Dialogue and Difference: Worldviews

In the previous post, I discussed the relevance of epistemology in understanding others. One perspective should not dominate the other, nor should it be isolated from the other. Rather, the only way to honestly hold to a critical realism is to bring differing perspectives into dialogue.

In this post, I want address how worldviews guide our thinking and inevitably result in interpersonal and political tension. I will begin by addressing our inability to understand how others can hold opinions different from our own. In on-line essay, sociologist Allan G. Johnson refers to this as a failure of the imagination.5 Johnson writes:

What I can imagine depends on what I already know or think I know, a huge collection of beliefs, values, and assumptions that make up a worldview. Like everyone else, my worldview shapes how I see everything, from the cosmos and what happens when we die to why people do what they do. It is the stuff out of which I construct a taken-for-granted reality that I don’t have to question. It shapes not only what I perceive as real, but how I make sense of it, how I explain what happens and what is and is not, and how I justify what I do in any given situation.

...Worldviews shape not only how we experience what’s right in front of us, but also what we cannot see and what hasn’t happened yet.

….Because worldviews enable us to feel like we know what’s real from one moment to the next, it’s not hard to see why we’d feel we cannot live without them, which is why opposing worldviews can provoke extreme reactions like calling people idiots or morons or evil. To nullify the threat, we draw upon those same worldviews to understand our opponents in ways that leave our worldviews intact while discrediting theirs.

 When people think differently than we do, it challenges our sense of reality. Worldviews not only enable us to have a sense of what's real and what's not, but we also derive meaning from them as well as a sense of identity. So worldviews are necessary, but but they also inevitably lead to judgments about others. Johnson continues: 

Which brings me to what is, I’ve long believed, a general pattern among human beings that applies to both sides of any argument. It goes like this—when we lack information that is important to us, we tend to make it up. Our worldview is our primary source of such material. We can’t really know what’s going to happen next, for example, and we can’t really know why people believe and do what they do. We cannot see into their hearts and minds. But that doesn’t keep us from acting as though we can. I don’t actually know what the driver of that other car is going to do in the next ten seconds, for example, but watch me act as if I do.We make up reality as a way to avoid the anxiety and fear that come from uncertainty and from the need to feel solid ground beneath our feet.Where this can go wrong is when we pretend that what we’ve made up is the actual person or group or thing we’re dealing with. Look at the daily waves of anger, fear, outrage, and disbelief around one issue or another and we can see the result—I’m right, you’re wrong; I’m good, you’re bad; I’m sane, you’re crazy; I’m smart and you’re an idiot or a moron.

This is an important point. A worldview mediates to us a sense of reality (what is out there) and a sense of identity (how we relate to that). We experience our worldviews as “based in something larger than and beyond ourselves” which “only increases our tendency not only to experience them as true, but to be unaware that we even have a worldview in the first place.” We take them for granted. It is therefore inevitable to have judgments of others – it is the only way we can have a coherent worldview. And when we get into a disagreement, we “defend our worldview not simply because we like a particular set of what we consider to be facts, but because our sense of reality itself—of who we are and the difference between what is real and what is not—depends on it. This makes it impossible to completely separate ourselves from whatever worldview we’ve come to have.” Our worldviews make it inevitable that we hold certain ideologies about what it means to be human and what other people are like, but they also have “safe” explanations for why others disagree with us. And so a worldview necessarily entail having prejudice about and interpersonal tensions with other people. Therefore, the only way to maintain civil relationships with others is to be able to reflect and examine one's own worldview.

Examining our own worldview is not an easy thing to do. It is hard work that can be confusing and uncomfortable and threatening and, at times,frightening. But it is also the only alternative we have to angry refusals to compromise or even listen to one another. Yesterday a caller to an NPR radio show expressed support for gun control and then blurted out in exasperation, “Why should we have to compromise?” while at a recent gun rights rally in Hartford, a man was heard to say that the two sides are on opposite sides of the moon, with people like him on the light side and their opponents in the dark. It would be easier if this were true, because we’d have no reason to reconcile our differences. But we inhabit the same society. We live down the street from one another. Our children and grandchildren attend the same schools, go to the same movie theaters.

Finding a way out of this doesn’t mean making our worldviews all the same, which is impossible. It does mean opening our own worldviews to the reality that they are just that, that they are not the only ones, and that those who see things differently are not crazy or stupid or malevolent. Then we can talk about evidence and consequences and how to construct a society in which worldviews can coexist without our being at one another’s throats.

Examining our own worldview does not come natural to us, especially as we are already geared towards scrutinizing the worldviews of others. But that is the way forward. Dialogue and introspection go together.

Try to be aware, when you witness or participate in a debate, how easily it slides into defensive and accusatory attitudes, and issues become more about “us vs them” than the actual topic being discussed. Try to pay attention to the assumptions made about others, the ad hominem and straw men arguments.

In the last section I characterized attitudes of judging and attitudes of learning. It may be more accurate to characterize our attitudes of judging as attitudes of protecting. We all behave in ways to protect our worldview as a way of self-protection. Therefore there must be a building of trust in order to facilitate an attitude of learning

Dialogue and Difference: Epistemologies

In the following posts, I am going to discuss some issues related to our knowledge, imagination, and rationality, etc., and relate them to the prospect of connecting with others with different viewpoints. (I may not have all my references written down because I am copying and pasting from my journals, and the process does not include footnotes).

I do not believe that foundationalist epistemology is helpful for a critical realism perspective. I think of knowing is more embedded ion structures of learning. Since foundationalism seems resistant to learning, it is not a helpful philoslophy of knowledge.

a. Critical Realism and Difference

When you encounter a perspective that is in conflict with your own (a disagreement!), two options may present themselves. Either you can assume that your own perspective is dominant and so determines the conclusion of the conflict, or you can assume that the two perspectives cannot find a common ground, either because they are so entrenched in their own contexts or because they refer to two separate realities; they are incommensurable. The difference of perspectives may be of religious traditions, political views,scientific research programs, or between religious practitioners and scientists. Both of these options are ways of attending to difference and both are problematic.

Neither of these options exemplifies critical realism. Realism is the belief that there is a reality, specifically a reality that has existential precedence over the content of human thought. That is,that there is a reality “outside the mind”, as it were. What makes a realismcritical is how the mind relates to that reality. For instance, naïve realism suggests that what is real is readily available to the mind, and what the mind perceives is literally an exact impression of what is real. A critical realism accounts for the fallibility of human knowing. That is, what is real is not always obvious and knowing involves attending to the limitations of human epistemic resources. A simple reason as to why the first option does not entail critical realism is because it does not take seriously the limitations of human knowledge. A simple reason the second option does not exemplify critical realism is because it does not take seriously that reality is one and takes precedence over thought. A more profound reason why each option does not represent a critical realism is that both do not take seriously that each perspective is conditioned by that which is beyond it. That is, there may be something novel (a concept or a piece of information) that lies outside your perspective that has implications for your beliefs. The mistaken assumption is that one's own beliefs cannot be modified or informed by an outside alternative resource;that is, that one's own epistemic resources are enough. Both the absolutism of the first option and the relativism of the second option are subject to a naïve realism because they don't consider the importance of learning from beyond one's immediate perspective.

Therefore,is a third option is presented. That is the option of a critical engagement with the different and the new. One need not assume that one perspective will consume the other, nor that they should be isolated from each other, but rather they can coexist and create a new perspectivism through dialogue. Of course it's not that simple. However, we should thematize the challenge of navigating through difference in this society by attending to tendencies of naïve realism. The only way to reduce the threatening presence of alternative perspectives is make meaningful dialogue.

I am going to consider insights from philosophical theologians that address the epistemic challenges in the dialogue between science and theology. Then I'm going to look at an example of a controversy from within evangelical theology. I'm going to assume that the insights and examples I use are interesting and useful to nonreligious persons as well.

b. Postfoundationalism

I will draw insights from a number of theologians who recognize that,in order to meet the challenge of facilitating an interdisciplinary dialogue between theology and the sciences, they must first address the postmodern challenge of maintaining the conviction of the unity of truth while navigating through multiple perspectives. I am mainly following the lead of philosophical theologian J. Wenzel vanHuyssteen, whose solution is to propose a postfoundationalist epistemology. Postfoundationalism is a mediating solution to the antithetical positions of foundationalism and nonfoundationalism.  We will first need to explain each of these positions.

Foundationalism “insists that there is some way to ground all human knowledge in a set of objective, self-evident beliefs which then supports a universal understanding of rationality where reason remains invariant across every context.”1 Foundationalism is present when knowledge-claims are assumed to be certain and universal. Foundationalism is found in the assumption that certain content of knowledge excuses people from learning from or being informed by alternative perspectives. A reaction to this view is nonfoundationalism, which “highlights the fact that every historical context, and every cultural or social group, has its own distinct rationality. This kind of contextualism easily leads to a relativism of rationalities, where every social or human activity could in principle function as a framework for human rationality.”2 Theologian F. Leron Shults summarizes this way:

Foundationalism,in the “classical” sense, was a part of the Enlightenment project: human reason could attain certain knowledge based oneself-evident foundational experiences or a priori propositions,from which necessary and universal conclusions could be reached. Absolutism guides the definition of Reason (and so the drive for systematicity). Nonfoundationalism is diametrically opposed to this approach, asserting that we have no foundational beliefs that are independent of the support of other beliefs; rather, we subsist in a groundless web, attempting merely to maintain coherence in our local praxis. Justifying beliefs is only a matter of determining whether they cohere with the other beliefs in a particular web or context. Relativism often shapes the view of reason (and so also of the ideal ofsystematicity).3

Postfoundationalismis a third option that tries to find a way between foundationalismand nonfoundationalism. “Postfoundationalismattempts to split the difference between foundationalism and nonfoundationalism by affirming the epistemic importance of making responsible judgments characteristic of the former while acknowledging the ineluctable contextuality of interpreted experience emphasized by the latter.”4 Philosophical theologian J. Wenzel van Huyssteen proposes a postfoundational theory of rationality by focusing on real life accounts of belief formation. Van Huyssteen argues that the human species universally shares resources that attribute to belief formation, including seeking intelligibility with problem-solving abilities and intersubjective accountability. Van Huyssteen also argues for a transversal rationality – that is, for rationality that is exemplified by shared concerns and practices among various disciplines. In this way, van Huyssteen attends to the interpretive aspects of knowing.

In general, I would argue that we should attempt to uphold the integrity of rationality within various contexts (for instance, differing disciplines or differing religious systems) while also finding connectivity with cross-contextual rationality – attending to the integrity and limitations of each perspective. In order to uphold a critical realism, we should have attitudes of learning rather than judgment as we seek understanding.

c.  Biblical Theology and History

I’m going to borrow an example from within evangelical theology. Suppose there is a body of scholarship that recognizes the need to interpret the New Testament text in terms of historical scholarship. Suppose also that there is a school of thought that suggests that historical scholarship should not inform one’s interpretation of scripture because scripture itself is an epistemic foundation and hence cannot or should not be informed by “outside” sources. The question is then begged: What is the relationship between history and biblical theology? Does one of these two spheres determine the conclusions in the other? Does one perspective dominates the other. Should the bible-believing Christian assume the bible determines closure on all differences or tensions found in historical scholarship? (Similarly,should the supposed neutral secular scholarship determine the conclusions of the former?). Or perhaps we should conclude that history and theology are simply two different disciplines that should not account for the other; they are incommensurable spheres too deeply entrenched in their own contexts. Each of these options are problematic. In the first option, the Christian (or the historian)is a foundationalist, assuming that certain content of knowledge excuses her from the prospect of being informed by an alternative perspective, that such knowledge is immune to correction or adjustment. The second option is a nonfoudnationalism, assuming that each perspective is so deeply contextual that they cannot find common ground. Therefore a postfoundationalist approach should be recommended where the Christian can attend to connectivity of history and theology. I would not assume that this is easy. In fact, I suspect that part of the real problem behind these differences is the rigor involved in mediating positions.

d.  Learning and Judging

In conclusion, I would like to propose the challenge of the assumption of foundationalism. The assumption that a given source of knowledge excuses one from further learning, or the assumption that one cannot be informed by further study. These assumptions constitute a naïve realism. On the other hand, we should be careful not to assume something to be irrelevant to our own context. One should take seriously the notion that we are conditioned by that which is beyond us. In which case I think a fair starting point is to assume that we can all learn from each other.

When one encounters something that is new or different, one has a choice. One can either interpret the new and the different in terms of their already present tacit categories, or one can reconfigure one's categories in their engagement with what is new or different. The first response can be referred to as “judging”, the second as“learning.” This reveals an important aspect of engaging with different perspectives – that the engagement would be an opportunity to learn and involves introspection. Hence,introspection and dialogue go together.

Is the Mathematics Imagined or Discovered?

For a very, very long time I have been meaning to read up on contemporary views of the philosophy of mathematics and the relevance of phenomenology.  I have not had the time.  Yet the topic haunts me.  I think about it a lot.  I would nonetheless like to share my current thoughts on the subject, despite the present ignorance and incompleteness.  So below are my thoughts.....

On the question as to whether mathematics is a part of reality or a mere mental construct, I offer the following account. I hold to a mathematical realism. That is, mathematical reality - the truth value of mathematical statements, for instance – are discovered, not constructed. That said, I will add that the reality(and properties) of mathematics are dependent on the mind. It is important to note that just because something's existence depends on the mind does not mean that it is “created” by the mind. There being an “out” depends on there being an “in.” The point is that mathematics is real because the mind is real. Mathematics is areal aspect of the real finitude of the mind.

The truth of mathematics depends on the reality of the mind being conditioned from without. That is, it derives from the fact that the mind is necessarily conditioned by that which is beyond it. The fact that the human mind is impinged upon by what's beyond it is an aspect of the mind and this aspect is key in understanding the reality of mathematics.

All philosophy from mathematics should start here. Beyond that I adhere to some extent to a form of mathematical structuralism which suggests that mathematical objects are constituted by their relation in a system. In this sense mathematical objects are also meanings. The details of the phenomenology of mathematics beyond this are yet to be spelled out tome.

This is the starting point of the discussion of the relationship between mathematics and hermeneutics. They both rest on the finitude of human perspective.  

I should end by saying a philosophical theologian with whom I'm connected on Facebook, said to me that this view is, which I consider a kind of "realism" is closer to a "Kantian Idealism." That may be. However, I'm actually not fully convinced. At this time I suspect that if I can flesh out my ideas, then they would provide an interesting argument for realism.

Then, again, as I said, I have not given this subject the time and thought it diserves for a long, long time. At the moment, I think Euler's identity e^(iπ) = -1 will make more intuitive sense to the mathematical community in the future, because their are aspects of it that is yet to be discovered.

William Lane Craig's Confusion of the Mathematical Infinite and the Metaphysical Infinite

Some time ago I wrote a response to an article by evangelical theologian/apolologist William Lane Craig. Craig's article argued that Wolfhart Pannenberg, Phillip Clayton, and F. LeRon Shults hold a kind of pantheism despite their efforts not to. Craig's argument rested on his interpretation of the theologians as saying something like, "Given X, we must conclude Y", when in fact the theologians are saying something more like, "If we think in terms of X, we must then conclude Y. However, we need not think in terms of X." More specifically, the theologians were arguing that (by my interpretation), "If infinity relates to finite reality the same way that finite things relate to other finite things, then we must conclude pantheism. However, Infinity does not relate to finite objects they way that finite objects relate to eachother."

Two things struck me as curious about the article. (1) Craig does not address the problem the theologians themselves are addressing in making their arguments- perhaps they are off his radar and this is why he misunderstands them; (2) Craig does not seem conversant with the subject.

Below is an excerpt from the article I wrote, pointing out Craig's confusion.

Craig's Confusion of the Mathematical Infinite and the Metaphysical Infinite

There are two approaches to describing infinity: the mathematical and the metaphysical. The mathematical infinite is quantitative and has to do with extension. The metaphysical is qualitative and has to do with such concepts as ultimacy, perfection, completeness, ground of being, etc. Historically, these two accounts of infinity have interacted with and informed each other in different ways.  One way to speak of the infinite is to say that it is that which is always beyond. In this sense, insofar as mathematical analysis always presupposes a point of reference (from a finite perspective), a mathematical account of infinity will always be confined and limited; there always will yet be a beyond.  In other words, a mathematical or quantitative description of infinity is a domesticated infinity.  Many theologians are concerned about construing God's infinity in a quantitative way.  This brings us to the next section of Craig's paper.

Craig's paper goes on to argue that the vague metaphysical definition of infinity put forth by these theologians have been supplanted by a clear and concise mathematical definition of infinity derived from Georg Cantor.  Craig seems to think the two definitions represent opposing approaches to understanding Infinity. He then compares the metaphysical descriptions he takes from our theologians to the mathematical account of Cantor in a way that only confuses the issues.  Those who are familiar with the topic understand that the mathematical approaches to infinity are a part of the broader philosophical discussion regarding metaphysical infinity.  Much of what Craig says can be accounted for by his confusion..

According to Craig, Cantor's definition of infinity is a feature of a set of objects whereby each object in that set can be “paired off” with objects in one of it's proper subsets. Craig then says that,

Cantor’s definitions completely subvert the Hegelian argument. For it is not true, as Pannenberg’s version of Hegel’s argument affirms, that

2. The infinite is defined as that which is not finite.

According to Craig, Cantor's work on set theory subverts the notion of infinity in Hegelian metaphysics and hence the theology of Pannenberg, Clayton, and Shults. However, it is not that simple. I would argue that a proper discussion on the interaction between the work of Cantor and Hegel (and our theologians) is quite involved and requires a degree of elucidation.

Craig says:

Two questions then present themselves. First, why think that the metaphysical infinite is privileged over the mathematical infinite as the concept of the “true infinite”? Why not think that the true infinite is the mathematical concept, and the qualitative idea just an analogical notion? Indeed, given the rigor and fecundity of Cantor’s analysis in contrast to the imprecise, subjective, and poorly understood metaphysical concept, do we not have good grounds for elevating the mathematical concept to the status of the true infinite? At least there is no reason to make it play second fiddle to its metaphysical cousin.

Part of the problem with Craig's question is that it does not recognize the present philosophical discussions concerning infinity.  Current philosophical reflection holds the mathematical infinite is an incomplete, inappropriate, and finite infinity as it is rooted in conceptions of extension and quantification; the mathematical infinite is something of a poor parody of the metaphysical infinite. It should be pointed out that Cantor himself would never have regarded the mathematical infinite as superior to, or even alternative to, the metaphysical infinite.  Indeed, he understood his mathematical work as reflective of the greater metaphysical infinity that is beyond mathematical description. Cantor wrote:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third, when the mind grasps it in abstracto as a mathematical magnitude, number, or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite.3

Cantor makes a sharp contrast between the metaphysical infinite (which he describes as God) and the (actual) mathematical infinite in his work.  He understands his mathematical infinite as not really infinite, but itself finite.  Philosophers recognize the difference and mathematicians understand that theoretical study of transfinite mathematics touches on the metaphysical.

To better understand this, it may be helpful to review the more interesting and more novel aspects of Cantor's discussion of infinite sets that Craig does not mention. Remember, a set is infinite if its elements can be “paired off” with the elements of one of it's proper subsets. For instance, we can pair off each element of the set of natural numbers {1, 2, 3, 4, …, n, ....} with each element from the set of all squares {1, 4, 9, 16, …, n2, …}. The set of all squares is a proper subset of the set of natural numbers; that is, all of the elements in the set of squares are also in the set of natural numbers. Yet each element in one set can be paired off with an element in the other set (with none leftover).  This is a feature not enjoyed by finite sets. For instance, we cannot pair off all of the elements in {1, 2, 3, 4, 5} with the elements in one of it's proper subsets. If we try to pair off each element in this set with the subset {1, 2, 3, 4}, there will be an element left over.

Cantor showed that one can “pair off” each of the elements of the natural numbers with all of the integers as well as with all the rational numbers.  However, one cannot evenly pair off all of the natural numbers with all of the real numbers.  He demonstrated that no matter how one paired off the elements of the set of natural numbers with the set of real numbers, there will always be found a real number left over. In other words, given the definition of infinity outlined by Cantor (i.e., the feature of a set whereby each element can be paired off with each element in one of it's proper subset), some infinities are “larger” than others.  Because the set of real numbers have “more” elements in it than the set of natural numbers, we say that the set of real numbers have a larger “cardinality” than the set of natural numbers.  That's not all.  No matter what cardinality an infinite set may have, there will always be a set with a larger cardinality.  The power set of a set, that is, the set of all subsets of a given set, will always have a larger cardinality.4  The point is that while one would think that Cantor's set theory successfully subjects infinity to mathematical analysis, the truth is that such an attempt is futile. There are always larger infinities.

Furthermore, the attempt to capture “true infinity” in terms of set theory leads to paradoxes. Consider, for example, the paradox of the set of all sets: If there existed the set of all sets (that is, a set whose elements would be all sets, including itself) then, according to set theory, it's power set would have a higher cardinality! (Hence, it would not be the set of all sets). Paradoxes such as these are what Cantor called “inconsistent totalities”, which he believed to be (at least alluding to) the metaphysical infinite, or the 'true infinite.'

On this aspect of Cantor's research, philosopher A.W. Moore says:

This relates back to a view of Cantor's, namely that whatever is subjected to mathematical investigation, even if it is infinite in a suitably technical sense, is thereby seen to enjoy a kind of finitude: the truly infinite is that which resists mathematical investigation.5

Moore then comments on this result:

….the concerns and preoccupations that dominated the history of thought about the (mathematically) infinite until the time of Cantor had at least as much to do with inconsistent totalities as with infinite sets. In fact the history serves as a useful corrective against those inclined to say that, through the combined efforts of such people as Bolzano, Dedekind, and Cantor, we have at last been brought to see what infinitude really is: it is a property enjoyed by any set whose members can be paired off with the members of one of it's proper subsets – as though this were the last word on everything that exercised Aristotle, Kant, Hegel, and all the rest.6

Craig does not seem to be familiar with this part of the discussion. His conception of the mathematical account of infinity being in opposition to a metaphysical account of infinity deviates from mainstream philosophical discussion and is indeed problematic.  For the reasons just outlined, we can respond Craig's question – Do we not have good grounds for elevating the mathematical concept to the status of the true infinite? – No, we do not.

After conceding that it may be appropriate to speak of God in terms of a metaphysically infinite, Craig later says:

But then we come to the second question occasioned by the distinction between the mathematical and metaphysical infinite, namely, why think that the Hegelian concept of the metaphysical infinite is correct? Why think that Hegel has correctly understood the notion of the metaphysically infinite?

I think that it is fair to say that the theologians in question do not completely agree with Hegel's account of the metaphysical infinite, but do try to understand Hegel's place in the discussion well enough to know what aspects of his work are worthy of interacting with and what questions of Hegel are worthy of a response.  Hegel, like Cantor and Kierkegaard, has a place in the overall discussion as philosophers and theologians critically assess his unique contributions and questions. It does not do to simply say, as Craig does, that the theologians in question are under the bad influence of Hegel.  Rather, we must assess how these theologians have critically appropriated Hegel, which involves a more in-depth exploration of issues.  In any case, what is at issue here is not simply Hegel's influence but the broader conversation of the metaphysically infinite (in which Hegel plays one role), and I do not believe that Craig has successfully evaluated these theologians' engagements with that overall topic.  For instance, Shults has argued for a retrieval of divine infinity from within the Christian tradition, where the same philosophical issues are found without relying on Hegel’s contributions.7  Discussion of Hegel is reserved for section that outlines modern philosophical movements.

Craig's confusion of the relationship between the metaphysical and mathematical infinite leads him to some problematic comparisons as he tries to show how Cantor's notion of an infinite set displaces the metaphysical definitions put forth by these theologians. Consider, for instance, the following:

Neither, on Cantor’s account, is it true, as Pannenberg suggests, that

2′. The infinite is that which includes the finite.

For (2′), on Cantor’s definitions, is clearly false, for one can have infinite collections which have no members in common. So, for example, -2 is not included in the natural number series, despite the fact that that series is infinite.

Cantor’s definitions also make it clear that Clayton’s premiss

1. If something is infinite, it is absolutely unlimited.

is false. The collection of natural numbers have a lower bound 0 but is nonetheless infinite. The series of fractions between 1 and 2 has both an upper and lower bound, namely, 2/1 and 1/1, but is for all that infinite. Thus, given Cantor’s definitions, the crucial premises in the monistic arguments are false.

Craig is evaluating the statements he takes from Pannenberg and Clayton in terms of the properties of sets.  However, there simply are no grounds that allow him to evaluate these statements within the criteria of set theory.  To show that the statements do not correspond to sets (the way that Craig suggests) does absolutely nothing to invalidate them.  The above argument suggests that Craig interprets infinity primarily in a mathematical or quantitative way.  It is precisely this tendency that the theological notion of true infinity is meant to avert.  I would suggest that much of Craig's analysis in this section is rooted in this confusion.

Craig's dependance on quantitative categories are revealed in his last sentence:

Rather God’s metaphysical infinity should be understood in terms of His superlative attributes which make Him a maximally great being.

To say that God has “superlative” attributes that makes God a “maximally great being” is to put God at the top of a quantitative scale. The terms “superlative” and “maximally” are concepts that involve a kind of comparative relationship that only make sense in terms of something relatively 'less than.'  They are extensive concepts and depicts God as finite.  Again, this is precisely the kind of relationship that the criteria of 'true infinity' is meant to avert.

In sum, Craig believes that the Hegelian definition of infinity is “subverted” by Cantor's set-theoretical definition.  This obscures the understanding of current philosophical discussion on infinity. Craig supposes there is no reason the mathematical infinity cannot be elevated to the status of the 'true infinity' discussed in theology.  Cantor himself and thinkers thereafter have shown that the mathematical infinity enjoys a kind of finitude that precludes this option.  Craig's preference for mathematical descriptions lead him to problematic theological conceptions that his theologians critique in the first place.

From INFINITY.....and BEYOND!

I have come to associate many of my thoughts on the concept of "that which is beyond oneself and conditions oneself."  This is a kind of way of talking about infinity, I think, from the perspective of one that is finite (from one having perspective).

I tend to think of this in terms of my mathematical philosophy - that the reality of mathematics is woven into the being-conditioned-from-beyond-ness of the mind.  In a sense, mathematics are discovered because they are part of the real world, but they are dependent on the mind, involves the imagination, though not itself "imagined."

My thoughts on epistemology often uses this theme. For instance, my critique of foundationalism is that epistemic foundations - their correspondance with reality and their meaning - would have to depend on reality that is beyond the frame of reference they depend on (or are conditioned by). This dependence defeats the reliance on such foundations' epistemic integrity.

Once I presented some basics of Derrida's deconstruction approach - but I translated his thinking in terms of "that which is beyond oneself and conditions oneself." The consumation of meaning cannot be arrived at because it is conditioned by that which is beyond the moment, the perspective, and the self.

And of course in my religious thinking: "that which is beyond the self and conditions the self" may refer to the Infinite - or GOD.