannot be regarded as more, because if 2 is counted as "more", 1 should be "less") , and this number must have another relative item representing absolute "many", such as 10 (if there is no number greater than 10), or 10,000.

From this point of view, how can a number consist of less and more, or both signify the number, or neither; but in fact, a number can only signify one or the other of the two. one item. Chapter Two We must inquire whether eternal things can be composed of elements.If so, they would have matter; for everything composed of elements is a composite of matter and form.Then though things are supposed to be eternal, if they were ever composed, they must be composed, whether they have been long ago or are now, and all composite things must be derived from their potentialities (if they were not). Potentiality cannot be generated, nor can it contain such elements), since potentialities can be realized or not realized—this is realized as an eternal number, but since it contains matter, it must still be like all things that contain material elements. It is possible not to exist; from here, any number that is old in age may lose its existence, and a number that has survived for a day may lose its existence; can always lose its existence.They cannot, then, be eternal, and we have had occasion elsewhere to show that all that may perish are not eternal.If what we say now is generally true—that no substance which is not actualized is not eternal—if the element is the matter underlying the substance, no such constituent element can exist in any eternal substance.

Some people have stated that the elements that work together with "Yuanyi" are "undetermined two", and use this to blame the "unequal" statement for causing confusion. The reasons they hold can be said to be sufficient; Difficulties arise from "as relations, and from "relations" as elements, but these thinkers use those elements to make numbers, whether they are Italian or mathematical numbers, and encounter the same objections in other respects. Many reasons lead them to such explanations, not least of which is the antiquity of their way of dealing with problems.They believe that if they do not violate and deny Parmenides' famous saying, all existing things should be "one", that is, "absolute reality".

"Not being can never be proved to exist as being" They held that if things are more than "one", this must prove not to be; "Things" are combined to form "many". But, first, if it has multiple meanings (for this is sometimes substance, sometimes a quality, sometimes a quantity, and sometimes other categories), and not if it is supposed to be non-existent, then What kind of "one" would the oneness of all existing things be?Whether the beings are one, or the other categories of evolutions and similarities are one, or the categories are one—so that "this" and "this" and "so many" and other categories, which refer to A certain level is true, all belong to "one"?But it is strange or impossible that the appearance of a single thing (not being) in the world brings out so many parts, one part is an existing "this and that", and the other part is an "such and such" That", another part is a "that size", and another part is a "here and there".

Second, what kind of "non-is and is" are things actually composed of?Because like "is", "non-is" also has multiple meanings; "not a person" means not one of the body, "non-straight" means the non-being of a certain quality, and "not three cubits long" means a certain measure. Not yes.So which kind of combination of "is and what is not" makes things multiply?The "non-is" that this thinker combines with "is" to make existing things have their multiplicity is falsity and falsity.It is as if a geometer assumes "not a foot long" to be a foot long, and claims that this is the reason why we must assume some falsity.The geometer neither presupposes anything false (for the premise is irrelevant to the inference), nor does the "non-being" by which things are created or made man mean so.But because "non-being" is different in various categories, and in addition, both falsehood and potentiality belong to "non-being" to create non-being that actually comes from potentiality; Human beings are generated, whiteness is generated by non-whiteness and potential whiteness, as for what is generated as one, it is nothing and nothing. Clearly, the question is how what is meant to be substance is multiplied; for there are many created numbers and lines and bodies.But this is just strange, because it is enough to examine what it is for "what", but it is enough to not consider what it is for quality and quantity.Of course, "undecided two" or "big and small" will not mean that there are two kinds of white, or that there are many colors, flavors, and shapes; Small", then color, taste, etc. will also become numbers and units.But if they study these other categories, they will also understand the cause of the multiplicity of substances; and the cause of the multiplicity of beings in each category is this same or comparable thing.In seeking the antithesis of reality and monadity, so that the opposite and reality are co-generated with monadity, they go into the same astray and point to the relative term (i.e. "not equal"), "relation" is not Reality is the antithesis of Yuanyi, and it is not their negation, but just like noumenon and essence, it is a category of reality.They should ask the question why there are many related terms instead of just one.Ordinarily, they have studied why there are many 1s besides the first 1 (the original one), but they did not proceed to inquire into the many "ranges" besides this "range".However, they just applied these many "inequalities" and often talked about big and small, many and few (from this number), long and short (from this to make a line), wide and narrow (from this to make a noodle), Deep and shallow (from this system); they also speak many kinds of relative words.Where does the multiplicity of these relational things come from? In our case, then, this must presuppose a potentiality for every thing that is; and one who holds such a claim must also declare that potentiality is a "this" that is also potentially a being. is, but does not become a being by itself—for example, to say that it is "the relation" (as in saying "the quality") is neither potentially monadic or real, nor is it the negation of monadic and real. , but only one of many things.According to what we have already said, if he wants to inquire why there are many beings, he need not inquire further how there are many beings in the same category—why there are many substances, why there are many qualities—he should inquire about all Why are there so many; Some are actually substances, some are evolutions; some are relations.In categories other than ontology, there is another problem inherent in multiplicity.Because the other categories cannot be separated from the substances, just because their bases are many, so the quality and quantity also become many; at each level it should have some substance; but this substance cannot be separated from the substance.If one thing is not regarded as an "individual" but also as a general character, this may explain why "individuals" are multiplied on each individual ontology.Here lies the perplexity arising from the question of why substances are not only one, but are indeed many. But, again, if there is a difference between the individual and the quantity, we have not yet known how and why the existing things are multiplied. They only talked about how the quantity is multiplied.For all "numbers" signify quantity, except as measurement, or indistinguishable in quantity, their meaning is also number.Therefore, if the quantity is different from the "what" (ontology), no one has explained to us clearly how and why the "what" becomes multiplied; and if the "what" is the same as the quantity , then he has to face many inconsistencies. Regarding numbers, they can also focus on this issue, believing that these exist, and what is the value of this.To those who believe in patterns, this furnishes the cause of certain kinds of existing things, since every number is a pattern, and patterns are always causes of other things to be; let them have this supposition.However, due to the violation of the connotation of the Italian theory and the person who does not insist on the Italian formula (so he does not use the Italian formula to discuss numbers), what he is discussing is only the number of mathematics; why should we believe his statement and Admitting the existence of Italian numbers, what effect do such numbers have on other things?He who says that such a number exists does not claim that it is the cause of anything, nor do we observe that it has been the cause of anything (he rather says that it is an independent reality existing only for itself); The theorems of the mathematicians, we have said before, are all valid even when applied to sensible things. Chapter three As for those who conceived the existence of forms, and took them as numbers according to their assumption—a method of abstractly prescribing words from instances—they assumed the coherence of universal terms, and went on to explain the necessary existence of numbers.Their reasons, however, are neither sufficient nor possible, by which one must not believe that the existence of numbers is an independent reality.Furthermore, the Pythagoreans saw that many sensible things have the attribute of number, and they assumed that real things are numbers—not that things can be counted by numbers, but that things are composed of numbers.Why?There are countless attributes in the rhythm, in the celestial body, and in other things.Those who say that only mathematical numbers exist, who, on their own grounds, ought not to have said such things, yet often say that these sensible things cannot be the subject of scholarship.As we have said before, we affirm that these are the subjects of scholarship.Mathematical objects obviously cannot exist independently of sensible things; if they existed, their properties would not be seen in substances.In this respect the Pythagoreans do not invite objection; it is only to be criticized that they constitute natural bodies out of numbers, and light and heavy things out of insignificant things, what they call celestial bodies, and Other substances are not like the things of this sensible world.But those who regard number as separable often think that "perceivable things are not real", and "number formula is the real axiom", and appeal to the spirit to point out that number must exist and must be independent of things; Geometric objects are also similar.It is evident, then, that the counter-theory of numbers, which contradicts it, we are now about to ask, how can sensible things exhibit the property of being number, if number does not exist in sensible things, Those who insist on the unique existence of number should answer this question. Some people see that the point is the end of the line and the limit of the line, the line is to the surface, and the surface is to the body, so they think that these must be a kind of real objects.So we have to check, perhaps for weak reasons.For (1) the extreme is only the limit of these things, and is not itself the substance.Walking or locomotion in general must come to an end, and, according to their argument, each of these will also become a "this," a substance.This is ridiculous. (2) Even if these are noumenon, they should be noumenon in this sense world; and their argument is trying to get out of this sense world.How can they be separated and free? Also, regarding all numbers and mathematical objects, if we still think that what we have discussed is not complete, we can raise this question carefully. The a priori number (mathematical object) and the postnatal number (geometric object) are not mutually beneficial. .For those who preoccupied with maintaining the existence of mathematical objects, if numbers did not exist, the measure of space would not exist, but if the measure of space did not exist, souls and sensible substances would exist.But the natural system does not look like a bad script with disconnected acts, as seen in the world as it really is.For those who believe in Italian, this difficulty is overlooked; they make the measure of space out of matter and number, the line out of the number 2, and, no doubt, the surface of 3, the body of 4,—or they make another There is no difference in making it with other numbers. But will these measures become meanings, or what is the condition of their existence, and what effect do they have on things?These are useless, just as mathematical objects are useless.It is difficult for a man to derive practical utility from any of his theorems if he does not want to interfere with mathematical objects to establish his own principles, but it is not difficult to imagine some arbitrary assumptions from which to spin a long chain of conclusions. These thinkers, then, commit such errors in order to combine mathematical objects with Italian forms.Those who originally focused on the two types of numbers, formulas and mathematics, did not and could not say how mathematical numbers exist and what they consist of.They place mathematical numbers between Italian and sensible numbers. (i) If this consisted of "big and small", this would be the same as Italian numbers, (he made spatial measures from certain varieties of large and small.) (ii) If he cited other elements, the number of There are too many material elements.If the first principles of the two types of number systems are the same thing, then the unitary will make these the common formal principles.And we have to ask how "one" can be regarded as many things, and why, according to him, numbers cannot be made from one, but can only be derived from "one" and "undetermined two". All of this is absurd, and it all conflicts and contradicts itself. In these theories we seem to find the long essays of Chemonides, which the slaves put on affectation while concealing the real cause. The elements "big and small" also seem to protest against being forced to do what they cannot do; in fact they can make no different numbers than those obtained by multiplying one by two. It is also absurd, or even impossible, to attribute eternal things to the creative process. There is no need to doubt whether the Pythagoreans ever held that creation was of eternal things; for they expressly said that whether by face or surface, or seed, or those elements which they could not express, The constitutive element is always, as soon as it is constituted, that which was infinite is at once bounded by these limits.Since they are constructing a world, but constructing theories in the language of the natural sciences, it is not unreasonable for us to examine such theories, but let us do so in the present investigation; we are dealing with In the principles that act upon immutable things, we must study the creation of numbers of this kind. These thinkers say that odd numbers have no creation process, which is equivalent to saying that even numbers are created; even.Then, "unequal" must belong to "big and small" before being balanced.If greatness and smallness are always balanced, then there is no "unequal" in the first place; because what always exists is only waiting, and inequity means non-existence.So obviously, their introduction of the theory of creation of numbers is not beneficial to the theory. Chapter Four In the question of how elements and principles relate to the beautiful and the good there is a difficulty which men are to blame for failing to admit.The problem is this: whether there is, among the elements, such an element as we mean the good and the highest good, or whether the essential good and the highest good should come after the elements.The theologians, who seem to agree with some modern thinkers, answer this question in the negative, saying that goodness and beauty can only appear in things after nature has already had something to do with it. (They did this to avoid the objection that some people encounter when they regard "oneness" as the first principle. The fact that the objection is caused is not because they regard goodness as an attribute of the first principle, but because they regard oneness as The elements of number making make it a principle, and this is the cause of objection. The old poets said that it is not the night and sky or chaos that represent the original power of the universe, or the Ochian <Ocean>, that reigns over the universe and rules everything. But Zeus, and here their poetic sentiments correspond to this thought. These poets say this precisely because they think that the rulers of the world are changing; Merge the good and the beautiful and take the "Supreme Good" as the original creator; the same is true of the Magi and the later sages, such as Empedocles and Anaxagoras: the former took friendship as the main creator. One of the elements, the latter takes rationality as the first principle. For those who insist on the existence of the unchanging noumenon, some people say that this one is the original good; but they think that the nature of the original good is mainly the one. So, which is right?It would be surprising if the basic and eternal, the most self-sufficient, were not primarily endowed with the most self-sufficient quality of "goodness."Things are self-sufficient and indestructible, and there is really no other reason than the goodness of their nature.Therefore, it must be right to say that the good is the first principle; it is impossible to say that this principle should be the unity, or that if it is not the unity, at least it should be an element of the sequence.In order to avoid strong objections, some have abandoned the theory (those who maintain that one is also a first principle, have since restricted "one" to the principles and elements of mathematical numbers); That is to say, the theory of "principal goodness" means that the ones are the same as the varieties of goodness, and there are too many goodnesses in the world.Also, if all the general forms are numbers, then all the general forms will be the same as the good varieties.The Italian way to make people imagine anything.If only the modes of good are supposed, these are not modes of substances (but only modes of essences); Both will be good (because Italian has the quality of good). These absurd inferences all follow the theory of "the unity of the yuan and the goodness of the original". Another question also arises, whether the elements relative to the unity, whether they are numerous or unequal, such as large and small, are inherently evil (so a thinker sees that creation is evil because it comes from opposites. would be the nature of many, avoiding good as one; while others simply say that inequality is the nature of evil).It follows, then, that all things, except the one and the one, share in this evil, and the participation of the series in this evil has a more immediate form than the spatial measure, so that the evil becomes the realization of the good in it. sphere of activity, and since the object has a tendency to destroy its object, to participate in it is to hope to destroy it.As we have just said, if matter is potentially everything, such as potential fire has to be actualized fire, then evil is potential "good." All these fallacies arise from (1) taking every principle as an element; (2) taking pairs as principles; (3) taking one as a principle; Formula, also as the original ontology that can exist independently. Chapter five If, then, it is impossible not to include the good in each of the first principles, and it is also impossible to place the good in this way, it is clear that there is something unclear about the assumption of principles and original noumena.Whoever compares animals and plants with the cosmic principle, has not thought carefully about matter; in animals and plants, the more complete is always the less complete and unformed, because of this view. Let the thinker say that the first principle should be the same, so this one should not be a real thing.This is not true, because even for the animals and plants in this world, the principle of their origin is still complete; because this is the reproduction of human beings, the seeds are not the first. It is also absurd to say that the creation of space also creates a mathematical solid (because individual things have the property of occupying space, so they are separated in space; but mathematical objects do not have a definite place), and that the mathematical solid is always in some places, but cannot explain where they are. Those who say that things come from elements, and numbers are the most primitive things, should first explain what it means to say that a thing comes from only one thing, and then explain how numbers are derived from first principles.due to mixing?But (1) not everything can be mixed; (2) the things produced by the elements will be different from the elements, and such a mixture will be inseparable, and the unity will not always remain as a distinct reality, as they hoped. yes.Like a syllable, due to the combination?But (1) there must be a place to arrange the constituent elements; (2) whenever people think of numbers, they should be able to think of one and many separately, so the number will be such a composition—— "One" plus "many", or "one" plus "unequal". Again, if a thing comes out of something, that something is still in its product, or there is no such thing in the product; if a number comes out of those elements, the element is in the number or not in the number. ?Only created things can be out of elements and elements remain in them.Is the number then derived from the elements as from the seeds?But the indistinguishable should be that which cannot be squeezed out.Is it out of antithesis, out of its mutable antithesis?But all things that come out of pairs must be different and unchanged as the bottom layer.One thinker takes the one as the antithesis of "many", another takes the one as "equal" and makes it the antithesis of "not equal", so the number must be counted as coming out of antithesis.Therefore, the number derived from its antithesis must still have some invariant.Also, why all the things in the world that come from or have pairs are destroyed (even if all the pairs are used to make them, they must be destroyed), but only numbers are not destroyed?There is nothing to say about this.But presence or absence in its product is always destructive to the compound, for example the struggle destroys the "mixture" (but this should not be destroyed; since the mixture is not really the pair with it).In what way, number is the cause of substance and reality, the question has not yet been decided - (1) Is it due to number as a limit (for example, a point is the limit of spatial measurement)?This is how Eurytos determined the number of all things. He tried to number them after the forms of natural objects, as some men number triangles and squares with pebbles (for example, men and horses have their own numbers). number), or (ii) because music is a ratio of numbers, so are people and everything else?But how can attributes such as white, sweet, and hot be counted?Obviously, number is not the how or the cause of things; the how is the proportion, and the number is the matter of this proportion.For example, it is said that there is a certain amount of muscle or bone, and its meaning is as follows: three parts of fire and two parts of earth.The number, whatever the number, always refers to the number of certain things, or how many fires or how many earths, or how many units; but what it is is the proportion of each thing in a mixture; A mixed ratio (either entity or other class ratio). Therefore, whether it is a general number or is composed of abstract units, the number is neither the substance of the thing, nor the formula or the cause of the form, nor the effective cause of the thing.Of course, this is not the ultimate reason. Chapter Six One can ask this question, because the composition of things can be described by an easily calculated number or an odd number, so what advantage things can get from numbers. In fact, honey water is not better because it is a ratio of three to three. There is no special ratio, but honey water that is properly diluted is more suitable than honey water that can be expressed numerically and is too sweet.Also, the proportion of a mixture is the addition of numbers, not the multiplication. For example, if it is "three parts water plus two parts honey", it cannot be "three times two".Because the family and genus (category) of the multipliers of things must be the same; therefore, the product of 1×2×3 must be measurable by 1, and the product of 4×5×6 must be measurable by 4, and all products must be measured by each principle. The multiplier is used to measure it.Therefore, when the number of water is 2×3, the number of fire cannot be 2×5×3×6 at the same time. If all things must take part in numbers, many things must be the same, and the same number must belong to both this and that.So, is number the cause?Do things exist because of factors?or this is not sure?For example, the movements of the sun are innumerable, and the movements of the moon are also innumerable—so that the life span and growth period of each animal are innumerable.So, isn't it possible that these numbers cannot be squared, or cubed, and some are equal or some are multiplied?Since all things are assumed to belong to numbers, and the range of commonly used numbers is often limited, it is impossible for different things not to belong to the same number.Certain things, then, being assigned the same number, must be the same by virtue of their number being the same; for example, the sun and the moon must be the same.But why are these the reasons?It is said that there are seven vowels, the melody depends on the seven strings, the pleiades are seven, the animals are seven years old and have teeth (at least some are like this, some are not), and the heroes who fight against the bottom are also seven.This is because the number must be in the shape of seven, so the battle heroes will be counted as seven, and the Pleiades will also make up seven?In fact, there are seven heroes in battle, because there are seven in the gate of the castle or other reasons; as for the Pleiades, we only have seven points, which is the same as the Ursa Major constellation has twelve stars, and people with sharp eyes can point in both constellations more stars.Not only that, they even said that Ξ, Ψ, and Ζ are consonants, and because there are three consonants, there are also three consonants (consonants).They suddenly forget that there can be thousands of such phonetic notations, for example, ΓΡ can also be counted as one.However, if they say that only these three letters are equivalent to the other two letters, then the reason is that there are three parts in the oral utterance, and those three parts corresponding to the σ sound can only have these three letters, and there is nothing else to count. Polyphony, which has nothing to do with triads; there are more than three actual consonants, and there are only three polyphonics.These people, like the old-fashioned Homeric scholars, tend to see the small differences but not the big differences. Some people say that there are many examples of this kind. For example, the numbers shown by the two middle strings are nine and eight. The epic uses seventeen syllables as a line, and the rhythm of these two strings. The cadence and stagnation of the recitation correspond to the nine notes in the front right half of the line, and the eight notes in the back half of the left line.They also say that the number of letters from A to Ω is equal to the number of notes on the flute from the lowest to the highest note, and that the number of notes is equal to the number of days in the celestial chorus.It is doubtful that no one has difficulty in drawing such comparisons, and it is easy to find such similes in eternal things, and it is not difficult to find them in secular things. After such an examination as we have done, the admirable properties which some have ascribed to numbers as the causes of nature, and their pairs, and the general relations of mathematics, seem to have vanished; No number can be established as the cause of things in any of the meanings of principles.There is, however, a meaning which they also discerned, that the good belongs to numbers, and odd, straight, square, and certain number potentialities are ordered in the paired ranks of beauty.Seasons correspond to certain numbers (such as four); they collect examples with similar functions in mathematical theory. These are actually some "matches".They are originally coincident, and those who coincide with things can be adapted to each other, and can also be compared.In every category of reality there is always an analogical term to be found—what is straight to a line is analogous to a plane, strange perhaps to number, and white to color. Furthermore, the causes of musical phenomena, etc., do not concern the number of numbers (even though the numbers are equal, they are of different kinds; and the same is true of the units); so, for this reason alone, we do not need to pay attention to the numbers. These are the consequences of the theory of numbers. , Of course, this can also bring together more paradoxes.他们在制数时遭遇到很多麻烦，始终未能完成一个数论体系，这似乎就显示了数学对象，并不如有些人所说，可分离于感觉事物之外，它们也不能是第一原理。