The conception of quant.i.ty, therefore, if rigorously a.n.a.lyzed, will indicate _a priori_ the natural and impa.s.sable boundaries of the science; while a subsequent examination of the quant.i.ties called infinite in the mathematical sense, and of the algebraic symbol of infinity, will be seen to verify the results of this _a priori_ a.n.a.lysis.
Quant.i.ty is that attribute of things in virtue of which they are susceptible of exact mensuration. The question _how much_, or _how many_ (_quantus_), implies the answer, _so much_, or _so many_ (_tantus_); but the answer is possible only through reference to some standard of magnitude or mult.i.tude arbitrarily a.s.sumed. Every object, therefore, of which quant.i.ty, in the mathematical sense, is predicable, must be by its essential nature _mensurable._ Now mensurability implies the existence of actual, definite limits, since without them there could be no fixed relation between the given object and the standard of measurement, and, consequently, no possibility of exact mensuration. In fact, since quantification is the object of all mathematical operations, mathematics may be not inaptly defined as _the science of the determinations of limits_. It is evident, therefore, that the terms _quant.i.ty_ and _finitude_ express the same attribute, namely, _limitation_--the former relatively, the latter absolutely; for quant.i.ty is limitation considered with relation to some standard of measurement, and finitude is limitation considered simply in itself. The sphere of quant.i.ty, therefore, is absolutely identical with the sphere of the finite; and the phrase _infinite quant.i.ty_, if strictly construed, is a contradiction in terms.
The result thus attained by considering abstract quant.i.ty is corroborated by considering concrete and discrete quant.i.ties. Such expressions as _infinite sphere, radius, parallelogram, line,_ and so forth, are self-contradictory. A sphere is limited by its own periphery, and a radius by the centre and circ.u.mference of its circle. A parallelogram of infinite alt.i.tude is impossible, because the limit of its alt.i.tude is a.s.signed in the side which must be parallel to its base in order to const.i.tute it a parallelogram. In brief, all figuration is limitation. The contradiction in the term _infinite line_ is not quite so obvious, but can readily be made apparent. Objectively, a line is only the termination of a surface, and a surface the termination of a solid; hence a line can not exist apart from an extended quant.i.ty, nor an infinite line apart from an infinite quant.i.ty. But as this term has just been shown to be self-contradictory, an infinite line can not exist objectively at all. Again, every line is extension in one dimension; hence a mathematical quant.i.ty, hence mensurable, hence finite; you must therefore, deny that a line is a quant.i.ty, or else affirm that it is finite.
The same conclusion is forced upon us, if from geometry we turn to arithmetic. The phrases _infinite number, infinite series, infinite process_, and so forth, are all contradictory when literally construed.
Number is a relation among separate unities or integers, which, considered objectively as independent of our cognitive powers, must const.i.tute an exact sum; and this exact.i.tude, or synthetic totality, is limitation. If considered subjectively in the mode of its cognition, a number is infinite only in the sense that it is beyond the power of our imagination or conception, which is an abuse of the term. In either case the totality is fixed; that is, finite. So, too, of _series_ and _process_. Since every series involves a succession of terms or numbers, and every process a succession of steps or stages, the notion of series and process plainly involves that of _number_, and must be rigorously dissociated from the idea of infinity. At any one step, at any one term, the number attained is determinate, hence finite. The fact that, by the law of the series or of the process, _we_ may continue the operation _as long as we please_, does not justify the application of the term infinite to the operation itself; if any thing is infinite, it is the will which continues the operation, which is absurd if said of human wills.
Consequently, the attribute of infinity is not predicable either of "diminution without limit," "augmentation without limit," or "endless approximation to a fixed limit," for these mathematical processes continue only as we continue them, consist of steps successively accomplished, and are limited by the very fact of this serial incompletion.
"We can not forbear pointing out an important application of these results to the Critical Philosophy. Kant bases each of his famous four antinomies on the demand of pure reason for unconditioned totality in a regressive series of conditions. This, he says, must be realized either in an absolute first of the series, conditioning all the other members, but itself unconditioned, or else in the absolute infinity of the series without a first; but reason is utterly unable, on account of mutual contradiction, to decide in which of the two alternatives the unconditioned is found. By the principles we have laid down, however, the problem is solved. The absolute infinity of a series is a contradiction _in adjecto_. As every number, although immeasurably and inconceivably great, is impossible unless _unity_ is given as its basis, so every series, being itself a number, is impossible unless a _first term_ is given as a commencement. Through a first term alone is the unconditioned possible; that is, if it does not exist in a first term, it can not exist at all; of the two alternatives, therefore, one altogether disappears, and reason is freed from the dilemma of a compulsory yet impossible decision. Even if it should be allowed that the series has no first term, but has originated _ab terno_, it must always at each instant have a _last term_; the series, as a whole, can not be infinite, and hence can not, as Kant claims it can, realize in its wholeness unconditioned totality. Since countless terms forever remain unreached, the series is forever limited by them. Kant himself admits that it _can never be completed_, and is only potentially infinite; actually, therefore, by his own admission, it is finite. But a last term implies a first, as absolutely as one end of a string implies the other; the only possibility of an unconditioned lies in Kant"s first alternative, and if, as he maintains Reason must demand it, she can not hesitate in her decisions. That _number is a limitation_ is no new truth, and that every series involves number is self-evident; and it is surprising that so radical a criticism on Kant"s system should never have suggested itself to his opponents. Even the so-called _moments_ of time can not be regarded as const.i.tuting a real series, for a series can not be real except through its divisibility into members whereas time is indivisible, and its part.i.tion into moments is a conventional fiction.
Exterior limitability and interior divisibility result equally from the possibility of discontinuity. Exterior illimitability and interior indivisibility are simple phases of the same attribute of _necessary continuity_ contemplated under different aspects. From this principle flows another upon which it is impossible to lay too much stress, namely; _illimitability and indivisibility, infinity and unity, reciprocally necessitate each other_. Hence the Quant.i.tative Infinites must be also Units, and the division of s.p.a.ce and time, implying absolute contradiction, is not even cogitable as an hypothesis.[220]
"The word _infinite_, therefore, in mathematical usage, as applied to _process_ and to _quant.i.ty_, has a two-fold signification. An infinite process is one which we can continue _as long as we please_, but which exists solely in our continuance of it.[221] An infinite quant.i.ty is one which exceeds our powers of mensuration or of conception, but which, nevertheless, has bounds and limits in itself.[222] Hence the possibility of relation among infinite quant.i.ties, and of different orders of infinities. If the words _infinite, infinity, infinitesimal_, should be banished from mathematical treatises and replaced by the words _indefinite, indefinity,_ and _indefinitesimal_, mathematics would suffer no loss, while, by removing a perpetual source of confusion, metaphysics would get great gain."
[Footnote 220: By the application of these principles the writer in the "North American Review" completely dissolves the antinomies by which Hamilton seeks to sustain his "Philosophy of the Conditioned." See "North American Review," 1864, pp. 432-437.]
[Footnote 221: De Morgan, "Diff. and Integ. Calc." p. 9.]
[Footnote 222: Id., ib., p. 25.]
The above must be regarded as a complete refutation of the position taken by _Hume_, to wit, that the idea of nature eternally existing in a state of order, without a cause other than the eternally inherent laws of nature, is no more self-contradictory than the idea of an eternally-existing and infinite mind, who originated this order--a G.o.d existing without a cause. The eternal and infinite Mind is indivisible and illimitable; nature, in its totality, as well as in its individual parts, has interior divisibility, and exterior limitability. The infinity of G.o.d is not a _quant.i.tative_, but a _qualitative_ infinity.
The miscalled eternity and infinity of nature is an _indefinite_ extension and protension in time and s.p.a.ce, and, as _quant.i.tative_, must necessarily be limited and measurable, therefore _finite_.
The universe of sense-perception and sensuous imagination is a phenomenal universe, a genesis, a perpetual becoming, an entrance into existence, and an exit thence; the Theist is, therefore, perfectly justified in regarding it as disqualified for _self-existence_, and in pa.s.sing behind it for the Supreme Ent.i.ty that needs no cause. Phenomena demand causation, ent.i.ties dispense with it. No one asks for a cause of the _s.p.a.ce_ which contains the universe, or of the Eternity on the bosom of which it floats. Everywhere the line is necessarily drawn upon the same principle; that ent.i.ties _may_ have self-existence, phenomena _must_ have a cause.[223]
[Footnote 223: "Science, Nescience, and Faith," in Martineau"s "Essays,"
p. 206.]
IV. _Psychological a.n.a.lysis clearly attests that in the phenomena of consciousness there are found elements or principles which, in their regular and normal development, transcend the limits of consciousness, and attain to the knowledge of Absolute Being, Absolute Reason, Absolute Good_, i.e., G.o.d.
The a.n.a.lysis of thought clearly reveals that the mind of man is in possession of ideas, notions, beliefs, principles (as _e.g._, the idea of s.p.a.ce, duration, cause, substance, unity, infinity), which are not derived from sensation and experience, and which can not be drawn out of sensation and experience by any process of generalization. These ideas have this incontestable peculiarity, as distinguished from all the phenomena of sensation, that, whilst the latter are particular, contingent, and relative, the former are _universal_, _necessary_, and _absolute_. As an example, and a proof of the reality and validity of this distinction, take the ideas of _body_ and of _s.p.a.ce_, the former unquestionably derived from experience, the latter supplied by reason alone. "I ask you, can not you conceive this book to be destroyed?
Without doubt you can. And can not you conceive the whole world to be destroyed, and no matter whatever in existence? You can. For you, const.i.tuted as you are, the supposition of the non-existence of bodies implies no contradiction. And what do we call the idea of a thing which we can conceive of as non-existing? We call it a _contingent_ and _relative_ idea. But if you can conceive this book to be destroyed, all bodies destroyed, can you suppose s.p.a.ce to be destroyed? You can not. It is in the power of man"s thought to conceive the non-existence of bodies; it is not in the power of man"s thought to conceive the non-existence of s.p.a.ce. The idea of s.p.a.ce is thus a _necessary_ and _absolute_ idea."[224]
[Footnote 224: Cousin"s "Hist. of Philos.," vol. ii. p. 214.]
Take, again, the ideas of _event_ and _cause_. The idea of an event is a _contingent_ idea; it is the idea of something which might or might not have happened. There is no impossibility or contradiction in either supposition. The idea of cause is a _necessary_ idea. An event being given, the idea of cause is necessarily implied. An uncaused event is an impossible conception. The idea of cause is also a _universal_ idea extending to all events, actual or conceivable, and affirmed by all minds. It is a rational fact, attested by universal consciousness, that we can not think of an event transpiring without a cause; of a thing being the author of its own existence; of something generated by and out of nothing. _Ex nihilo nihil_ is a universal law of thought and of things. This universal "law of causality" is clearly distinguishable from a _general_ truth reached by induction. For example, it is a very general truth that, during twenty-four hours, day is succeeded by night.
But this is not a necessary truth, neither is it a universal truth. It does not extend to all known lands, as, for example, to Nova Zembla. It does not hold true of the other planets. Nor does it extend to all possible lands. We can easily conceive of lands plunged in eternal night, or rolling in eternal day. With another system of worlds, one can conceive other physics, but one can not conceive other metaphysics. It is impossible to imagine a world in which the law of causality does not reign. Here, then, we have one absolute principle (among others which may be enumerated), the existence and reality of which is revealed, not by sensation, but by reason--a principle which transcends the limits of experience, and which, in its regular and logical development, attains the knowledge of the Absolute Cause--the First Cause of all causes--G.o.d.
Thus it is evident that the human mind is in possession of two distinct orders of primitive cognitions,--one, contingent, relative, and phenomenal; the other universal, necessary, and absolute. These two distinct orders of cognition presuppose the existence in man of two distinct faculties or organs of knowledge--_sensation_, external and internal, which perceives the contingent, relative, and phenomenal, and _reason_, which apprehends the universal, necessary, and absolute. The knowledge which is derived from sensation and experience is called _empirical_ knowledge, or knowledge _a posteriori_, because subsequent to, and consequent upon, the exercise of the faculties of observation.
The knowledge derived from reason is called _transcendental_ knowledge, or knowledge _a priori_, because it furnishes laws to, and governs the exercise of the faculties of observation and thought, and is not the result of their exercise. The sensibility brings the mind into relation with the _physical_ world, the reason puts mind in communication with the _intelligible_ world--the sphere of _a priori_ principles, of necessary and absolute truths, which depend upon neither the world nor the conscious self, and which reveal to man the existence of the soul, nature, and G.o.d. Every distinct fact of consciousness is thus at once _psychological_ and _ontological_, and contains these three fundamental ideas, which we can not go beyond, or cancel by any possible a.n.a.lysis--the _soul_, with its faculties; _matter_, with its qualities; _G.o.d_, with his perfections.
We do not profess to be able to give a clear explication and complete enumeration of all the ideas of reason, and of the necessary and universal principles or axioms which are grounded on these ideas. This is still the grand desideratum of metaphysical science. Its achievement will give us a primordial logic, which shall be as exact in its procedure and as certain in its conclusions as the mathematical sciences. Meantime, it may be affirmed that philosophic a.n.a.lysis, in the person of Plato, Aristotle, Kant, and Cousin, has succeeded in disengaging such _a priori_ ideas, and formulating such principles and laws of thought, as lead infallibly to the cognition of the _Absolute Being_, the _Absolute Reason_, the _Absolute Good_, that is, G.o.d.
It would carry us too far beyond our present design were we to exhibit, in each instance, the process of _immediate abstraction_ by which the contingent and relative element of knowledge is eliminated, and the necessary and absolute principle is disengaged. We shall simply state the method, and show its application by a single ill.u.s.tration.
There are unquestionably _two_ sorts of abstraction: 1. "_Comparative_ abstraction, operating upon several real objects, and seizing their resemblances in order to form an abstract idea, which is collective and mediate; collective, because different individuals concur in its formation; mediate, because it requires several intermediate operations." This is the method of the physical sciences, which comprises comparison, abstraction, and generalization. The result in this process is the attainment of a _general_ truth. 2. "_Immediate_ abstraction, not comparative; operating not upon several concretes, but upon a single one, eliminating and neglecting its individual and variable part, and disengaging the absolute part, which it raises at once to its pure form." The parts to be eliminated in a concrete cognition are, first, the quality of the object, and the circ.u.mstances under which the absolute unfolds itself; and secondly, the quality of the subject, which perceives but does not const.i.tute it. The phenomena of the me and the not-me being eliminated, the absolute remains. This is the process of rational psychology, and the result obtained is a _universal_ and _necessary_ truth.
"Let us take, as an example, the principle of cause. To be able to say that the event I see must have a cause, it is not indispensable to have seen several events succeed each other. The principle which compels me to p.r.o.nounce this judgment is already complete in the first as in the last event; it can not change in respect to its object, it can not change in itself; it neither increases nor decreases with the greater or less number of applications. The only difference that it is subject to in regard to us is that we apply it, whether we remark it or not, whether we disengage it or not from its particular application. The question is not to eliminate the particularity of the phenomenon wherein it appears to us, whether it be the fall of a leaf or the murder of a man, in order immediately to conceive, in a general and abstract manner, the necessity of a cause for every event that begins to exist. Here it is not because I am the same, or have been affected in the same manner in several different cases, that I have come to this general and abstract conception. A leaf falls; at the same moment I think, I believe, I declare that this falling of the leaf must have a cause. A man has been killed; at the same instant I believe, I proclaim that this death must have a cause. Each one of these facts contains particular and variable circ.u.mstances, and something universal and necessary, to wit, both of them can not but have a cause. Now I am perfectly able to disengage the universal from the particular in regard to the first fact as well as in regard to the second fact, for the universal is in the first quite as well as in the second. In fact, if the principle of causality is not universal in the first fact, neither will it be in the second, nor in the third, nor in the thousandth; for a thousandth is not nearer than the first to the infinite--to absolute universality. It is the same, and still more evidently, with _necessity_. Pay particular attention to this point; if necessity is not in the first fact, it can not be in any; for necessity can not be formed little by little, and by successive increments. If, on the first murder I see, I do not exclaim that this murder had necessarily a cause, at the thousandth murder, although it shall be proved that all the others had causes, I shall have the right to think that this murder has, very probably, also a cause, but I shall never have the right to say that it _necessarily_ had a cause. But when universality and necessity are already in a single case, that case is sufficient to ent.i.tle me to deduce them from it,"[225] and we may add, also, to affirm them of every other event that may transpire.
[Footnote 225: Cousin, "True, Beautiful, and Good," pp. 57, 58.]
The following _schema_ will exhibit the generally accepted results of this method of a.n.a.lysis applied to the phenomena of thought:
(i.) _Universal and necessary principles, or primitive judgments from whence is derived the cognition of Absolute Being_.
1. _The principle of Substance_; thus enounced--"every quality supposes a _subject_ or real being."
2. _The principle of Causality_; "every thing that begins to be supposes a _power_ adequate to its production, _i.e._, an efficient cause."
3. _The principle of Unity_; "all differentiation and plurality supposes an incomposite unity; all diversity, an ultimate and indivisible ident.i.ty."
4. _The principle of the Unconditioned_; "the finite supposes the infinite, the dependent supposes the self-existent, the temporal supposes the eternal."
(ii.) _Universal and necessary principles, or primitive judgments, from which is derived the cognition of the Absolute Reason_.
1. _The principle of Ideality_; thus enounced, "facts of order--definite proportion, symmetrical arrangement, numerical relation, geometrical form--having a commencement in time, present themselves to us as the expression of _Ideas_, and refer us to _Mind_ as their a.n.a.logon, and exponent, and source."
2. _The principle of Consecution_; "the uniform succession and progressive evolution of new existences, according to fixed definite archetypes, suppose a unity of _thought_--a comprehensive _plan_ embracing all existence."
3. _The principle of Intentionality or Final Cause_; "every means supposes an _end_ contemplated, and a choice and adaptation of means to secure the _end_."
4. _The principle of Personality_; "intelligent purpose and voluntary choice imply a personal agent."
(iii.) _Universal and necessary principles, or primitive judgments, from whence is derived the cognition of the Absolute Good_.
1. _The principle of Moral Law_; thus enounced, "the action of a voluntary agent necessarily characterized as _right_ or _wrong_, supposes an immutable and universal standard of right--an absolute moral Law."
2. _The principle of Moral Obligation_; "the feeling of obligation to obey a law of duty supposes a _Lawgiver_ by whose authority we are obliged."
3. _The principle of Moral Desert_; "the feeling of personal accountability and of moral desert supposes a _judge_ to whom we must give account, and who shall determine our award."
4. _The pnnciple of Retribution_; "retributive issues in this life, and the existence in all minds of an impersonal justice which demands that, in the final issue, every being shall receive his just deserts, suppose a being of _absolute justice_ who shall render to every man according to his works."
A more profound and exhaustive a.n.a.lysis may perhaps resolve all these primitive judgments into one universal principle or law, which Leibnitz has designated "_The principle or law of sufficient reason_," and which is thus enounced--there must be an ultimate and sufficient reason why any thing exists, and why it is, rather than otherwise; that is, if any thing begins to be, something else must be supposed as the adequate ground, and reason, and cause of its existence; or again, to state the law in view of our present discussion, "_if the finite universe, with its existing order and arrangement, had a beginning, there must be an ultimate and sufficient reason why it exists, and why it is as it is, rather than otherwise_." In view of one particular cla.s.s of phenomena, or special order of facts, this "principle of sufficient reason" may be varied in the form of its statement, and denominated "the principle of substance," "the principle of causality," "the principle of intentionality," etc.; and, it may be, these are but specific judgments under the one fundamental and generic law of thought which const.i.tutes the _major_ premise of every Theistic syllogism.
These fundamental principles, primitive judgments, axioms, or necessary and determinate forms of thought, exist potentially or germinally in all human minds; they are spontaneously developed in presence of the phenomena of the universe, material and mental; they govern the original movement of the mind, even when not appearing in consciousness in their pure and abstract form; and they compel us to affirm _a permanent being_ or _reality_ behind all phenomena--a _power_ adequate to the production of change, back of all events; a _personal Mind_, as the explanation of all the facts of order, and uniform succession, and regular evolution; and a _personal Lawgiver_ and _Righteous Judge_ as the ultimate ground and reason of all the phenomena of the moral world; in short, to affirm _an Unconditioned Cause of all finite and secondary causes; a First Principle of all principles; an Ultimate Reason of all reasons; an immutable Uncreated Justice, the living light of conscience; a King immortal, eternal, invisible, the only wise G.o.d, the ruler of the world and man_.
Our position, then, is, that the idea of G.o.d is revealed to man in the natural and spontaneous development of his intelligence, and that the existence of a Supreme Reality corresponding to, and represented by this idea, is rationally and logically demonstrable, and therefore justly ent.i.tled to take rank as part of our legitimate, valid, and positive _knowledge_.
And now from this position, which we regard as impregnable, we shall be prepared more deliberately and intelligibly to contemplate the various a.s.saults which are openly or covertly made upon the doctrine that _G.o.d is cognizable by human reason_.
CHAPTER VI.
THE UNKNOWN G.o.d (_continued_).