Limit

“ Limit is the negation of a being, or of something real, applied to a being: the limit of a line is the point which terminates it; the limit of a force is the point beyond which it does not extend.
155. The idea of the infinite, denying limit, denies a negation; therefore it is an affirmative idea: the idea of the finite is negative, because it affirms a negation.
156. The idea of the infinite is applied to many orders of beings, and presents strange anomalies, which seem contradictions. ”

“ The I feels its limit because it presses beyond it; and it presses beyond the limit because it divines something to which it has not yet fully attained. For these results, are needed different forms of activity that can be compared between themselves, and some basis or standard for this comparison. In order to make the discussion more easily understood, we should, perhaps, define more carefully the terms used. We have to ask, then, What is meant by the limit with which the I finds itself confronted? The limit is the world of objects within which the soul seems to be inclosed. ”

“ The same experience teaches that what is the limit of some things is not the limit of others, and that the limit applied to one object must be denied of another. When we compare different beings together, we frequently find ourselves denying certain limits. As our understanding has the faculty of generalizing, it is evident that we may conceive in general the negation of certain limits, and form an indeterminate conception, including the two ideas of negation and limit. ”

“ What a man adopts as true, and what he rejects as false, are conditioned alike by this limit: a limit not merely different in different individuals, but variable and frequently varying in the same individual. ”

“ Does the character of finite, which is met with in all created beings, involve a determinate limit beyond which they cannot pass? If this limit exists, is not the number of possible species also limited? And if these species are not infinite, is not an infinite number an illusion? ”

“ This limit is found in that impinging which gives occasion to the I for the limitation of itself. This limit is not the reality of what we know as object. Our objective world stands in no relation with it. ”

“ Among the foundations of the Higher Mathematics is also the Idea of a Limit. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses, The Axiom which we employ in introducing this Idea into our reasoning is this:—What is true up to the Limit is true at the Limit. This Idea and Axiom are the bases of all Methods of Limits, Fluxions, Differentials, Variations, and the like. ”

“ The sum of all the possible objects of our cognition seems to us to be a level surface, with an apparent horizon—that which forms the limit of its extent, and which has been termed by us the idea of unconditioned totality. ”

“ It must affirm the non-Ego as limiting, determining the Ego; and at the same time must affirm or posit tins limitation, as a limitation of the Ego. The limit shall be posited only in so far as the Ego is affirmed as passive; the Ego shall be affirmed only in so far as the limit is posited. ”

“ The limit exists by the very act of concentration. We see now how it is possible that this limit should become enlarged; and whence comes the content of the endless life that shall fill out the expanding limit into infinitude. ”

“ The notions of limit and continuity which we have been defining must not be confounded with the notions of the limit of a function for approaches to a given argument, or the continuity of a function in the neighbourhood of a given argument. ”

“ We know the conditions which must be fulfilled, but at the same time, we see the impossibility of fulfilling them. When any one tries to persuade us of the contrary, we reflect on the idea of the infinite, and say: "No; it is a contradiction of infinity; it is not infinite, but finite." We distinguish perfectly well between the absence of the perception of the limit and its non-existence. ”

“ Now since the extreme limit of being is defined, the whole is like a well-rounded sphere, of equal radius in all directions, for it may not be less or greater in one part or another. For neither is there not-being to prevent its attaining to equality, nor is it possible that being should in one place be more and in another less than being, since all is inviolably one. ”

“ Because, of two propositions, one of which must be true, it proves both impossible—it proves that space cannot have a limit, because a limit is inconceivable, and yet that it must have a limit, because unlimited space is inconceivable; it proves, therefore, that space has a limit and has no limit, which is absurd. ”

“ The answer is that infinity is perfection without lack, and if you say that it has power without limit and no power with limit, you are detracting from its perfection. And if you say that the world, which is lacking in perfection, was the initial limit, you are lacking its power. Therefore, we must say that it is a limit without limit, and the initial limit is the spheres, which are the complete power and the lacking power. When they receive influence from its perfection, they are complete power, and when they are lacking influence, they are lacking power. ”

“ As a fact, one of the first things to be noted about our conception of Being is that, as a matter of Logic, it is the concept of a limit, namely of that limit to which the internal meaning or purpose of an idea tends as it grows consciously determinate. ”

“ You can voluntarily shut the door of salvation and hamper the lock, and no man can open. A limit is no absolute limit to you because your very consciousness of the limit involves your consciousness of the beyond which makes it a limit. ”

“ One ceases to believe that a definite limit is the indispensable means of existence. Where does la Place de la Trinité begin? The streets mingle their bodies. The squares isolate themselves with great difficulty. ”

“ We have explained the idea of infinity in general, by the indeterminate conceptions of being and the negation of limit. In order to assure ourselves that the explanation is well grounded, and that we have pointed out the essential marks of the conception, let us examine whether their application to determinate objects corresponds to what we have established in general. ”

“ When this Limit chances to be definable by us in terms quite other than those which the infinite series embodies, we are able to be, at once, in possession of the Limit, aware that this is the Limit of the infinite series, and able to see how the infinite series is absolutely incapable of ever attaining this its own goal. ”

“ The whole object of the Prophets and the Sages was to declare that a limit is set to human reason where it must halt. ”

“ “And I suppose where no limit exists, as in the case of a rich man with a wide taste who wants to do something, it will be better to choose a limit capriciously than to have none.” ”

“ Liberate yourself as far as you can, and you have done your part; for it is not given to every one to break through all limits, or, more expressively: not to every one is that a limit which is a limit for the rest. Consequently, do not tire yourself with toiling at the limits of others; enough if you tear down yours. Who has ever succeeded in tearing down even one limit for all men? Are not countless persons to-day, as at all times, running about with all the "limitations of humanity"? He who overturns one of his limits may have shown others the way and the means; ”

“ For as the absolute infinite number implies the absolute negation of all limit, when, in treating of the realization of this conception, I meet with things that are contradictory, I say that the realization of the conception is contradictory, because the general and indeterminate conception is more extended than all possible number. ”

“ for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought) .
OGD [→GER | →P/M]
The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense. ”

“ But whether the distances at which these powers act be great or small, it is certain that they are all finite and fixed in the nature of things, so that there is a certain limit never exceeded; and a limit which depends either on the mass or quantity of matter in the bodies acted on ”

“ We have learned how the internal meaning is related to its own Limit, in so far as that is just a limit. But thus to view Being is still not to take account of what seems to common sense the most important of all our relations to the Real. ”

“ Internal sensible representations must always retain this limitation; their object may be expanded, or the limit removed to a greater distance, but to destroy this limit would be to destroy themselves. ”

“ If we could conceive a limit to the total sum of mental power which will be possessed by future multitudes of well-instructed men, yet could we not conceive a limit to the discovery of the properties of materials which they will bend to their service. ”

“ This theory boldly affirms a limit to the divisibility of matter, and thus seems to defy the logic of the metaphysician, who, passing the limit set by the necessary imperfections of manipulation, carries the process of subdivision mentally downward through the scale of littleness, until, finding no place where his conception of subdivision must halt, declares that no limit exists. ”

“ There is a limit of Opakeness, and a limit of Contraction;
30In every Individual Man, and the limit of Opakeness,
Is named Satan: and the limit of Contraction is named Adam.
But when Man sleeps in Beulah, the Saviour in mercy takes
Contractions Limit, and of the Limit he forms Woman: That
Himself may in process of time be born Man to redeem
35But there is no Limit of Expansion! there is no Limit of Translucence. ”

“ The maximum limit cannot be fixed, and there is no need of attempting it. But there is great need of knowing and keeping in mind the minimum limit; for in the pressure to hurry forward there is grave danger that even this limit will not be reached. ”

“ But if they get smaller and smaller, while of any two of the set there is always one that encloses the other, then we begin to have the kind of conditions which would enable us to treat them as having a point for their limit. ”

“ They are not limited for themselves; they have simply learned that in the view of others they are limited. We never recognize a limit that we have not in some sense or degree already passed. If we have partly passed the limit, and in part are restrained by it, then only are we really conscious of it. ”

“ For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which is limited, see ing that the latter is the matter and the former the essence of the system. ”

“ Similarly, is read approaches the limit minus infinity, and is read , in numerical value, approaches the limit infinity.While the above notation is convenient to use in this connection, the student must not forget that infinity is not a limit in the sense in which we defined a limit on p. 11, for infinity is not a number at all. ”

“ It shows us, if we may employ a mathematical expression, that by integrating the equation of man’s development between the limits zero, in which these disgusting practices had full sway, and the limit of A.D. 1891, the precise extent of his advancement in all that we call civilization can better be understood. ”

“ If mathematicians had been obliged to speak of "that to which a quantity, in increasing or diminishing, is always approaching nearer, so that the difference becomes less than any assignable quantity, but to which it never becomes exactly equal," instead of expressing all this by the simple phrase, "the limit of a quantity," we should probably have long remained without most of the important truths which have been discovered by means of the relation between quantities of various kinds and their limits. ”

“ When accused, for example, of laying down absolute principles in such cases, they reply that they are only speaking of 'tendencies,' and recognise the existence of 'checks.' They treat of what would be, if certain forces acted without limit, as a necessary step towards discovering what is when the limits exist. ”

“ While such extremely narrow limits are going to reduce the number of places in the universe where life can develop, it is also going to limit the differences. In our creation things operate by rule. The rule is that in similar circumstance there are similar solutions to a problem. ”

“ Our notion of the Limited is composed, firstly of a consciousness of some kind of being, and secondly of a consciousness of the limits under which it is known. In the antithetical notion of the Unlimited, the consciousness of limits is abolished; but not the consciousness of some kind of being. It is quite true that in the absence of conceived limits, this consciousness ceases to be a concept properly so called; but it is none the less true that it remains as a mode of consciousness. ”

“ The limit (in a quantum) is identical with the whole of the quantum itself. As in itself multiple, the limit is Extensive magnitude; as in itself simple determinateness (qualitative simplicity) , it is Intensive magnitude or Degree. ”

“ He is there. If the infinite had no person, person would be without limit; it would not be infinite; in other words, it would not exist. There is, then, an I. That I of the infinite is God.” ”

“ Who shall set a limit to the influence of a human being? ”

“ Now as to the infinite Power that knoweth no limitations; limitation itself proveth the existence of the unlimited, for the limited is known through the unlimited, just as weakness itself proveth the existence of power, ignorance the existence of knowledge, poverty the existence of wealth. ”