It has been a while since my last post. Ph.D. work, conference, and family have all kept me busy throughout the summer. I should hopefully have a few posts over the next few weeks that summarize the conferences that I have attend, the progress I have made in my Ph.D. research, and some general thoughts I have considered this summer. This post falls in the latter category. Enjoy.
I have written here before that education is inherently value-laden. If you are an educator then it is not a question of “are you teaching values?” but rather “which values are you teaching?” In this vein of thinking it can also be argued that education is inherently religious if it instills within us some sense of values and some sense of faith. Now, those values and the object(s) of that faith could vary greatly depending on the educational institution, but the fact is they are always there. This is why for centuries the work of education was undertaken by explicitly religious institutions and it is only fairly recently in society’s history that the state has taken on this endeavor (Wilson). So for everyone who feels that there is something wrong with our current state/system of education, I would argue that the root issue is primarily a religious one.
Every pedagogy assumes an anthropology (Smith). Before you can teach human beings you have to have some understanding of what human beings are. Ultimately I believe this is the reason for the existence of standardized testing (at least in America). The state approaches education from the perspective that all human beings are essentially good. It is simply a matter of providing education equally for all that will result in well-trained, productive citizens who contribute to the good of society. From this perspective, education is an act of justice. It is a citizen’s right to be educated. If the educational system is an administration of justice on the part of the state then it will inextricably be tied to universal standards that students and educators are required to meet. I mean, isn’t that how the justice system works? It sets standards in place that apply equally to everyone in a blanket approach and expects every individual to live up to those standards. There are also consequences when the standard isn’t met. Fail to meet the justice standard in society and go to jail. Fail to meet the standard in school and get remediation or don’t move to the next grade level or don’t graduate. As long as the state is in control of education, expect standardized testing to always be a part of the educational process.
What is the alternative? Maybe, just maybe, human beings aren’t inherently good. Maybe they are inherently evil and no amount of knowledge is going to save them from that. If we adopt this (Christian) anthropology then education will not be seen as an act of justice, as a right of the citizens, but rather as an act of grace. Education can be viewed as an act of grace that missionally reaches out to engage the lost mind. Grace doesn’t set a standard for you to meet. In fact, grace realizes that you can’t meet THE standard. So then the focus of education shifts from universal standards to individual and communal transformation. Results aren’t measured in knowledge gained but rather in affections formed.
My thoughts are still developing on this topic, but for now I can leave you with this fact: as a Christian educator (be it in an explicitly Christian setting or even when I was in public school), I care less about what my students know, and more about what my students love. This is the purpose of education.
Some books that I have been reading that have influenced my thinking on this issue:
Black Swan as a term derives from a Latin expression that characterizes something as being “a rare bird in the lands, and very like a black swan.” When the phrase was coined, the black swan was presumed not to exist. The importance of the simile lies in its analogy to the fragility of any system of thought. A set of conclusions is potentially undone once any of its fundamental postulates is disproved. In this case, the observation of a single black swan would be the undoing of the phrase’s underlying logic, as well as any reasoning that followed from that underlying logic.
This Latin phrase was a common expression in 16th century London as a statement of impossibility. For a long time Europeans believed that all swans were white. That notion only held true as long as their discovered world contained only white swans. At the time, all historical records of swans reported that they had white feathers. In that context, a black swan was impossible or at least nonexistent. Then Australia was discovered and along with it, the existence of the black swan. The term metamorphosed to connote that a perceived impossibility might later be disproven.
Upon this event, perceptions of the world and what swans were had to change.
A Black Swan event is any event that occurs outside the realm of expectations. Black Swan events were characterized by Nassim Nicholas Taleb in his book, The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as “black swans”—undirected and unpredicted. Taleb asserts in the New York Times:
What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.
I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives
Black Swan seems to be a relatively apt statistical description of the incarnation. When gathering resources for this post I even came across Black Swan Ministries who also recognize this connection. I’d briefly like to address Taleb’s three criteria for categorizing something as a Black Swan (with a slight change in wording on the last point).
Rarity
Obviously the incarnation is an extremely rare event: having occurred once in history. To further discuss this point, I’d like to make mention of The Logic of God Incarnate, a work by Tom Morris.
This work is a response to John Hick’s Myth of God Incarnate. Hick attacks a Chalcedonian Christology which affirms that Jesus is fully divine and fully human: two natures, one person. Hick’s objection falls along these lines: God is omnipotent, omniscient, omnibenevolent, eternal, immutable. Humans are limited in power, limited in knowledge, limited in goodness, temporally constrained, changeable. God is perfect. Humans are imperfect. Therefore it is logically incoherent to say that Jesus is God incarnate – no being could be both perfect and imperfect, both fully divine and fully human.
On Hick’s view it is not possible to have the two natures of the divine and human because they comprise incompatible attributes. If his premises are right, then his argument is true. But since the conclusion of his argument is false, there must be something wrong with his premise.
Hick’s argument begins by assuming being perfect is essential to divinity. God could not have failed to be perfect. This is true.
His argument also assumes that imperfection is essential to humanity, but is it? Morris argues this is wrongheaded. The essence of a “thing” is the set of properties which are individually necessary and jointly sufficient for being that thing; if you lack any one of those properties then you are not that thing. Hick assumes that the each of the properties listed under being human are part of the set of properties that are essential to being human and this is what Morris attacks.
Morris makes a difference between nearly universal properties and essential properties. Nearly universal property is one that almost every member of a kind possesses, but isn’t necessary for that thing. Case in point: having white feathers was a nearly universal property of swans, but it wasn’t essential to being a swan. Being limited in power, limited in knowledge, limited in goodness, etc. are nearly universal properties: Christians believe there is one human being in history who was human but lacked the property of being limited in power, limited in knowledge, limited in goodness, etc. Jesus of Nazareth.
Impact
To Christians, this category goes without explanation. But let’s try anyway…
As purposed by God, the eternal Son of God (Isa 9:6; John 1:1-2; 8:58; Col 1:17; Heb 1:10-12; Rev 1:8; 21:6) came into this world that He might manifest God to men, fulfill prophecy, and become the Redeemer of a lost world. To this end He was born of the virgin, and received a human body and a sinless human nature (Luke 1:30-35; John 1:18; 3:16; Heb 4:15). He was completely, 100% deity (John 1:1, 18; 10:30-33; 20:28; Rom 1:3-4; 9:5; 1 Cor 15:45-49; Phil 2:6-8; Titus 2:13; Pet 1:1). He was also completely, 100% human (Matt 13:55; John 1:14, 19:5; 1 Tim 2:5; Heb 2:14).
Jesus Christ was incarnate. The eternal second person of the Godhead entered space and time and became man for us and for our salvation (John 1:1, 14; 2 Cor 8:9; Phil 2:6-8; 1 Tim 3:16). He was miraculously born of a Virgin and the Holy Spirit (Matt 1:18-25; Luke 1:26-38). He led a sinless life (2 Cor 5:21; 1 Pet 2:22; 1 John 3:5) of perfect obedience to the Father (John 6:38; Rom 5:18-19; Phil 2:8). He spent His life preaching, teaching and performing miraculous wonders to evidence His divine mission and to proclaim the new advent of God’s kingdom (Matt 4:23-24; 7:28-29; 9:35-36; John 20:30-31). In the fulfillment of prophecy, He came first to Israel as her Messiah-King, was rejected of that nation (John 1:11; Acts 2:22-24), and gave His life as a ransom for all (1 Tim 2:6).
Jesus Christ was crucified as a substitutionary atonement for sin. On the cross in Christ, God bore the just penalty for the world’s sin, satisfied His justice, and thus made a way for reconciliation (Isa 53:4-12; John 3:15-17; Rom 3:21-26; 5:6-11; Heb 2:14-17). It was necessary for Him to be both true God and true man in order to redeem (1 Tim 2:5). As man, He represent us (Heb 4:15) and as God He saves us (Heb 7:24-25).
Belief in the divinity of Christ is a prerequisite of salvation (Rom 10:9; 2 Peter 1:3) and to deny His humanity is to be labeled the antichrist (2 John 7).
Retrospective Recognition
Gospel writers quote the Old Testament to show how Jesus in his life and ministry fulfilled the Old Testament Scriptures (Mat 21:4-9; Mar 11:7-10; Luk 19:35-38; Joh 12:12-15). Matthew includes nine additional proof texts (1:22-23; 2:15, 17-18, 23; 4:14-16; 8:17; 12:17-21; 13:35; 27:9-10) to drive home his basic theme: Jesus is the fulfillment of the Old Testament predictions of the Messiah.
Jesus himself makes this clear:
Beginning with Moses and with all the prophets, (Jesus) explained to them the things concerning Himself in all the Scriptures (Luke 24:27).
All the Scriptures center about the Lord Jesus Christ in His person and work in His first and second coming, and hence no portion, even of the Old Testament, is properly read, or understood, until it leads to Him.
If you are a regular visitor to the blog, then you know that I have been intermittently posting items on the relationship of process theology and a Christian philosophy of mathematics. Well I am presently at the ACMS (Association of Christians in the Mathematical Sciences) Conference at Westmont College where tomorrow I will be presenting the paper from which these blog posts derive.
For the benefit of giving the live audience a point of reference (and I suppose also for the benefit of the reader at home) I wanted to post the paper here in its entirety:
If you would like to read the entries in a more un-academified blog form, here you go (though I have not gotten around to posting the conclusions yet… you’ll have to read the paper for those):
While here at the ACMS conference I hope to blog regularly about different talks and conversations. Both for myself, as a way of working through the wealth of material I’m receiving, and for those readers at home (there I go being so thoughtful again) who might not have been able to attend the conference.
GOD & MATH: Thinking Christianly About Math Education 