Why we need a theology of climate change in the 21st century

I co-authored this article with Katrina Baldacchino. It will be published in the February/March 2019 edition of the Anglican Diocese of Newcastle’s magazine, Encounter, issues of which are hosted at Issuu.

Alex Grey GAIA 1989, 144 x 96 in. oil on linen.

“The heavens declare the glory of God, and the sky above proclaims his handiwork” (Ps 19:1)

At God’s Word, the universe exploded into being and all that exists was lovingly formed and illumined. Life was drawn forth to fill everypatch of land, every breath of air, every drop of ocean. Earth is intrinsically valuable to God. “God saw everything he had made, and indeed it was very good”(Gen 1:31). Take a moment to look heavenward, and stand in awe at the vast and intricate ways in which the natural universe works. God is constantly creating, fine-tuning Earth’s ecosystems, and endowing each living thing with dignity and purpose; drawing all into communion with Himself.

God has entrusted the sacred work of caring for His garden to us. We in the 21st century are struggling to fulfil our inherited responsibility. We have become starkly aware of our unintended power to change the Earth’s climate. We could easily push our world off-track. Perhaps we already have. So we might ask ourselves how we intend to respond to this power, in light of our ever-present responsibility to God.

It is often said that the future of the church, of our society, and of our world, rests on the shoulders of children. It is true thatchildren will inherit the world we leave them, yet they also participate inthat responsibility here and now. If a child asked you today what it means tofollow Jesus, what might you say? What could we say, knowing that we are calledin this era to follow Jesus through potential climatic upheaval, brought aboutby the hands of humankind? What example might we set our children to guide themin an ecologically uncertain future while honouring the great work of God?

To honour God is to ensure the ongoing flourishing of the earth and all that live on it. In his renowned encyclical Laudato Si, PopeFrancis reminds us that “The earth was here before us and it has been given to us. … Each community can take from the bounty of the earth whatever it needs for subsistence, but it also has the duty to protect the earth and to ensure its fruitfulness for coming generations.” Our ability to carry out our duty requires that we experience our interdependence with and reliance on nature. We cannot separate ourselves from the world created for us. Indeed, God becomingincarnate as a biological and sensate being emphasises the significance of thenatural. God, as a man, was reliant on the very world whose existence issimultaneously sustained by God!

The fruits of following Christ extend outwards from the continual renewing of the individual soul, to participation in the cultural, political and environmental context in which we live. As Mick Pope, an Australian ecotheologian, has written; “personal righteousness and public justice are on the same continuum…” The fulfilment of justice requires a spiritof ecological conversion; a turning away from the technologically saturated,consumer driven, chaotic and traumatised world, and towards a renewedexperience of the simplicity of God, seen through Creation.

Jesus, who is God, and is a revelation of God’s love for theworld, asked us to love one another. “By this everyone will know you are my disciples, if you have love for one another” (Jn 13:35). In the 21stcentury, to love our neighbour means that we love the planet that sustains us,taking only what we need for life and worship. Followers of Jesus ought to be recognised for their love of the natural world, while they joyfully await the perfection of the world through Christ.

Our desires have had unintended consequences for the climate and the world’s ecosystems. What might we say to our children as they ask about climate change and Christian faith? Changing the course of human desire is difficult, but only if we rely on ourselves. Jesus continually offers us the means. As we share in communion regularly, we develop humility and experience God with us. We are reminded that God is present in the living world and in us.We need reminding. We need a theology that can heal the world. As Pope Francissays “Everything is interconnected, and this invites us to develop aspirituality of that global solidarity which flows from the mystery of theTrinity”. We need then to stop, close the books, and allow our children to leadus in looking heavenward, with all of their hope, enthusiasm, and life.

The Visitation

Below is the text of my second homily, given for the Fourth Sunday in Advent.

The Visitation – Jerónimo Ezquerra (1660 – 1733)

THE FOURTH SUNDAY IN ADVENT – YEAR C

Hebrews 10:5-10 & Luke 1:26-38

Christmas is not yet here, and so on this fourth Sunday in Advent, we still have time to prepare our hearts as we wait to recognise the coming of our Lord in the birth of Jesus Christ, son of Mary, and son of the Most High.

Let’s reflect on the gift that we are about to receive and how we might prepare to receive Him.

Giving a gift is an act of love. In giving a gift, weseparate something from our self for the good of another. We make a loving sacrifice. When we are presented with a gift, we are presented with an invitation: an invitation to respond with thanksgiving. We are invited to enter more fully into the promise of a relationship that a gift offers, and this requires that we orient ourselves towards the other, not only in our attitude, but in our action.

Now, try to remember the best gift you’ve ever received. It might have been for your birthday, or Christmas, whatever the occasion, remember that gift. Think about what it felt like as you unwrapped it. Did you carefully peelaway the wrapping, or did you tear it open in excitement? What happened inside you when you saw it for the first time? What did you feel? Were your surprised? Did you laugh? Did you cry? Did you stare at it in wonder?

A carefully chosen gift matches the precise character and needs of the person receiving it. A well-chosen gift makes us feel loved, makes us feel seen for who we are.

The reading from the Letter to the Hebrews has Jesus referencing the burnt offerings and sin offerings that were required according to the Law of Moses, he then adds “See, God, I have come to do your will.”

It is written that Jesus abolishes the first in order to establish the second, and yet Jesus said he has not come to abolish the Law, but to fulfil it, and so he does. The coming of Jesus Christ and His victorious work on the cross is the great Yes to all the promises made to Israel.

He is the gift from God that perfectly meets the character and needs of the people of Israel.

For us Christians not to understand the temple, the prophets, the covenant and the Law is not to understand the person of Jesus Christ. All these things bring God and humankind together. They exist to align the will of God’s people with the will of God. At the heart of Christianity, we have the perfection of this alignment in one man, the perfect union of human and Divine, the perfection that Israel had so longed, waited, and hoped for.

And so we also wait, and we prepare.

For the first half of Advent, the readings have focussed our hearts and minds on the second coming of Christ, but in these last two weeks, our focus shifts to his first coming, and on this final Sunday, now so close to Christmas, the Gospel readings hone in on the pregnant mother of our Lord.

We pick up the story just after the Angel Gabriel has announced to Mary that she will bear a son. Mary has responded with her great Yes to God’s promise.

In saying Yes, she has offered herself as the new ark of the covenant, the ark that will hold and keep safe the Word of God until he enters the world at Christmas. She offers her motherly lap as the throne on which the infant Christ will sit. But what does she do then? What should we do once we trust in God’s promises? Mary gives us the model to follow.

The reading starts: ‘Mary set out and went with haste”. Her faithful response to God is followed by action. She sets out. Her faith is not idle. She has been given a promise by God, and in that promise, she finds purpose, which she runs to share in communion with another.

When she entered the house of Zechariah, she greeted Elizabeth. This greeting is an echo of the greeting Mary received from theAngel Gabriel. Mary comes to Elizabeth bearing good news of the gift of Salvation. Mary comes bearing a gift from God.

Upon receiving Mary’s greeting, Elizabeth is filled with the Holy Spirit, the Essence of God that is given by the Father, received by the Son, and poured out on the disciples at Pentecost in the self-giving love of the Trinity.

Elizabeth says to Mary “Blessed is she who believed”. But how is she blessed? Blessed here means a joy which is serene and untouchable. It is disconnected from the distractions and trappings of the world, the constant temptation to look away from God.

It is a blessedness which is grounded in faith and in the promises of God, and so cannot be touched, and yet it is a blessedness that would come to pierce the Blessed Mother’s heart as she watched her son die on the cross.

Upon receiving Mary’s greeting, her child leapt in her womb. John the Baptist recognises Christ and rejoices. Even in the womb, John recognised his Lord – such was his purpose.

We know that John will soon call us to repentance and baptism in preparation for the coming of the Messiah. John calls us to repent in order that we too might recognise Christ. So how can we hope to recognise our Lord if we are not facing Him? The first step in preparing to receive the gift of Salvation made present at Christmas, is to confess our sins and turn to Christ.

Is it possible for anyone to know you better than you know yourself? It is a difficult thing to believe, and we easily slip back into thinking that we know what is best for ourselves, and that we must prove ourselves worthy. When we live this way, are we living in the Grace of God? TheGrace of God is not that he has graciously provided some means for us to earn our way into Heaven: that is pride. No, the gates of the Kingdom are already open to all, and yet we all suffer from the blindness of pride. We all think we know ourselves, our desires and our needs better than anyone else, including God. If we think we have nothing to confess, we may well be mistaken. All are called to repentance.

In these last days of Advent, can I encourage you to examine your conscience? Would it help you to prayerfully review your thoughts, words, and deeds at the end of the day? If we can build up a habit of confessing our sins to one another, continually turning to Christ, we might better prepare ourselves to respond to the invitation of God’s love this Christmas.

Left on our own, our natural tendency is to drift along the wide road, away from God. The good news that Mary shares with Elizabeth is that we have not been left alone. We have been called to enter the narrow gate. We will each be given an invitation this Christmas. Will we respond with our lives?

God, in his infinite love, graces us with his eternal presence in a way that precisely meets each of us in our particular character and needs. Christianity is truly catholic, truly universal, the perfect gift given by God to all the people of the world. God knows the desires of your heart, but more than that he sees and shares in your need, and in your suffering, and he offers you Himself.

My heart turns to those who will join us for Christmas, those who have not been here in a while, and those who we might not see again for some time. I ask you to pray about how you might embrace them. I pray that something might stir in them during our Christmas celebrations, that they might hear the call and the beauty of the life of the church, its seasons, and its loving people. I pray that we too might even today as we share communion together, know that we are receiving the perfect gift, the gift that Mary bears for us: God Himself.

The Lord be with you.

Netflix on 2+ screens using a single screen account

Netflix mobile downloadThe Netflix mobile app provides the option of downloading (select) titles. This effectively means your family can watch Netflix on 2 or more screens using only a 1 screen account. Just download the shows onto your device(s), then turn off your data and watch them while someone else watches a what they want via streaming. Cheap and simple!

Learning the Virtues – Romano Guardini

An excellent book. Guardini expounds the intricacies of each virtue firstly as commonly understood, then in their subtlety as illuminated by grace, and finally the manner in which they emmanate from the character of God.
Full of wisdom leading towards personal responsibility and Godly depth of character, ‘Learning the Virtues’ awakens a longing for one’s own potential; not as a possession of the individual, but as a gift from God, which we each must cultivate.

The Annunciation

Below is the text of my first homily, given for the Fourth Sunday in Advent.

Annunciation – Caravaggio – 1608

THE FOURTH SUNDAY IN ADVENT – YEAR B

Luke 1:26-38 – The Annunciation

‘In an age of speed, nothing could be more invigorating than going slowly. In an age of distraction, nothing can feel more luxurious than paying attention, and in an age of constant movement, nothing is more urgent than sitting still.’ – Pico Iyer (adapted)

Like most people, I used to think that life was about finding happiness. “We don’t mind what you do, son,” my parents would tell me, “as long as you are happy.” At that time I was actively seeking, and happiness was near the top of my list.

At one point, I accidentally stumbled on a secret piece of advice that I have forgotten many times, but try to remind myself of whenever I can. It is this: “I don’t care about happiness!” Now that might sound crazy, but when I honestly said that to myself for the first time what I was actually doing was letting go of the pursuit. It was then that I recognised that what I was seeking was already there, present within me. So it is with God.

Advent is the season of the exalted secret. Within the darkness and hiddenness of the womb is where all the excitement is going on.

In today’s reading, the Annunciation to Mary, the angel announces that God is reaching out to the world. God is extending His divine love into and through the barriers of arrogance, through our enviousness, desperation, and grief; through our possessiveness and confusion.

God has announced his intention to re-form His covenant with humanity, through the humility and faithfulness of this one young woman. This is not the beginning of the story, but it is a beginning; a beginning woven within Mary and her response to God’s call on her life. Today, the angel Gabriel announces news of the imminent beginnings of God’s Kingdom on Earth.

Great as this news is, notice that it is not announced in triumphant fanfare for all to hear. It is whispered, in private, by an angel of God.

‘Hail Mary, full of grace, the Lord is with thee!’

We hear that Mary was perplexed at the way that she was greeted, and the angel said to her “Do not be afraid.” God’s call on our life can be frightening, it can be unsettling and we, in our confusion and need for control so often turn away, back to the patterns of behaviour so ingrained in us over so many years: Our familiar and misguided ways of being.

‘Behold the Handmaid of the Lord. Be it done unto me according to thy word’.

Mary’s response to God’s call on her life has been held up to us by the church as a model to follow in our own responses. One that is full of grace, and favoured by God. Through her example, we are led to a life of devotion, to God and to our neighbours who we are called to love.

The ‘Yes’ that Mary offered was not “Yes, I will do this”, but “Yes, I will gently move aside and allow this to happen in and through me.”

Through humbling herself, Mary was exalted. Mary became for us the living temple through which God humbly entered His own creation.

Christmas is a time of renewal. Our Hope is in God made flesh, and our faith is in humbly turning away from ourselves to pay attention to God whispering in our lives.

The humility of Mary is in the recognition of herself as the one who will never stand against the radiant love of God, for there can be no bounds to the infinity of His love. She lifted herself up to God as the one through whom this divine love was to be poured into Creation in the person of Jesus Christ.

We are all called to be Mary, we are all called to say Yes to God in this way, giving our consent to the presence of God in our lives, and allowing Christ to be born into the world through us.

To follow Christ is to sell all that we have, a message the world is loath to hear, particularly at Christmas. We must empty ourselves so that God may work through us. Our life of following in the Way of the Cross is a life of continual conversion, the daily renewal of your decision, with Mary, to say Yes to God.

At Christmas, we will celebrate and remember the gift God gave us in love: Himself. Today, still in Advent, we celebrate and remember the gift Mary gave God: His humanity.

The gifts that we give at Christmas, as beautiful and thoughtful as they are, will ultimately degrade, break or become lost. They are merely symbolic of the true gifts that we give: the gift of love we are called to have for one another.

Now, of course, I’m sure you’ll immediately think of a few people in your life you find pretty difficult to love. And that’s ok. All you need to do is to say to God, ‘Look, I find myself unable to love this person, but Lord you love them. Please love them through me.’

If there is only one message of the Gospel, it is the message of the love of God. And if there is only one characteristic by which the world recognises us as Christians, it is how we love each other and those we meet along the way.

God chose to enter the world as a man, and Mary gave her assent, choosing to fully participate in the incarnation of the Lord. Christ is not forceful. Christ is gentle. He asks our permission to enter our lives, and through us, to enter the world. Once we give that permission, a seed is planted and our lives slowly grow into the shape of the life of Jesus of Nazareth.

As we draw closer to the Eucharist this morning, let us lift up our hearts as a chalice to the Lord. Let us allow Christ to fill us with His grace. Let us be vulnerable in faith before God and let the knowledge of the imminent birth of our Saviour, Jesus Christ allow us to love one another in humility.

May we each become bearers of Christ this Christmas, living by the beauty of Mary’s example. Let us say Yes to God and allow Jesus, the Living Word to be born into the world through us.

 The Lord be with you.

Paint a Nativity play backdrop

2017 Nativity Play backdrop

To make this Nativity backdrop, I used a queen-sized, navy blue sheet as the canvas. I chose this colour so that I wouldn’t have to paint the entire sheet and still have a beautiful colour for the silent night sky.

First, wash and dry the sheet. It’s probably also best to iron it, although I didn’t go that far.

To start your design, find an image that you like that you can appropriate. I chose a Nativity icon I found here.

It’s best to sketch out your design in a rectangle with the same proportions as the sheet you’ll be painting on. Divide the drawing with a grid so that it’s easier to upscale your design onto the sheet.

Nativity design sketch (my son decided to help)

When you’re ready, stretch your sheet out on the floor and pin the corners down. I used tables as they were heavy enough and available.

Stretched sheet

Using chalk, mark out the grid intervals on the edges of the sheet, but don’t draw lines across the sheet.

Use a tape measure in place of a grid line if you want to measure the relative position of an element.

Draw out your scene in chalk.

Once you have your scene sketched, start painting. Start with white paint in any areas you wish to be bright (like the stars). I thought I would need to do this under the leaves etc as well, but as I ran out of good quality white paint, and the paint the Sunday school had was watery, I had to go with straight colour, which came out quite nicely anyway.

Don’t be afraid to mix colours and see what works. If you need some advice on painting, check out Mural Joe on Youtube.

2017 Nativity Play backdrop

An Unfamiliar Love

It can be hard to love our family. Our family hold insight into our lives that is often hidden from our friends and enemies. When familial ties are damaged or under strain, we instinctively feel vulnerable. Christmas gatherings can be a time of submerged confrontation. For the sake of our children and ageing parents, we play nicely so as to avoid the hurt and embarrassment of arguments around the table.

This may not be descriptive of your Christmas, and I hope it is not, but for some, it will be. Like any other time of year, this can be one of suffering. It can be difficult to remember the joy of Christmas.

In forming His human body, God the Son glorified Himself and began the process of clarifying and perfecting Creation. The whole of humanity, and indeed all life on Earth, is one family. All life shares the same basic molecular structures that allow our cells to replicate and function. As a human being grows in its mother’s womb, the cells that comprise the webbing of its paddling hands and feet are programmed to die, so that fingers and toes capable of dexterity and control can form.

At least at this level, death seems inherent and necessary for the formation of life. We can only assume that in the fullness of His humanity, it was in this way that Jesus Christ, like us, came into the world. It is through death that new life arises. The Divine Invasion at Christmas was, and is, the explosion of hope and life into a muddied and dying world.

This Christmas, as you sit at the other end of the table from whomever it is in your life that has done you wrong, consider their suffering and their need for kindness. Consider the difficulty we all have in bearing the weight of our own lives. Consider His words about those that crucified Him: “Father, Forgive them; for they know not what they do.”

Without the love of Christ, the experience of cruelty can drive us to view the world as fundamentally meaningless and deeply scornful. A desire to subjugate the world to the will of the individual is both a cause and symptom of suffering. Loving those who have hurt us means choosing to peer through the veil of cruelty to see the suffering hiding there.

Through the kind eyes of the newborn Christ, we can see afresh those who inflict harm. It is they who are most desperately in need of the tenderness and unfamiliar love of God.

May you bear His gentleness in your actions,

May He bless your family through you, and

May you live in the joy of Christmas.

A Critical Evaluation of Hume’s Argument Against Induction

1. Introduction

This paper explains the Problem of Induction (the Problem) as it was set up by Hume (Hume, 1989) and will briefly discuss the major groupings of attempts made to refute such; including a particular emphasis on the attempt to dissolve the Problem. To conclude, the author will lay out an independent theory of induction constructed while considering the topic. The ‘Category-Property Theory of Induction’ (C-P Theory), as it is to be called, will be based on an analysis of induction that uses categories and property sets, and is perceived to provide a potential new direction from which to approach a possible resolution to the Problem.

For the purposes of constraining the topic to something manageable within the word limit, this essay will be limited to discussing enumerative induction, or universal inference. That is, inference from a sample to a general hypothesis. It should be noted that contemporary notions of induction extend beyond this; see Carnap’s (1962) taxonomy of induction.

Note also that in this paper, the term ‘object’ is used to refer to any observable component of the universe, irrespective of whether such an object is usually referred to in English by a noun or a verb.

 

2. Hume on Induction

Induction appears to be critical to everyday actions and choices. Common sense would imply that because the sun has come up every day of our lives thus far and for all of recorded history, it is reasonable to act as if it will do so again tomorrow. Please note the implicit distinction between ‘believe’ and ‘act as if’.

Hume did not use the term ‘induction’. He instead wrote of causal inferences (Vickers, 2016); the process contemporarily called universal inference (Carnap, 1962). Hume was interested in the “habit of the mind”, that we might refer to as behavioural conditioning, that begins with the fact that all past As have been Bs, and leading to an action consistent with the assumption that the next A will also be a B. I phrase the question in this particular manner so as to emphasise what Hume reasoned to be a biological / neurological basis for the prevalence of inductive experience in daily life and in scientific endeavour. That is, he reasoned that causal inferences must be a product of the imagination in some sense, and not of reason.

As regards the proposition that the problem of induction shows that there can be no claim to absolute knowledge (Barseghyan, 2015), the author claims that while correct, it is not because induction is not rationally justifiable. There can be no (verifiable) claim to absolute knowledge because in reality there are no absolute facts. Facts themselves are contingent; they are features which are stable and observable across a period of time, within a particular context. That is, one could say that properties of an object are dependent on their space-time coordinates. Induction is not justifiable when taken across the ‘infinity’ of time as ultimately all linguistic categories will break down at this scale.

The formal sense in which inductive logic is usually written is as follows:

1) All observed As have been Bs

2) O is an A; where O is an as yet unobserved object

Therefore, O is a B

The Problem as postulated by Hume (1989) and summarised by Salmon (1967) is a dilemma with deductive and inductive parts. Firstly, it is clear that inductive logic cannot be rationally justified via deduction as the conclusion does not follow necessarily from the premises because of its future predictive element. Secondly, we are unable to use induction to justify induction, as this is begging the question.

 

3. Attempts to resolve the Problem

There have been many attempts to show that induction is, in fact, rational, however many of these can be reduced to a case of using induction to justify induction.

None of the attempts at rationalising induction have been successful in my view, and instead of spending time summarising them here, I will move on to what I consider more interesting approaches which seek to dissolve the problem.

Those who seek to dissolve the problem attempt to offer a third solution to the dilemma: showing that the Problem is erroneous in its construction. This is usually aimed at by demonstrating the existence of a flaw in one of the few assumptions underlying the Problem. One of the main thrusts of dissolution attempts has been to show that the Problem (“Is induction rationally justifiable?”) is ill-formed. It is said to be an absurd formulation; as it is claimed, rationality assumes the use of induction (Skyrms, 1966). That is to say, the Problem of Induction is a kind of tautology; equivalent to asking “Is the Pope a Catholic?”

I believe that there is merit to this line of argument and I will come back to this topic of whether induction is a precondition of what is classified as rationality when I discuss the C-P Theory. In the interim, let us turn to a particular attempt to dissolve the Problem as an example of the direction these particular arguments can go in.

The Problem of Induction lies, in part, with how the conclusion of some inductive inference is interpreted. Induction necessarily includes projection into the future, however, this projection is not to be understood as a claim to knowledge, but a hypothesis which will either be shown to be true or false given further observations.

John D. Norton has presented both a Material Theory of Induction (Norton, 2003) and a Material Solution to the Problem of Induction (Norton, 2009). He begins by identifying an assumption of the Problem, which is that inductive inference is subject to universal rules and claims that without this assumption, the Problem cannot be laid out. In his Material Theory, he demonstrates that inductive inferences are “warranted by facts”. Norton notes that facts are contingent and not themselves logical truths. This, in turn, implies that there are no universal supports for any inductive inference and that each inductive system is applicable exclusively in the domain where the supporting facts are true.

Under Norton’s Material Theory of Induction, the Problem as classically set up by Hume collapses to the problem of justifying facts. The answer to the resultant question “What justifies a warranting fact?” is, according to Norton, the exploration back through the interconnected sets of scientific knowledge and back through the history of this knowledge towards the origins of belief. It should be clear that one doesn’t have to move far back into biological (and geological) history when tracing these ideas before we are dealing with the beliefs and perceptions of creatures vastly unlike modern man, and yet eerily familiar in their neuro-anatomy and now we have moved quickly out of the realm of philosophy.

The justification of facts, Norton points out, will also be based on some inductive processes, which in turn will be based on more facts; and so we launch into a multidirectional regress. Rather than appearing as petitio principii, Norton argues that this is a demonstration of the “inductive solidity of science”; the notion that science is a nested and interlocking set of facts and inductive processes with give to each other strength and integrity, like stone blocks in an arch.

4. The Category–Property Theory of Induction

In presenting this (new) theory of induction, the author does not mean to imply that he believes a complete refutation of Hume’s argument will follow. However, it is perceived that the theory presented will go some way in furthering the discussion.

C-P Theory begins with the entirely reasonable assumption that categorisation is the basis of cognition. The potentially infinite amount of sensory information confronting a conscious being needs to be filtered if it is to be processed and a decision to act made as a result. This is the reason for the emphasis of ‘act as if’ over and above ‘believe’ in the opening paragraph of section 3: the driving force is the need to act toward a specific aim. It is beneficial for the success of an organism if the system of categories that are inferred from observations of the world are congruent with reality. Induction, under this view, is the formalisation of the characteristic processes of all conscious human persons. That is, they use neurological structures to map their environment (including its components), themselves, and the relation between the two.

Take for example the inductive argument that every emerald observed has been green. Therefore the next emerald to be observed will also be green. Say that among your prior observations you observed an emerald that was blue. Would you acknowledge this object entry into the category ‘emerald’. I would argue that you would not, as ‘green’ is a part of the pervading definition of emerald. It would be classified as something else, or the category of emerald would need expansion to include these new blue emeralds. It is the claim of the C-P Theory that induction is actually a taxonomic process which forms the substrate of conscious thought. Rationality then is built on top of induction, as those who have attempted to dissolve the Problem have argued.

4.1 Formulating the Theory

The C-P Theory can be formulated as follows. All As are Bs is equivalent to saying that all objects categorised as A have the properties of objects categorised as B. This is equivalent to saying that there is sufficient overlap between property sets such that they can be considered to be within the same category. Or, that all things categorised as A have a particular property bi which is a property of Bs.

More formally, the definition of a category X is the set of properties {x1, x2, … , xn}. If, when observing an object, any one of the properties is not observed, the object cannot be admitted to membership of the category X without modification to the category. The inductive conclusion usually formulated all As are B, is then actually a definitional statement that all As have the property (of being) B, irrespective of whether B itself is a category of objects or a property. If the proposition is all Xs are xi, then any observation that does not have the property x­i is categorically not-X.

Let us apply C-P Theory to the classic example of swans. All past swans have been white; therefore the next swan observed will also be white (and similarly, all swans are white). Under C-P Theory, ‘white’ is one property in the property set that defines the category ‘swan’.

The category of swan (S) describes objects with the property set {s1, s2, … , ‘white’, … , sn}. There is, therefore, at this point, by definition, no such thing as a black swan. The inductive inference that ‘All swans are white’ is true by definition. It is a taxonomic question.

Now suppose you observe an object with the property set {s1, s2, … , ‘black’, … , sn}. You then have to make a decision. Either, you create a new category ‘black swan’ (Sblack), or you alter the property set that defines swan (S) such that this new object may be admitted. Now given that there is sufficient overlap in the property sets defining S and Sblack, the original category S is renamed ‘white swan’ (Swhite) and the property set defining ‘swan’ (S) is modified to { s1, s2, … , (‘white V ‘black’), … , sn}. That is, the property ‘white’ is replaced by the property ‘white OR black’.

Note that C-P Theory handles the Grue paradox. One common misconception because of the time component in the definition of the word grue, is that after time t, all things which are green prior to time t will change to being blue thereafter. This is not the case. The grue paradox is resolved, I claim, by the understanding of an expansion in the property set of the category in question as outlined above. That is, the category ‘emerald’ (E), originally defined by the property set {e1, e2, … , green, … , en}, is subsumed by the category ‘Grue emerald’, which in turn is defined by the property set {e1, e2, … , grue, … , en}, where grue is understood to contain a time component. At most, the grue paradox demonstrates that induction is context and language (read category) dependent, an assumption of C-P Theory.

The corresponding grue-like term with regard to the case of swans is ‘whack’ (White-black): that is, white up to time t, then white or black thereafter.

4.2 The C-P Theory and Karl Popper

Let’s say that your category ‘swan’ has thus far stood the test of repeated observations. In the Popperian sense, it is the accepted hypothesis. It has not yet been falsified but is indeed falsifiable. We have to consider what would be a falsification of the definition of swan.

One such falsification could take the form of an observation of an object that has all of the properties (and only the properties) of an object that would regularly be granted membership in the class ‘swan’ except that it does not have the property of being white. It is instead black. The question then arises, has induction failed? Well, no, not if we adjust the category of ‘swan’ to include things that are swans in every way except for the fact that they are black instead of white; or if we define a new category to encompass these new observations. Either way, induction is the process by which categories are continually realigned with reality as it is observed.

‘Scientific induction’ is the formalisation of the process by which we explore and learn about the world systematically. In this sense, even Popper cannot escape induction, for all (falsifiable) hypotheses are themselves the conclusions of some inductive process, which are tested by observation. They are the result of someone making observations about the world (or the current state of scientific literature) and inferring some generalisation (in fact they are forming a category) which they then set about testing.

5. Conclusion

Is induction rationally justifiable? The C-P Theory suggests that the question is unfounded. The question is better formulated: “Does induction lead to rational behaviour?” Even when induction ‘fails’ to make a correct prediction, it has succeeded in its purpose. That purpose being to bring into line the mental categories one uses to navigate the world, with reality itself. If induction provided no negative feedback, it would surely lead to irrational action, as it would allow categories to become misaligned with reality. In that sense, induction is not in itself rational, but nor is it irrational. Induction provides the cognitive basis for rationality (expressed as action in line with categories of objects, that are themselves in line with reality).

 

References

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