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A Critique of John Calvin's Philosophical Axiom finitum non capax infiniti

David R. Andersen, Ph.D.
Assistant Professor of Philosophy
Salt Lake City Community College

The fierce Reformation debates over the Lord's Supper might seem odd to modern Christians, preoccupied as they often are with unity, but the Reformers recognized that a mistake on this issue indicates a deeper problem concerning the two natures of Christ.Zwingli, Luther, and Calvin all understood that one's view of the personal union of Christ predetermines his understanding of the Communion texts.Because of this, considerable time was devoted to exposing illegitimate assumptions concerning the two natures, with the goal that a scriptural christological formulation would prevail.One such attempted formulation promoted in the Reformation period involved the reasonable sounding axiom finitum non capax infiniti.While this too might sound strange (and perhaps irrelevant) to a late twentieth century Christian, it does nevertheless have important consequences.If, for instance, one maintains the axiom as it relates to the doctrine of Christ, then his doctrine of the Lord's Supper is forced in a specific direction:namely, since the finite cannot contain the infinite, Christ's human nature must be contained (or placed) in a particular space with the consequence that he is incapable — according to his human nature — of being materially present in the Supper.[1]As theoretical as it may initially sound, the issue really is intensely practical; practical in the sense that if one embraces the axiom, then, at least from Luther's point of view, the body and blood of Christ are eliminated and with it the concrete application of the gospel to the individual.According to the Reformers, therefore, the debate should by no means be construed as merely theoretical or as detached from a sense of practicality.

This paper will deal with the christological portion of the debate as it relates to the thought of the Geneva Reformer, John Calvin.Specifically, I will argue that Calvin's application of the principle finitum non capax infiniti serves as a synthetic a priori within his thought that determines the limitations of Christ's human nature.With the principle at the heart of his christology he denies the material presence of Christ in the Eucharist, and it becomes the basis of his opposition to Luther's understanding of the words of institution.Accordingly, from Calvin's perspective human reason can deliver substantive (non-trivial) truths of empirical reality, and his necessary limitations of human nature is one example of his trust in reason's pronouncements.His assumptions require clarification, however, and my purpose here is to examine the foundation of his christological theory.To do so I will focus on three questions:(1) How are we to understand Calvin's philosophical a priori?(2) Can it be maintained in light of the critiques of the synthetic a priori from the modern philosophical tradition?(3) Do Calvin's philosophical assumptions have appropriate application to the historic person of Christ?I will argue that Calvin's christological position, and therefore his Eucharistic position, presupposes an axiom that lacks philosophical meaningfulness.Given that fact, he cannot properly rely on such thinking to argue against Luther's position on the Eucharist.

Calvin and finitum non capax infiniti

First, to be sure, one must ask whether Calvin actually explicitly or implicitly affirmed the finitum principle.Fortunately, this is easily answered.Attempting to refute the notion of ubiquity (and, interestingly enough, defending himself against the charge that he relies too heavily on human reason) Calvin states:

            But it pleased him that Christ be made like his brethren in all things except sin [Heb. 4:15; cf.ch. 2:17].What is the nature of our flesh?Is it not something that has its own fixed dimension, is contained in a place, is touched, is seen?And why (they say) cannot God make the same flesh occupy many and divers places, be contained in no place, so as to lack measure and form?Madman, why do you demand that God’s power make flesh to be and not to be flesh at the same time!It is as if you insisted that he make light to be both light and darkness at the same time!But he wills light to be light; darkness, darkness; and flesh, flesh.Indeed, when he pleases he will turn darkness into light and light into darkness; but when you require that light and darkness not differ, what else are you doing than perverting the order of God’s wisdom?Flesh must therefore be flesh; spirit, spirit — each thing in the state and condition wherein God created it.But such is the condition of flesh that it must subsist in one definite place, with its own size and form.With this condition Christ took flesh, giving to it, as Augustine attests, incorruption and glory, and not taking away from it nature and truth.[2]

He also insists that we speak of Christ's presence in a way that does not detract from his heavenly glory:

But we must establish such a presence of Christ in the Supper as may neither fasten him to the element of bread, nor enclose him in bread, nor circumscribe him in any way (all which things, it is clear, detract from his heavenly glory); finally, such as may not take from him his own stature, or parcel him out to many places at once, or invest him with boundless magnitude to be spread through heaven and earth.For these things are plainly in conflict with a nature truly human.Let us never (I say) allow these two limitations to be taken away from us:(1) Let nothing be withdrawn from Christ’s heavenly glory — as happens when he is brought under the corruptible elements of this world, or bound to any earthly creatures.(2) Let nothing inappropriate to human nature be ascribed to his body, as happens when it is said either to be infinite or to be put in a number of places at once. . . .But when these absurdities have been set aside, I freely accept whatever can be made to express the true and substantial partaking of the body and blood of the Lord, which is shown to believers under the sacred symbols of the Supper — and so to express it that they may be understood not to receive it solely by imagination or understanding of mind, but to enjoy the thing itself as nourishment of eternal life.[3]

Professor Wendel points out that, according to Calvin, Christ received a body identical with ours at the incarnation and has to have the same properties as our bodies:"On this point Calvin was, after all, blaming his adversaries for what Zwingli had already complained of in Luther; that is, for effacing the absolute distinction between flesh and spirit."[4] Apparently not unwilling to draw the logical consequences, Calvin insists that Christ's body had all the characteristics of the human body even as it dwells in heaven.So important is the localization of Christ's body to Calvin, as Wendel observes, that it becomes the decisive argument against the material presence of Christ in the host.With this in mind Calvin can say:

If we count among the qualities of a glorified body that it is infinite and fills all [space], obviously the substance of it will be abolished, and no distinction will remain between the divinity and human nature.Moreover, if the body of Jesus Christ is thus variable and of different sorts, to appear in one place and be invisible in another, what will become of the corporeal nature, which must have its limitations?And what will become of the unity?[5]

While there could be more said, this should be sufficient to establish the following:(1) Calvin insists that it is a defining property of a human body to be localized and have certain bounds.Thus he defines the body such that it must have certain limitations e.g., it has its own distinctive measure, keeps its own place and remains capable of being touched and seen.[6] (2) He appeals to the law of non-contradiction in an attempt to show that denial of any of these properties subverts the most fundamental law of human thought.In other words, to deny that the human body is limited in the way Calvin sees it is to commit the unpardonable error of asserting that A is not A.He takes these limitations to be part of the very definition of human beings, in the same way that we might take "A triangle is bounded by three straight lines" to be a defining property of triangles.An important thing to remember here is that a defining property is a sine qua non, or a characteristic in the absence of which the word would not be applicable to the thing in question.[7]In the case of the triangle, for instance, our definition is a logically necessary condition for something to be called a triangle.In Calvin's case, a logically necessary condition for something to be called a human body is that it keeps its own place and measure, conditions without which it could not be called human.(3) Points (1) and (2) are subsets of the more general principle finitum non capax infiniti.This is true in Calvin's case because the principle is the assumption that requires him to propose (1) and (2) in the first place.As he defends the "absolute distinction" (to use Wendel's phrase) between flesh and spirit — "Flesh must therefore be flesh; spirit, spirit..." (Carnem igitur carnem esse oportet:spiritum, spiritum) — he is forced to apply to the human nature defining characteristics consistent with his initial dualism.[8] So Calvin at least implicitly affirmed that the finite is incapable of the infinite;[9] and this affirmation is precisely what leads him to deny the material presence of Christ in the Eucharistic elements.

Because of his commitment to the finitum principle, Calvin is forced to some rather odd conclusions on certain passages.Speaking of Christ's appearance to Stephen in Acts, he insists that it was not necessary for Christ to change his place:rather, Stephen's eyes received clarity of vision capable of piercing the heavens (qui servi sui oculis perspicaciam dare potuit quae caelos penetraret).Immediately following this is Calvin's celebrated explanation of Christ's entrance into the closed room:

They object that Christ went forth from the closed sepulcher [Matt. 28:6], and went in to his disciples through closed doors [John 20:19].This gives no more support to their error.For just as the water, like a solid pavement, provided Christ with a path as he walked upon the lake [Matt. 14:25], so it is no wonder if the hardness of the stone yielded at his approach.Yet it is more probable that the stone was removed at his command, and immediately after he passed through, returned to its place.And to enter through closed doors means not just penetrating through solid matter but opening an entrance for himself by divine power, so that he suddenly stood among his disciples clearly, in a wonderful way, although the doors were locked.[10]                                        

In the same section Calvin argues that Christ's vanishing from the disciples on the Emmaus road proves no difficulty:"For to take the sight of himself away from them, he did not make himself invisible but only disappeared."(Even if we grant a distinction between "invisible" and "disappeared," we are still forced to admit some supernatural properties to Christ's human nature by virtue of his disappearance.At any rate, it would seem on Calvin's own account, that human bodies can no more disappear than be invisible.)Again, and for exactly the same reason, Calvin holds that the believer is lifted up to heaven via the Holy Spirit to feed on the substance of Christ's body and blood.[11]

In all of these cases Calvin's exegesis is determined by the finitum principle.The strange thing, though, about his use of the principle is that it tends to be one-sided.To establish the connection between the believer and Christ implied by each text, he ends up attributing to the believer the very thing he wishes to deny of Christ's human nature.It seems, in other words, that in Calvin's mind the believer is capable of a kind of ubiquity (particularly at the Eucharist) that Christ himself is not.

A Closer Look at the Finitum Principle

The abstract principle finitum non capax infiniti seems easy enough to embrace given certain definitions of the terms 'infinite' and 'finite'.If we define infinite as that which lacks limits and finite as that which has limitations (namely, it is not infinite) then we can say it would be contradictory to assert that the finite can contain the infinite.(Although, one must concede that much of this hangs upon our definitions of the terms 'finite', 'infinite', and 'contain'.)[12]How we choose to define the terms however really is not the central question here, for we could easily enough define any two propositions into a contradictory set; but such an exercise may be completed at the expense of saying absolutely nothing about the external world.The questions for our present examination are:What is the status of the abstract philosophical axiom (or any axiom of a similar nature) finitum non capax infiniti?Is it an informative proposition?Does any such a priori come to us with factual significance?

To answer it must be pointed out that, at least from the viewpoint of twentieth century analytical philosophy, all propositions are generally thought to be of two types.[13]Briefly, the first type is the analytic proposition where the predicate is already contained in the subject, e.g., "All barking dogs bark" or "Rectangles have four sides."These propositions are true by definition and cannot be denied without self-contradiction.Such assertions come with the luxury of certainty, but also (importantly) at the expense of telling us nothing about reality — they neither affirm nor deny the actual existence of anything.The statement "All barking dogs bark" only means that "If there are any barking dogs, then they bark".Or, to put it another way, the only self-evident truth is the tautology (if A then A), but this sort of truth reveals no factual information whatsoever.[14]In algebra it would make no difference to the certainty of its demonstrations whether there are any objects corresponding to its symbols.The truth of analytic propositions cannot be refuted by experience precisely because they are formal (void of factual content) and not empirical hypotheses.

The other type of proposition is the synthetic.Here the predicate adds something to the subject with the result that two distinct ideas are synthesized in one proposition e.g., "Water freezes at 32 degrees Fahrenheit" and "The sun will rise tomorrow."Because the synthetic proposition affirms or denies the existence of something it tells us something about the actual universe (because of this it has often been called an 'existential' proposition).We become acquainted with synthetic knowledge by experience i.e., it depends upon actual experience or observation.

Thus we cannot attain the same degree of evidence about analytic and synthetic knowledge:whereas an analytic proposition such as 2+2=4 cannot be denied without self-contradiction, the contrary of all synthetic propositions is possible because no contradiction whatsoever is implied.As Hume rightly pointed out, the assertion that the sun will not rise tomorrow is no less intelligible a proposition and implies no more a contradiction than the assertion that it will rise.There is, in other words, no logical contradiction involved in saying that the sun will not rise.

If Calvin's axiom is to be taken as an analytic proposition, then it obtains at the expense of giving no factual information about the world.But he is certainly eager to say that his axiom is not simply a matter of definition:it has a kind of ontic hold on empirical reality.So the only thing one can conclude is that he must have believed we can possess knowledge that is both a priori certain and synthetically informative.He believed, that is, that the axiom finitum non capax infinitiis an example of a synthetic a priori.

Unfortunately, the twentieth century philosophical tradition has cast considerable doubt on the possibility of the synthetic a priori and for several reasons.The most prominent of these involves the argument for the analytic-synthetic distinction as detailed above, and maintains that the only proposition affording absolute certainty is the empty (or literally contentless) tautology.In addition to this, though, many have pointed out that our empirical terms by nature could never establish certainty.One of the reasons for this is that vagueness is an inescapable feature of language.Hospers asks us to consider, for instance, the common word "dog."Can we give the term a satisfactory definition?Well, some typical dog-characteristics might be that dogs have four legs and fur; they typically have long noses in relation to other mammals; they are able to bark; they wag their tails when pleased.Now one or more of these could be absent; for example, a three-legged dog would still qualify as a dog as long as it had other dog-characteristics.As we examine other doggish characteristics we might theoretically find one that we could consider as per se sufficiently defining.But as Hospers notes, what we actually find is a cluster of characteristics associated with the word dog, not all of which have to be present for it to be considered a dog.In fact, each of them can be absent, which shows that the characteristic is not defining.We would, nevertheless, still consider the creature a dog as long as it had most, or some, of the other characteristics.Hospers asks us now to consider how our picture of language has changed:

We began with the picture of a word designating all of a definite number of characteristics, let's say A, B, C, and D; unless a thing had all four of these, it would not be an X.But now we find that in the case of many words (most words?), it can be an X and have only A, B, and C, or A, B, and D, or A, C, and D, or B, C, and D; thus none of the four is defining.Indeed, it might be an X and have only A and B, or A and C, or A and D, or B and D, etc.[15]

Analogously, Waismann has pointed out that, due to the "open texture" of empirical terms, in many cases there is no such thing as conclusive verification.He argues that most of our empirical concepts are not delimited in all possible directions:

Suppose I come across a being that looks like a man, speaks like a man, behaves like a man, and is only one span tall—shall I say it is a man?Or what about the case of a person who is so old as to remember King Darius?Would you say he is an immortal?Is there anything like an exhaustive definition that finally and once for all sets our mind at rest?[16]

Waismann continues by considering whether, in science at least, one can obtain exact definitions.Can we not, for a simple example, come to an absolutely precise definition of gold (e.g., by the spectrum of gold with its characteristic lines)?Waismann answers:

Now what would you say if a substance was discovered that looked like gold, satisfied all the chemical tests for gold, whilst it emitted a new sort of radiation?'But such things do not happen.'Quite so; but they might happen, and that is enough to show that we can never exclude altogether the possibility of some unforeseen situation arising in which we shall have to modify our definition.Try as we may, no concept is limited in such a way that there is no room for any doubt.We introduce a concept and limit it in some directions; for instance, we define gold in contrast to some other metals such as alloys.This suffices for our present needs, and we do not probe any farther.We tend to overlook the fact that there are always other directions in which the concept has not been defined.And if we did, we could easily imagine conditions, which necessitate new limitations.In short, it is not possible to define a concept like gold with absolute precision, i.e., in such a way that every nook and cranny is blocked against entry of doubt.That is what is meant by the open texture of a concept.[17]

As Waismann points out, open texture is a fundamental characteristic of most empirical concepts, and this feature of language is precisely what prevents us from conclusively verifying most empirical statements.If we take any material object statement we will notice that the terms which occur in it are non-exhaustive, and this means that we cannot foresee every possible condition in which they are to be used.In other words, the possibility always remains that we have failed to take into account something relevant to their usage.This implies of course that we can never foresee all the possible circumstances in which the statement is true or false.There will always be a margin of uncertainty.[18]

Consider for a moment Waismann's attempted description of his own right hand.He could say very different things about it — for instance he may state its size, color, shape, the chemical composition of its bones, cells, etc. — but he could never reach a point where his description is complete.It could always be extended by the addition of other details.So every description, no matter how simple or complex it may be, stretches into a "horizon of open possibilities."[19] In the end, we can never eliminate the possibility of an unforeseen factor emerging, and therefore can never be sure we have included in our definition everything that should be.Given this open-ended element in our empirical terms, the process of defining and refining an idea will go on forever without ever reaching a final stage."Thus the result is that the incompleteness of our verification is rooted in the incompleteness of the definition of the terms involved, and the incompleteness of the definition is rooted in the incompleteness of empirical description."[20]

Calvin's Problem

All of this has an important implication regarding Calvin's philosophical axiom, particularly the subset propositions (1) and (2) noted above.Although Calvin wants to insist that there is a logical necessity in his definition of human nature, the fact stands that because such a description cannot be delimited in all possible directions, it cannot claim a priori status.None of us, including Calvin, could foresee every possible condition in which the terms 'human', 'nature', and 'body' are to be used.Such a situation is due to the inherent incompleteness of the terms we use to describe empirical reality.Thus Calvin is not necessarily wrong in his description of human nature, but he is clearly mistaken to claim a priori status for his assertions that a human body must be so and so and possess a certain number of properties.

But, could we not establish Calvin's defining properties of the human body by appealing to past instances, building them up as it were by induction? Unfortunately, such a process no more yields the certainty that Calvin wishes than does his synthetic a priori claim.For even if we could establish that every past instance of a body that we call human has all of the properties Calvin lists, we would still not be able — by the very nature of the inference — to cover all future cases.That we have missed an important feature of human nature, which, up to this point has gone unobserved, is entirely possible.Simply put, we can never eliminate the possibility of an unforeseen factor emerging — and therefore we can never be sure we have included in our definition everything that is required for it to reach defining status.

One of the problems with providing a complete definition of human nature is the presence of competing claims.Which properties are we to take as truly defining, and which ones are more or less up for grabs?To expand on Waismann's illustration, what would we say if a man came on the scene today who had extraordinary capabilities:capabilities that Calvin would have excluded a priori from the possible properties of human nature?If we could establish empirically that a certain person was able to walk through walls and appear at two different places at the same time, yet had every other property that we might consider as defining for a human being, would we refuse to call him human?And if so, are we refusing to do so because he could not possibly be a man and possess such peculiar characteristics, or because his extraordinary properties do not happen to fit in our particular rules that govern the term man?If the former, then are we not begging the question raised above, i.e., which properties are truly defining?And if the latter, then do we not need to expand our rules to fit the fact that a man stands before us in possession of properties that most men lack?In other words, a man could conceivably be a genuine human being and have the properties A, B, and C, A and C, A and D, or B and D.The fact is, we simply do not have enough hold on empirical reality to be able to exclude a priori the possibility that a man could be endowed with extraordinary abilities.[21]

Hospers' comments on defining characteristics may be helpful at this point:

Often people refer to a defining characteristic as an essential characteristic.Being a bird is essential to being a swan; being an alloy of iron is essential to being steel; having a certain atomic weight is essential to being gold.But this language can be misleading:It makes many people believe that there is some "essence out there in the world" which people discover, whereas in fact what happens is that we select certain characteristics of things and make them defining, that is, we refuse to apply the word to the thing if the thing lacks that characteristic.And we could change this if we wanted to, especially in the light of new knowledge.The definition of "gold" was changed in the light of modern chemistry, and the definition of "whale" changed when it was discovered that those creatures were not fish but mammals, and being mammalian was incorporated into the definition.[22]

Conclusion

Given the above factors one can conclude that a synthetic a priori cannot be established if the terms used to describe it are not fully disclosed; and since the terms used to describe empirical reality have an incompleteness about them, not having the precision required for absolute certainty, it seems clear that Calvin's subset propositions (1) and (2) cannot claim the status of a priori certainty.The universe appears to be more open-ended than Calvin would have us believe.

An important issue follows.Waismann observes that because the boundary regions of our knowledge are ever enveloped in a dust cloud, out of which something new may always emerge, one empirical proposition is not a strict logical consequence of another.To say that the class of premises is not 'closed' is to suggest that the conclusion is lacking in stringency, and this implies that the relation between, say, a law of nature and the evidences for it is looser than previously imagined.This means that the application of logic is limited in an important sense, namely, that the "known relations of logic can only hold between statements which belong to a homogeneous domain; or that the deductive nexus never extends beyond the limits of such a domain."[23]

Calvin insists, as we have seen, that anyone who denies certain limitations of the human body — limitations, of course, that he determines — commits the error of asserting A is not A (or, contradicts the meaning of the term body).However, we now see that Calvin has no basis for making such a sweeping statement.One who holds that Jesus' human nature participates in the divine omnipresence has not contradicted himself.Strictly speaking, there is no contradiction at all in saying that a human body may be empowered with divine gifts.In fact, in order to say that it is self-contradictory for Christ's human nature to participate in his divine nature, one would have to be able to give a complete definition of both natures e.g., the limitations of each of their properties.So we may say that, although, given certain presupposed definitions of the terms "finite" and "infinite," it would appear contradictory to say that the finite contains the infinite, there is no contradiction in asserting that Christ's human nature receives gifts (or participates) in the activities and properties of the divine nature.

One of the problems with Calvin's axiom is that he collapses the distinction between two fundamental questions:he implicitly fails to distinguish between the highly abstract question, "Is the finite capable of containing the infinite?" (whatever that could actually mean) from, "Could the hypostatic union of the historic Christ be such that his divine nature is nowhere present without his human nature?" He moves from the former to the latter without sufficient qualification.Or to put it another way, Calvin assumes that the former question stands in exactly the same logical domain as the latter.But it is this particular inference — the movement from an abstract philosophical principle to a concrete empirical reality — that is untenable in light of modern philosophical criticism.As fantastic as we may think it would be for Christ's human nature to share in the divine omnipresence, we have to say that it is one of many open possibilities. We therefore cannot exclude it merely on the ground that it implies a contradiction with some contrived definition of man.In the final analysis, the christological question turns not on ontological analysis, but, as Luther argued with Zwingli at Marburg, on biblical exegesis:"Hoc est corpus meum."[24]

*****ENDNOTES*****

[1] Opponents of this were also suspicious that it inevitably divides the person of Christ i.e., it seems to invalidate the personal union itself.

[2] Calvin: Institutes of the Christian Religion, trans. Ford Lewis Battles and ed. John T. McNeill, vol. 2 in The Library of Christian Classics, vol. 21 (Philadelphia, 1960), p. 1391. “Atqui haec est propria corporis veritas, ut spatio contineatur, ut suis dimensionibus constet, ut suam faciem habeat. Facessat igitur stultum illud commentum quod tam mentes hominum quam Christum pani affigit.” See Institutionis Christianae religionis 1559: librum IV. continens eds. Petrus Barth and Guilelmus Niesel in Joannis Calvini Opera Selecta, vol. 5 (Monachii, 1974), 386.9-12. For the extended reference above in Latin see 376.12-30.

[3] Calvin: Institutes of the Christian Religion, vol. 2, pp. 1381-82. Institutionis Christianae religionis 1559, 365.6-366.1.

[4] Francois Wendel, Calvin: Origins and Developments of His Religious Thought, trans. Philip Mairet (Durham, North Carolina), pp. 347-48 (emphasis mine).

[5] Inst., IV, 17, 29 (emphasis mine) as quoted in Wendel, Calvin: Origins and Developments of His Religious Thought pp. 348-49. "Deinde si ita multiforme et varium est Christi corpus, ut uno in loco appareat, in altero sit invisibile: ubi ipsa corporis natura, quod suis dimensionibus constat? et ubi unitas?" Institutionis Christianae religionis 1559, 384.28-31.

[6] Thus, again, Calvin argues the following: “Observe that the truth of the flesh is proved by Christ’s own lips because he can be touched and seen. Take these away and flesh now ceases to be. . . . He proves himself no specter, for he is visible in his flesh. Take away what he claims as proper to the nature of his body; will not a new definition of body then have to be coined?” Calvin: Institutes of the Christian Religion, vol. 2, p. 1399. Institutionis Christianae religionis 1559, 385.2-11.

[7] On this see, for example, John Hospers' An Introduction to Philosophical Analysis, 3rd ed. (Englewood Cliffs, New Jersey, 1988) pp. 117-18.

[8] I am taking the phrases "human body" and "human nature" to be roughly equivalent, as Calvin seems to make no clear distinction between the two in this particular respect. Also, his simple dualism between "flesh" and "spirit" suggests that he would not split hairs between nature and body i.e., both terms appear to mean the same thing as the term flesh.

[9] My argument in no way rests on the assumption that Calvin explicitly refers to the axiom finitum non capax infiniti. The fact that he sees certain properties as defining establishes that he implicitly affirms the axiom (or one very much like it).

[10] Calvin: Institutes of the Christian Religion, vol. 2, p. 1400. Institutionis Christianae religionis 1559, 386.21ff.

[11] See, for example, Calvin: Institutes of the Christian Religion, vol. 2, pp. 1381, 1403. Institutionis Christianae religionis 1559, 364.15-365.5, 389.21-31.

[12] Or, if we take the proposition p "The finite has limitations" and q "The infinite has no limitations," we could conceivably introduce a third proposition r that is consistent with both p and q; if such a process were successful it would be shown that p and q did not in fact stand in mutually exclusive realms. Paul Helm describes this sort of process in his description of "procedural" reason. See Faith and Understanding (Grand Rapids, 1997), pp. 7-8.

[13] This has for the most part been maintained despite Willard Van Orman Quine's objections developed in his "Two Dogmas of Empiricism" in From a Logical Point of View (2nd rev. ed; Cambridge, Mass., 1953). Many responses have followed the publication of Quine's arguments, for instance, H. P. Grice and P. F. Strawson, "In Defense of a Dogma," in Philosophical Review, vol. 65 (1956), 141-158; G. H. Herburt, "The Analytic and the Synthetic," in Philosophy of Science, vol. 26 (1959), 104-113. On the basis of these thorough responses to Quine, I shall assume that the analytic-synthetic distinction is a valid one.

[14] Thus Hospers: "What is it that makes people call definitions analytic? Once you introduce (or assume or presuppose) the rule that the word 'father' is substitutable for the phrase 'male parent', then, against the background of that rule, you can say they are identical in their meaning, that is, that the statement 'Fathers are male parents' is an instance of 'A is A' (which is analytic)." See John Hospers, An Introduction to Philosophical Analysis p. 117.

[15] John Hospers, An Introduction to Philosophical Analysis p. 122 (emphasis mine).

[16] Friedrich Waismann, "Verifiability," in Logic and Language (First Series) edited by A. G. N. Flew (Oxford, 1963) pp. 119-20.

[17] Waismann points out that another way to say this is that definitions of open terms are 'always corrigible or emendable'.

[18] Waismann, "Verifiability" p. 121.

[19] “Contrast this case with others in which completeness is attainable. If, in geometry, I describe a triangle, e.g., by giving its three sides, the description is complete: nothing can be added to it that is not included in, or at variance with, the data. . . . Such cases serve merely to set off the nature of an empirical description by the contrast: there is no such thing as completeness in the case in which I describe my right hand, or the character of a person; I can never exhaust all the details nor foresee all possible circumstances which would make me modify or retract my statement." See Waismann, "Verifiability" pp. 121-22.

[20] Waismann, "Verifiability" pp. 122-23.

[21] Such a priori exclusion of open possibilities is not only philosophically bankrupt, but also (importantly) patently counterproductive in the scientific enterprise. It has often been noted that if Kant were correct in his belief that causality is a synthetic a priori, then it would be inconceivable to come across any events, which did not conform, to the principle of causality. But, in fact, quantum phenomena have forced physicists to modify their previous notions of causality. Despite all the hope in synthetic a priori judgments, nature continues to baffle us. "How reassuring it would be to say that nature must obey causal laws. . . The question is only whether Nature will conform to Kant. You will realize that such over-confidence is no longer permissible to-day, in the age of quantum mechanics." On this see Waismann's extended discussion in "Verifiability" pp. 130ff.

[22] Hospers, An Introduction to Philosophical Analysis p. 119.

[23] Waismann, "Verifiability" pp. 127-28.

[24] Hermann Sasse, This Is My Body: Luther's Contention for the Real Presence in the Sacrament of the Altar (rev ed.; Adelaide, S. A., 1977) p. 210.

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