Anselm of Canterbury is most famous for his Ontological Argument for the existence of God, which is that "God is the greatest necessary being that which may be thought of" (paraphrase). Although this argument has been presented as unassailable and irrefutable, there have been, however, some very important attempted refutations from very reputable and important scholars. Anselm's argument does hold against these criticisms, but each of them do need to be considered and addressed without simple dismissal. The most important of which is that of Immanuel Kant's refutal.   

I discovered that a concise collection of these refutations are available in one volume online, which I have copied here from this online volume at Calvin College:

CRITICISMS OF ANSELM'S ONTOLOGICAL ARGUMENT FOR THE BEING OF GOD.

Mirror: http://www.ccel.org/ccel/anselm/basic_works.toc.html

DESCARTES

The Philosophy of Descartes in Extracts from His Writings. H. A. P. Torrey. New York, 1892. P. 161 et seq.

"But now, if from the simple fact that I can draw from my thought the idea of anything it follows that all that I recognise clearly and distinctly to pertain to this thing pertains to it in reality, can I not draw from this an argument and a demonstration of the existence of God? It is certain that I do not find in me the less the idea of him, that is, of a being supremely perfect, than that of any figure or of any number whatever; and I do not know less clearly and distinctly that an actual and eternal existence belongs to his nature than I know that all that I can demonstrate of any figure or of any number belongs truly to the nature of that figure or that number: and accordingly, although all that I have concluded in the preceding meditations may not turn out to be true, the existence of God ought to pass in my mind as being at least as certain as I have up to this time regarded the truths of mathematics to be, which have to do only with numbers and figures: although, indeed, that might not seem at first to be perfectly evident, but might appear to have some appearance of sophistry. For being accustomed in all other things to make a distinction between existence and essence, I easily persuade myself that existence may perhaps be separated from the essence of God, and thus God might be conceived as not existent actually. But nevertheless, when I think more attentively, I find that existence can no more be separated from the essence of God than from the essence of a rectilinear triangle can be separated the equality of its three angles to two right angles, or, indeed, if you please, from the idea of a mountain the idea of a valley; so that there would be no less contradiction in conceiving of a God--that is, of a being supremely perfect, to whom existence was wanting, that is to say, to whom there was wanting any perfection--than in conceiving of a mountain which had no valley. "But although, in reality, I might not be able to conceive of a God without existence, no more than of a mountain without a valley, nevertheless, as from the simple fact that I conceive a mountain with a valley, it does not follow that there exists any mountain in the world, so likewise, although I conceive God as existent, it does not follow, it seems, from that, that God exists, for my thought does not impose any necessity on things; and as there is nothing to prevent my imagining a winged horse, although there is none which has wings, so I might, perhaps, be able to attribute existence to God, although there might not be any God which existed. So far from this being so, it is just here under the appearance of this objection that a sophism lies hid; for from the fact that I cannot conceive a mountain without a valley, it does not follow that there exists in the world any mountain or any valley, but solely that the mountain and the valley, whether they exist or not, are inseparable from one another; whereas from the fact alone that I cannot conceive God except as existent, it follows that existence is inseparable from him, and, consequently, that he exists in reality; not that my thought can make it to be so, or that it can impose any necessity upon things; but on the contrary the necessity which is in the thing itself, that is to say, the necessity of the existence of God, determines me to have this thought. "For it is not at my will to conceive of a God without existence, that is to say, a being supremely perfect without a supreme perfection, as it is at my will to conceive a horse with wings or without wings. "And it must not also be said here that it is necessarily true that I should affirm that God exists, after I have supposed him to possess all kinds of perfection, since existence is one of these, but that my first supposition is not necessary, no more than it is necessary to affirm that all figures of four sides may be inscribed in the circle, but that, supposing I had this thought, I should be constrained to admit that the rhombus can be inscribed there, since it is a figure of four sides, and thus I should be constrained to admit something false. One ought not, I say, to allege this; for although it may not be necessary that I should ever fall to thinking about God, nevertheless, when it happens that I think upon a being first and supreme, and draw, so to speak, the idea of him from the store-house of mind, it is necessary that I attribute to him every sort of perfection, although I may not go on to enumerate them all, and give attention to each one in particular. And this necessity is sufficient to bring it about (as soon as I recognise that I should next conclude that existence is a perfection) that this first and supreme being exists: while, just as it is not necessary that I ever imagine a triangle, but whenever I choose to consider a rectilinear figure, composed solely of three angles, it is absolutely necessary that I attribute to it all the things which serve for the conclusion that there three angles are not greater than two right angles, although, perhaps, I did not then consider this in particular."

SPINOZA

The Chief Works of Benedict de Spinoza. Translated by R.H.M.Elwes. London, 1848. VoI. II., P. 51 et seq.

PROP. XI. God, or substance, consisting, of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists. "Proof.--If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (by Prop. vii.) is absurd. Therefore God necessarily exists. "Another Proof.--Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non-existence--e. g., if a triangle exist, a reason or cause must be granted for its existence; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the non-existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance follows also solely from its nature, inasmuch as its nature involves existence. (See Prop. vii.) "But the reason for the existence of a triangle or a circle does not follow from the nature of those figures, but from the order of universal nature in extension. From the latter it must follow, either that a triangle necessarily exists, or that it is impossible that it should exist. So much is self-evident. It follows therefrom that a thing necessarily exists, if no cause or reason be granted which prevents its existence. "If, then, no cause or reason can be given, which prevents the existence of God, or which destroys his existence, we must certainly conclude that he necessarily does exist. If such a reason or cause should be given, it must either be drawn from the very nature of God, or be external to him--that is, drawn from another substance of another nature. For if it were of the same nature, God, by that very fact, would be admitted to exist. But substance of another nature could have nothing in common with God (by Prop. ii.), and therefore would be unable either to cause or to destroy his existence. "As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God's own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect, is absurd; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q. E. D. "Another proof.--The potentiality of non-existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. If, then, that which necessarily exists is nothing but finite beings, such finite beings are more powerful than a being absolutely infinite, which is obviously absurd; therefore, either nothing exists, or else a being absolutely infinite necessarily exists also. Now we exist either in ourselves, or in something else which necessarily exists (see Axiom i. and Prop. vii.). Therefore a being absolutely infinite--in other words, God (Def. vi.)--necessarily exists. Q. E. D. "Note.--In this last proof, I have purposely shown God's existence a posteriori, so that the proof might be more easily followed, not because, from the same premises, God's existence does not follow a priori. For, as the potentiality of existence is a power, it follows that, in proportion as reality increases in the nature of a thing, so also will it increase its strength for existence. Therefore a being absolutely infinite, such as God, has from himself an absolutely infinite power of existence, and hence he does absolutely exist. Perhaps there will be many who will be unable to see the force of this proof, inasmuch as they are accustomed only to consider those things which flow from external causes. Of such things, they see that those which quickly come to pass--that is, quickly come into existence--quickly also disappear; whereas they regard as more difficult of accomplishment--that is, not so easily brought into existence --those things which they conceive as more complicated. "However, to do away with this misconception, I need not here show the measure of truth in the proverb, What comes quickly, goes quickly,' nor discuss whether, from the point of view of universal nature, all things are equally easy, or otherwise: I need only remark, that I am not here speaking of things, which come to pass through causes external to themselves, but only of substances which (by Prop. vi.) cannot be produced by any external cause. Things which are produced by external causes, whether they consist of many parts or few, owe whatsoever perfection or reality they possess solely to the efficacy of their external cause, and therefore their existence arises solely from the perfection by their external cause, not from their own. Contrariwise, whatsoever perfection is possessed by substance is due to no external cause; wherefore the existence of substance must arise solely from its own nature, which is nothing else but its essence. Thus, the perfection of a thing does not annul its existence, but, on the contrary, asserts it. Imperfection, on the other hand, does annul it; therefore we cannot be more certain of the existence of anything, than of the existence of a being absolutely infinite or perfect--that is, of God. For inasmuch as his essence excludes all imperfection, and involves absolute perfection, all cause for doubt concerning his existence is done away, and the utmost certainty on the question is given. This, I think, will be evident to every moderately attentive reader."

LOCKE

An Essay Concerning Human Understanding. London: Ward, Lock, Co. P. 529 et seq.

"Our idea of a most perfect being, not the sole proof of a God.--How far the idea of a most perfect being which a man may frame in his mind, does or does not prove the existence of a God, I will not here examine. For, in the different make of men's tempers, and application of their thoughts, some arguments prevail more on one, and some on another, for the confirmation of the same truth. But yet, I think this I may say, that it is an ill way of establishing this truth and silencing atheists, to lay the whole stress of so important a point as this upon that sole foundation: and take some men's having that idea of God in their minds (for it is evident some men have none, and some worse than none, and the most very different) for the only proof of a Deity; and out of an over-fondness of that darling invention, cashier, or at least endeavor to invalidate, all other arguments, and forbid us to hearken to those proofs, as being weak or fallacious, which our own existence and the sensible parts of the universe offer so clearly and cogently to our thoughts, that I deem it impossible for a considering man to withstand them."

LEIBNITZ

New Essays Concerning Human Understanding. Translated by A.G. Langley. New York, 1896. P. 502 at seq.

"Although I am for innate ideas, and in particular for that of God, I do not think that the demonstrations of the Cartesians drawn from the idea of God are perfect. I have shown fully elsewhere (in the Actes de Leipsic, and in the Memoires de Trevoux) that what Descartes has borrowed from Anselm, Archbishop of Canterbury, is very beautiful and really very ingenious, but that there is still a gap therein to be filled. This celebrated archbishop, who was without doubt one of the most able men of his time, congratulates himself, not without reason, for having discovered a means of proving the existence of God a priori, by means of its own notion, without recurring to its effects. And this is very nearly the force of his argument: God is the greatest or (as Descartes says) the most perfect of beings, or rather a being of supreme grandeur and perfection, including all degrees thereof. That is the notion of God. See now how existence follows from this notion. To exist is something more than not to exist, or rather, existence adds a degree to grandeur and perfection, and as Descartes states it, existence is itself a perfection. Therefore this degree of grandeur and perfection, or rather this perfection which consists in existence, is in this supreme all-great, all-perfect being: for otherwise some degree would be wanting to it, contrary to its definition. Consequently this supreme being exists. The Scholastics, not excepting even their Doctor Angelicus, have misunderstood this argument, and have taken it as a paralogism; in which respect they were altogether wrong, and Descartes, who studied quite a long time the scholastic philosophy at the Jesuit College of La Fleche, had great reason for re-establishing it. It is not a paralogism, but it is an imperfect demonstration, which assumes something that must still be proved in order to render it mathematically evident; that is, it is tacitly assumed that this idea of the all-great or all-perfect being is possible, and implies no contradiction. And it is already something that by this remark it is proved that, assuming that God is Possible, he exists, which is the privilege of divinity alone. We have the right to presume the possibility of every being, and especially that of God, until some one proves the contrary. So that this metaphysical argument already gives a morally demonstrative conclusion, which declares that according to the present state of our knowledge we must judge that God exists, and act in conformity thereto. But it is to be desired, nevertheless, that clever men achieve the demonstration with the strictness of a mathematical proof, and I think I have elsewhere said something that may serve this end." 

KANT

Critique of Pure Reason. Translated by F. Max Muller. New York, 1896. P. 483 et seq.

"Being is evidently not a real predicate, or a concept of something that can be added to the concept of a thing. It is merely the admission of a thing, and of certain determinations in it. Logically, it is merely the copula of a judgment. The proposition, God is almighty, contains two concepts, each having its object, namely, God and almightiness. The small word is, is not an additional predicate, but only serves to put the predicate in relation to the subject. If, then, I take the subject (God) with all its predicates (including that of almightiness), and say, God is, or there is a God, I do not put a new predicate to the concept of God, but I only put the subject by itself, with all its predicates, in relation to my concept, as its object. Both must contain exactly the same kind of thing, and nothing can have been added to the concept, which expresses possibility only, by my thinking its object as simply, given and saying, it is. And thus the real does not contain more than the possible. A hundred real dollars do not contain a penny more than a hundred possible dollars. For as the latter signify the concept, the former the object and its position by itself, it is clear that, in case the former contained more than the latter, my concept would not express the whole object, and would not therefore be its adequate concept. In my financial position no doubt there exists more by one hundred real dollars, than by their concept only (that is their possibility), because in reality the object is not only contained analytically in my concept, but is added to my concept (which is a determination of my state), synthetically: but the conceived hundred dollars are not in the least increased through the existence which is outside my concept. "By whatever and by however many predicates I may think a thing (even in completely determining it), nothing is really added to it, if I add that the thing exists. Otherwise, it would not be the same that exists, but something more than was contained in the concept, and I could not say that the exact object of my concept existed. Nay, even if I were to think in a thing all reality, except one, that one missing reality would not be supplied by my saying that so defective a thing exists, but it would exist with the same defect with which I thought it; or what exists would be different from what I thought. If, then, I try to conceive a being, as the highest reality (without any defect), the question still remains, whether it exists or not. For though in my concept there may be wanting nothing of the possible real content of a thing in general, something is wanting in its relation to my whole state of thinking, namely, that the knowledge of that object should be possible a posteriori also. And here we perceive the cause of our difficulty. If we were concerned with an object of our senses, I could not mistake the existence of a thing for the mere concept of it; for by the concept the object is thought as only in harmony with the general conditions of a possible empirical knowledge, while by its existence it is thought as contained in the whole content of experience. Through this connection with the content of the whole experience, the concept of an object is not in the least increased; our thought has only received through it one more possible perception. If, however, we are thinking existence through the pure category alone, we need not wonder that we cannot find any characteristic to distinguish it from mere possibility. "Whatever, therefore, our concept of an object may contain, we must always step outside it, in order to attribute to it existence. With objects of the senses, this takes place through their connection with any one of my perceptions, according to empirical laws; with objects of pure thought, however, there is no means of knowing their existence, because it would have to be known entirely a priori, while our consciousness of every kind of existence, whether immediately by perception, or by conclusions which connect something with perception, belongs entirely to the unity of experience, and any existence outside that field, though it cannot be declared to be absolutely impossible, is a presupposition that cannot be justified by anything. "The concept of a Supreme Being is, in many respects, a very useful idea, but, being an idea only, it is quite incapable of increasing, by itself alone, our knowledge with regard to what exists. It cannot even do so much as to inform us any further as to its possibility. The analytical characteristic of possibility, which consists in the absence of contradiction in mere positions (realities), cannot be denied to it; but the connection of all real properties in one and the same thing is a synthesis the possibility of which we cannot judge a priori because these realities are not given to us as such, and because, even if this were so, no judgment whatever takes place, it being necessary to look for the characteristic of the possibility of synthetical knowledge in experience only, to which the object of an idea can never belong. Thus we see that the celebrated Leibnitz is far from having achieved what we thought he had, namely, to understand a priori the possibility of so sublime an ideal Being. "Time and labor therefore are lost on the famous ontological (Cartesian) proof of the existence of a Supreme Being from mere concepts; and a man might as well imagine that he could become richer in knowledge by mere ideas, as a merchant in capital, if, in order to improve his position, he were to add a few noughts to his cash account."

HEGEL

Lectures on the History of Philosophy. Translated by E. S. Haldane and F.H. Simson. London, 1896. Vol. III., p. 62 et seg.

"This proof was included among the various proofs up to the time of Kant, and--by some who have not yet reached the Kantian standpoint--it is so included even to the present day. It is different from what we find and read of amongst the ancients. For it was said that God is absolute thought as objective; for because things in the world are contingent, they are not the truth in and for itself--but this is found in the infinite. The scholastics also knew well from the Aristotelian philosophy the metaphysical proposition that potentiality is nothing by itself, but is clearly one with actuality. Later, on the other hand, the opposition between thought itself and Being began to appear with Anselm. It is noteworthy that only now for the first time through the Middle Ages and in Christianity, the universal Notion and Being, as it is to ordinary conception, became established in this pure abstraction as these infinite extremes; and thus the highest law has come to consciousness. But we reach our profoundest depths in bringing the highest opposition into consciousness. Only no advance was made beyond the division as such, although Anselm also tried to find the connection between the sides. But while hitherto God appeared as the absolute existent, and the universal was attributed to Him as predicate, an opposite order begins with Anselm--Being becomes predicate, and the absolute Idea is first of all established as the subject, but the subject of thought. Thus if the existence of God is once abandoned as the first hypothesis, and established as a result of thought, self-consciousness is on the way to turn back within itself. Then we have the question coming in, Does God exist? while on the other side the question of most importance was, What is God? "The ontological proof, which is the first properly metaphysical proof of the existence of God, consequently came to mean that God as the Idea of existence which unites all reality in itself, also has the reality of existence within Himself; this proof thus follows from the Notion of God, that He is the universal essence of all essence. The drift of this reasoning is, according to Anselm (Proslogium, C. 2), as follows: It is one thing to say that a thing is in the understanding, and quite another to perceive that it exists. Even an ignorant person (insipiens) will thus be quite convinced that in thought there is something beyond which nothing greater can be thought ; for when he hears this he understands it, and everything that is understood is in the understanding. But that beyond which nothing greater can be thought cannot certainly be in the understanding alone. For if it is accepted as in thought alone, we may go on farther to accept it as existent; that, however, is something greater' than what is merely thought. Thus were that beyond which nothing greater can be thought merely in the understanding, that beyond which nothing greater can be thought would be something beyond which something greater can be thought. But that is truly impossible; there thus without doubt exists both in the understanding and in reality something beyond which nothing greater can be thought.' The highest conception cannot be in the understanding alone; it is essential that it should exist. Thus it is made clear that Being is in a superficial way subsumed under the universal of reality, that to this extent Being does not enter into opposition with the Notion. That is quite right; only the transition is not demonstrated--that the subjective understanding abrogates itself. This, however, is just the question which gives the whole interest to the matter. When reality or completion is expressed in such a way that it is not yet posited as existent, it is something thought, and rather opposed to Being than that this is subsumed under it. "This mode of arguing held good until the time of Kant; and we see in it the endeavor to apprehend the doctrine of the Church through reason. This opposition between Being and thought is the starting-point in philosophy, the absolute that contains the two opposites within itself--a conception, according to Spinoza, which involves its existence likewise. Of Anselm it is however to be remarked that the formal logical mode of the understanding, the process of scholastic reasoning is to be found in him; the content indeed is right, but the form faulty. For in the first place the expression the thought of a Highest' is assumed as prius. Secondly, there are two sorts of objects of thought--one that is and another that is not; the object that is only thought and does not exist, is as imperfect as that which only is without being thought. The third point is that what is highest must likewise exist. But what is highest, the standard to which all else must conform, must be no mere hypothesis, as we find it represented in the conception of a highest acme of perfection, as a content which is thought and likewise is. This very content, the unity of Being and thought, is thus indeed the true content, but because Anselm has it before him only in the form of the understanding, the opposites are identical and conformable to unity in a third determination only--the Highest--which, in as far as it is regulative, is outside of them. In this it is involved that we should first of all have subjective thought, and then distinguished from that, Being. We allow that if we think a content (and it is apparently indifferent whether this is God or any other), it may be the case that this content does not exist. The assertion Something that is thought does not exist' is now subsumed under the above standard and is not conformable to it. We grant that the truth is that which is not merely thought but which likewise is. But of this opposition nothing here is said. Undoubtedly God would be imperfect, if He were merely thought and did not also have the determination of Being. But in relation to God we must not take thought as merely subjective; thought here signifies the absolute, pure thought, and thus we must ascribe to Him the quality of Being. On the other hand if God were merely Being, if He were not conscious of Himself as self-consciousness, He would not be Spirit, a thought that thinks itself. "Kant, on the other hand, attacked and rejected Anselm's proof--which rejection the whole world afterwards followed up--on the ground of its being an assumption that the unity of Being and thought is the highest perfection. What Kant thus demonstrates in the present day--that Being is different from thought and that Being is not by any means posited with thought--was a criticism offered even in that time by a monk named Gaunilo. He combated this proof of Anselm's in a Liber pro insipiente to which Anselm himself directed a reply in his Liber apologeticus adversus insipientem. Thus Kant says (Kritik der reinen Vernunft, P. 464 of the sixth edition): If we think a hundred dollars, this conception does not involve existence. That is certainly true: what is only a conception does not exist, but it is likewise not a true content, for what does not exist, is merely an untrue conception. Of such we do not however here speak, but of pure thought; it is nothing new to say they are different--Anselm knew this just as well as we do. God is the infinite, just as body and soul, Being and thought are eternally united; this is the speculative, true definition of God. To the proof which Kant criticises in a manner which it is the fashion to follow now-a-days, there is thus lacking only the perception of the unity of thought and of existence in the infinite; and this alone must form the commencement."

J. A. DORNER

A System of Christian Doctrine. Translated by A. Cave and J. S. Banks, Edinburgh, 1880. Vol. I., p. 216 et seq 

"According to the Monologium, we arrive at the mental representation of God by the agency of faith and conscience, therefore by a combined religious and moral method; by the same means we arrive at the representation of the relativity of the world. But as there seemed to Anselm something inadequate in making the Being of the Absolute dependent upon the existence of the Relative, as if the latter were more certain than the former, he has interpolated in the Proslogium (Alloquium Dei) the Ontological method. The thought of God, which is always given, and the being of which is to be proved, claims, at any rate, to be the highest thought possible; indeed, upon close comparison with all other thoughts which come and go, with thoughts of such things as may just as well not exist as exist, it has the essential peculiarity, the prerogative, so to speak,--and this is Anselm's discovery,--that, if it is actually thought of as the highest conceivable thought, it is also thought of as existent. Were it not thought of as being, it would not for a moment be actually thought. Anselm then proceeds with his proof as follows: We believe Thou art something, beyond which nothing greater can be thought. The fool (Ps. xiv.) denies the existence of such a Being. Is He therefore non-existent? But the very fool hears and understands what I say, "something, greater than which there is nothing," and what he understands is in his understanding. That it also exists without him would thus have to be proved. But that, beyond which nothing greater can be thought, cannot exist in mere intellect. For did it exist only in intellect, the thought might be framed that it was realised, and that would be a greater thought. Consequently, were that, a greater than which cannot be thought, existent in mere intellect, the thought quo majus cogitari non potest would at the same time be quo majus cogitari potest, which is impossible. Consequently, there exists, in reality as well as in the understanding, something a greater than which cannot be thought. And this is so true that its non-existence cannot be thought. Something may be thought which is only to be thought as existent, and that is a majus than that the non-existence of which may be thought, and that Thou art, O Lord, my God, I must think though I did not believe.' The nerve of the Anselmic argument lies therefore in the notion that an idea which has an objective existence is a majus than that to which mere subjective existence appertains; that, consequently, as under the idea of God the highest thought possible is at any rate expressed, the idea of God is not thought unless it is thought as existent. For, he says in another place, it may be thought of everything that it does not exist, with the exception of that quod summe est to which being pre-eminently belongs. That is, the non-existence may be thought of everything which has beginning or end, or which is constituted of parts and is nowhere whole. But that, and it alone, cannot be thought as non-existent which has neither beginning nor end, and is not constituted of parts, but is thought of as everywhere existing whole. Gaunilo, Count of Montigny, makes a twofold answer in defence of the atheist. He says that that highest essence has no being in the understanding; it only exists therein by the ear, not by being; it only exists as a man who has heard a sound endeavors to embrace a thing wholly unknown to him in an image. And therein, he says, it is concluded that the mental representation of God in mankind is already a purely contingent one, and is produced from without by the sound of words; its necessary presence in the spirit is not proved. Thus, he adds, much is wanting to the ability of inferring its existence from the finding of such an image in the spirit. In the sphere of mere imagination no one thing has a less or a greater existence than any other thing; each has equally no existence at all. Therefore, he writes, granted that the presence of the idea of God in the spirit is not contingent, still the thought or the concept of God does not essentially argue the being of God. Similarly says Kant later on: We are no richer if we think of our ability as one cipher more.' That Anselm also undoubtedly knew, but he opined that the concept of God is different to any other thought, which remains unaltered, whether it is thought of as existent or non-existent; the concept of God is that thought, which is no longer thought unless it is thought as existent, and which, therefore, essentially involves being. But, of course, it is insufficiently established by Anselm that a concept of God which does not necessarily include existence, is not the highest thought, and therefore is not the concept of God, and that, consequently, the really highest thought must also be thought of as existent. To this the following objection attaches. Inasmuch as Anselm treated existence as a majus compared with non-existence, he treated existence as an attribute, whereas it is the bearer of all attributes. So it is not proved by Anselm that the origin of this idea, which, when thought, is thought as existent, is not contingent to the reason, but necessary; and that reason only remains reason by virtue of this idea. Finally, Anselm thinks, thus overrating the Ontological moment, that he has already attained therein the full concept of God. These shortcomings were to be obviated, stage by stage, by his successors."

LOTZE

Microcosmus. Translated by E. Hamilton and E. E. C. Jones. Edinburgh, 1887. Vol. II., p. 669 et seq. 

"To conclude that because the notion of a most perfect Being includes reality as one of its perfections, therefore a most perfect Being necessarily exists, is so obviously to conclude falsely, that after Kant's incisive refutation any attempt to defend such reasoning would be useless. Anselm, in his more free and spontaneous reflection, has here and there touched the thought that the greatest which we can think, if we think it as only thought, is less than the same greatest if we think it as existent. It is not possible that from this reflection either any one should develop a logically cogent proof, but the way in which it is put seems to reveal another fundamental thought which is seeking for expression. For what would it matter if that which is thought as most perfect were, as thought, less than the least reality? Why should this thought disturb us? Plainly for this reason, that it is an immediate certainty that what is greatest, most beautiful, most worthy is not a mere thought, but must be a reality, because it would be intolerable to believe of our ideal that it is an idea produced by the action of thought but having no existence, no power, and no validity in the world of reality. We do not from the perfection of that which is perfect immediately deduce its reality as a logical consequence; but without the circumlocution of a deduction we directly feel the impossibility of its non-existence, and all semblance of syllogistic proof only serves to make more clear the directness of this certainty. If what is greatest did not exist, then what is greatest would not be, and it is not impossible that that which is greatest of all conceivable things should not be."

PROFESSOR ROBERT FLINT

Theism. New York, 1893. Seventh edition. P. 278 et seq. 

"Anselm was the founder of that kind of argumentation which, in the opinion of many, is alone entitled to be described as a priori or ontological. He reasoned thus: The fool may say in his heart, There is no God; but he only proves thereby that he is a fool, for what he says is self-contradictory. Since he denies that there is a God, he has in his mind the idea of God, and that idea implies the existence of God, for it is the idea of a Being than which a higher cannot be conceived. That than which a higher cannot be conceived cannot exist merely as an idea, because what exists merely as an idea is inferior to what exists in reality as well as in idea. The idea of a highest Being which exists merely in thought, is the idea of a highest Being which is not the highest even in thought, but inferior to a highest Being which exists in fact as well as in thought.' This reasoning found unfavorable critics even among the contemporaries of Anselm, and has commended itself completely to few. Yet it may fairly be doubted whether it has been conclusively refuted, and some of the objections most frequently urged against it are certainly inadmissible. It is no answer to it, for example, to deny that the idea of God is innate or universal. The argument merely assumes that he who denies that there is a God must have an idea of God. There is also no force, as Anselm showed, in the objection of Gaunilo, that the existence of God can no more be inferred from the idea of a perfect being, than the existence of a perfect island is to be inferred from the idea of such an island. There neither is nor can be an idea of an island which is greater and better than any other that can ever be conceived. Anselm could safely promise that he would make Gaunilo a present of such an island when he had really imagined it. Only one being--an infinite, independent, necessary being--can be perfect in the sense of being greater and better than every other conceivable being. The objection that the ideal can never logically yield the real--that the transition from thought to fact must be in every instance illegitimate--is merely an assertion that the argument is fallacious. It is an assertion which cannot fairly be made until the argument has been exposed and refuted. The argument is that a certain thought of God is found necessarily to imply His existence. The objection that existence is not a predicate, and that the idea of a God who exists is not more complete and perfect than the idea of a God who does not exist, is, perhaps, not incapable of being satisfactorily repelled. Mere existence is not a predicate, but specifications or determinations of existence are predicable. Now the argument nowhere implies that existence is a predicate; it implies only that reality, necessity, and independence of existence are predicates of existence; and it implies this on the ground that existence in re can be distinguished from existence in conceptu, necessary from contingent existence, self-existence from derived existence. Specific distinctions must surely admit of being predicated. That the exclusion of existence--which here means real and necessary existence --from the idea of God does not leave us with an incomplete idea of God, is not a position, I think, which can be maintained. Take away existence from among the elements in the idea of a perfect being, and the idea becomes either the idea of a nonentity or the idea of an idea, and not the idea of a perfect being at all. Thus, the argument of Anselm is unwarrantably represented as an argument of four terms instead of three. Those who urge the objection seem to me to prove only that if our thought of God be imperfect, a being who merely realised that thought would be an imperfect being; but there is a vast distance between this truism and the paradox that an unreal being may be an ideally perfect being."

BIBLIOGRAPHY. Patrologioe Cursus Completus. Series Secunda. Tomi CLVIIICLIX. S. Anselmus. [Ed. ABBE MIGNE]. Paris, 1853. CHURCH. A. W. St. Anselm. [Third Edition]. London, 1873 FRANCK, G F. Anselm von Canterbury. Tubingen, 1842. HASSE, F. R. Anselm von Canterbury. Leipzig, 1843. 2 volumes. -The same. Translated and abridged by W.Turner. London, 1850. REMUSAT, CHARLES DE. Anselme de Canterbury. Paris, 1854; 2nd ed., 1868. RIGG, J. M. St. Anselm of Canterbury. London, 1896. RULE M. The Ltfe and Times of St. Anselm. London, 1883. 2 volumes. DE VOSGES, LE COMTE DOMET. Saint Anselme, in the series Les Grands Philosophes. Paris, 1901. WELCH, A. C. Anselm and His Work. Edinburgh, 1901. BAUR, F. C. Vorlesungen uber die christliche Dogmengeschichte. Leipzig, 1866. Zweiter Band, 249-251, 298 ff. ERDMANN, J. E. A History of Philosophy. English Translation [Ed. W. S. HOUGH]. London, 1891. Vol I., 303-314. HEGEL, G. W. F. Lectures on the History of Philosophy. Translated from the German by E. S. Haldane and F. H. Simson. London, 1896. Vol. III., 61-67. HOOK, W. T. Lives of the Archbishops of Canterbury. London, 1862. Vol. VIII., 169-276. MAURICE, F.D. Moral and Metaphysical Philosophy. London, 1882. Vol. I., 507-533. PFLEIDERER, 0. The Philosophy of Religion. Translated by A. Menzies. London, 1888. Vol. III., 271-276. UEBERWEG, F.^1 History of Philosophy. Translated by G. S. Morris. New York, 1892. Vol. I., 377-386. ^1 Ueberweg gives the titles of German and Latin dissertations on Anselm not included in this list.

Related: Anselm, Criticisms, Descartes, Dorner, Flint, for the Being of God, Hegel, Kant, Leibnitz, Locke, Lotze, Ontological Argument, Spinoza