This is another letter I wrote to New Scientist - in response to an essay by Helen Phillips entitled, Is God good? She discusses various studies done by academics examining the effects of religion on people's behaviour and ethics. The general consensus seemed to divide people between 'extrinsic' (those who are overtly religious and belong to religious organisations) and 'intrinsic' (those whose religious beliefs are more personal and less overt). It was found that the 'extrinsic' tended to have an 'in group' mentality, though it must be emphasised this is a broad generalisation, that made them less tolerant of people of 'other' religious persuasions, whereas the 'intrinsic' were more tolerant of 'others'.
This is a brief synopsis - she also discussed the evolutionary (social) value that may have been inherent in forming religious beliefs, as well as how we may have come to believe in a God or Gods as external supernatural beings. There was also a consensus that, while morality seems to be inherent in humans, it is not dependent on religiosity per se.
As a side issue, Karen Armstrong in The History of God, puts forward a thesis that our idea of God changes over history. In other words, God seems to exist, at least in our writings, in a historical context. But I would reference Augustine who seemed to appreciate that God was part of our 'inner journey' as much as something external. Or to quote 19th century German philosopher, Ludwig Feuerbach: God does not exist independently of humanity.
Reference: New Scientist, 1 September 2007, pp32-6
When I was a young child, my father, who had spent 2.5 years as a POW, told me something I’ve never forgotten. He said: there are 2 types of Christians. There are Christians who go to church every week and wear their religion on their sleeve. Then there are Christians who don’t claim to be Christians yet they behave like Christians. In my now 56 years of living I’ve never seen anything to contradict that statement.
More relevant to Phillips’ topic, there are 2 types of religion: institutional religion that is political in every sense of the word; and religion as a personal experience, that is part of life’s journey, either as a unique, possibly one-off experience, or as an evolvement of one’s spirituality. I believe this is the distinction between ‘extrinsic’ and ‘intrinsic’ religion that is discussed by Phillips.
In the case of intrinsic or ‘quest’ religion, it is experienced as something ‘beyond’ the self. We can’t even explain how consciousness emerges from the neuron activity of our brain, so how can we explain a sense of ‘supra-consciousness’, and why should it be dismissed simply because it is no more explicable than ordinary consciousness? After all, they are both an experience as opposed to an objective observable phenomenon.
Saturday 8 September 2007
Sunday 2 September 2007
Where does mathematics come from?
This is a more serious philosophical discourse than other theses, or mini-theses, I’ve posted so far. It’s an argument I’ve had with a number of philosophers, and non-philosophers. It's a question that most philosophers, indeed most people, seem to have an opinion on.
The short answer is that it’s a mixture of both invention and discovery. Mathematics requires creativity to achieve breakthrough discoveries as does any field of science. But I’m short-circuiting the argument. A good starting point is to reference a book I’ve read, Where Mathematics Comes From, by George Lakoff and Rafael E. Nunez. This is an excellent book on mathematics, covering all the basics and a number of esoteric topics like calculus, transfinite numbers and Euler’s famous equation: eiΠ + 1 = 0. This equation brings together such diverse fields as trigonometry, logarithms, calculus, complex algebra and power series into one simple relationship. The physicist, Richard Feynman, who discovered the equation a month before his 15th birthday, called it ‘the most remarkable formula in math’. Lakoff and Nunez provide a very accessible derivation of this equation as the crowning piece of exposition in their book. I must say at the outset that I have neither the expertise nor the ability to write a book like this. It is a very good book on mathematics. All my arguments and contentions deal with its philosophical content.
Lakoff and Nunez eschew any notion that mathematics is ‘discovered’, which is not an uncommon position. They argue, reasonably enough, that mathematics can only come from an ‘embodied mind’, therefore any suggestion that mathematics ‘already exists a priori’ is a conundrum that defies rational explanation. They argue that the only mathematics we know of comes from the human mind, therefore the onus of proof for any alternative view rests with the proponent of that view. In other words, the default point of view has to be that mathematics only exists as a product of the human mind. There is no evidence to support any other point of view.
Just to address that last point: all scientific discoveries are products of the human mind, nevertheless they exist independently of the human mind as well. The specific problem with giving mathematics the same status is that it doesn’t exist materially independently of the human mind. I will come back to this point later.
But my main problem with Lakoff’s and Nunez’s book is the assertion that all mathematics can be explained by ‘conceptual metaphor’. I’ve since learned that this particular philosophical premise is a brainchild of George Lakoff’s, who has written numerous books explaining the significance of metaphor in human endeavour, including philosophy, science, and, of course, mathematics. George Lakoff is Professor of Linguistics at Berkeley University, and I’ve since had correspondence with him. I’ve come to the conclusion that we agree to disagree, though he never responded to my last correspondence.
Many of my criticisms of Professor Lakoff’s philosophy addressed in this blog (though not all) have been made to him directly. In his book, Philosophy in the Flesh, which he co-wrote with Mark Johnson (not Nunez), Lakoff seems to find fault with every philosopher he’s acquainted with, both living and dead. He does this by employing his own 'philosophy of metaphor' (my terminology, not his) to give the reader his interpretation of their ideas. Much of this posting deals with Lakoff's use of the word metaphor. Its relevance to mathematical epistemology is explained in the next paragraph.
Basically, a conceptual metaphor ‘maps’ from a ‘source domain’ to a ‘target domain’ to use Lakoff’s own nomenclature. In the case of mathematics, the source domain is the grouping of objects, and activities that involve removal or combining elements of groups or complete groups in various ways. The target domain are the concepts inside our heads, which we call numbers, and how we manipulate them to represent events in the real world. Target domains can also be graphical representations like number lines and geometrical figures. This is not a verbatim representation of Lakoff’s and Nunez’s ideas, but my interpretation to ensure brevity of exposition without losing the gist of their philosophical premise. I have no problem with this aspect of their argument. I agree that mathematics is one of the most efficacious mediums we have for bridging the external world with our internal world. I have previously explained that the experiential concept of the external and internal world seems to be the starting point for many of my philosophical discourses. Where I disagree with Lakoff and Nunez is their assertion that this ‘bridge’ is strictly metaphorical.
According to The Oxford Companion to the Mind, metaphor is determined by context. This definition of a metaphor assumes that a word, phrase or term that is used in a metaphorical context must also have a literal context. In the case of Lakoff’s conceptual metaphors, that comprise all of mathematics, the metaphorical and literal contexts appear to be the same. I asked Professor Lakoff: ‘In what context is 2+2=4 metaphorical and in what context is it literal? If I say I want 3 of those, am I talking metaphorically and literally at the same time?’ The impression I got from his book is that mathematics has no literal context, only a metaphorical context. In other words, with ‘conceptual metaphors’, he has created a whole new field of metaphors that are permanently metaphorical. I can see no other interpretation and Lakoff has failed to enlighten me when I challenged him specifically on this. Assuming my interpretation is correct, this begs the question: they are metaphors for what? The obvious answer, going back to the original ideas set out in the ‘source domain’ and the ‘target domain’, is that they are metaphors for reality.
In Philosophy in the Flesh, Lakoff continually talks about metaphor as if it’s the progenitor of all ideas and concepts. He analyses a philosophical idea by reducing it to metaphor then presents it as if the metaphor came first. I will discuss an example that’s relevant to the topic: time and space. Lakoff rightly expounds on how we often use terms associated with distance to talk about time – it’s like we visualise time as distance. In relativity theory, this visualisation is real, due to a peculiar property of light. In ancient cultures and some indigenous cultures, however, the reverse is true: they refer to distance in terms of time. When Eratosthenes calculated the earth’s circumference around 230BC, he measured the distance he traveled from the well in Syene (Aswan) to Alexandria by the number of days he traveled by camel. If this was a metaphor and not literal then his whole enterprise would have failed. As it was, his calculation of the earth’s circumference was out by 15% according to modern measurements (ref: Encyclopaedia Britannica).
Everyone knows that there is a mathematical relationship between distance, time and speed, which is literal and not metaphorical. Now all physicists know that this relationship breaks down at sub-atomic speeds and astronomical distances due to relativity, so how can we say it’s true or literal or real? To add a further spoke in the works, when we have quantum tunneling the relationship ceases to exist altogether. But these anomalies are not resolved by saying that they are all metaphors and not real. They are resolved by finding the correct mathematical relationships that nature follows in these circumstances.
Physicists like Roger Penrose and Paul Davies have written extensively on the remarkable concordance we find between mathematics and the physical world. Lakoff claims that this concordance is purely metaphorical, and by his definition of metaphor (source domain: events in real world; target domain: concepts in our heads) I would agree. Using Lakoff’s own logic, mathematics is a metaphorical representation of the real world, but in this use of the term metaphor there is no distinction between metaphorical language and literal language – metaphor is a direct translation. Lakoff often uses the term metaphor where I would use the word definition. When he defines a concept in terms of other known concepts he calls it a conceptual metaphor or a conceptual blend. Conceptual blend is bringing 2 or more concepts together to form a new concept. Conceptual blend makes sense, but conceptual metaphor doesn’t if there are no distinct literal and metaphorical contexts in which to make it a metaphor. I’ve also argued that where there is a causal relationship between 2 concepts, one is not necessarily, by default, a metaphor for the other. An example of this is periodicity being a direct consequence of rotation; day and night resulting from the earth’s rotation is the best known example. In Where Mathematics Comes From, Lakoff implies that this relationship is metaphorical.
Personally, I call Lakoff’s conceptual metaphors literal metaphors, because if they were literal then my entire argument on this issue would evaporate, which, of course, would be preferable for both of us.
Lakoff also maintains that all theories (in physics at least) are metaphorical, which is not an issue I will pursue here. I did point out to him, however, that some of his metaphorical interpretations (of Einstein’s theories in particular) were incorrect or misleading. I referenced Roger Penrose, who is more knowledgeable on this subject than either of us.
Lakoff argues that physics is effectively mathematical modeling that happens to get very close to what we observe, and there are many who would agree with this interpretation. (Renowned physicist, Stephen Hawking, subscribes to this view.) But many physicists would say that the mathematical concordance we find in nature goes beyond modeling because there are too many cases where the mathematics provides an insight into nature that we didn’t expect to find (for example: Maxwell’s equations giving us the constant speed of light in a vacuum or Dirac’s equation giving us anti-matter). Irrespective of this argument, nature follows mathematical relationships at all observable levels of scale. Lakoff, by the way, argues that there are no ‘laws of nature’, which is another argument, though not altogether irrelevant, that I won’t pursue here.
This has been a lengthy detour, but it brings me back to the point I made about the status of mathematics existing independently of the human mind. Most people struggle with this notion – it’s like believing in God. It evokes the idea of an abstract realm independent of human abstract thought. People call this the Platonic realm after Plato’s fabled realm of perfect ‘forms’. The real world, in which we live, being a shadow of this perfect transcendental world. Roger Penrose calls himself a Platonist (refer The Emperor’s New Mind), mathematically speaking, because he believes the mathematics we discover already exists ‘out there’. Paul Davies eschews the idea of Platonism (refer The Goldilocks Enigma) but in The Mind of God, he devotes a whole chapter to what he calls ‘the mathematical secret’: the way the physical world is ‘shadowed’ by mathematics.
I call myself a Pythagorean because Pythagoras was the first (in Western philosophy at least) who seemed to appreciate that mathematics is an inherent aspect of the natural world, like a latent code waiting for someone like us to decipher it. As our knowledge of physics progresses, this realisation only seems to become more necessary to our comprehension of the universe. I can’t help but feel that Pythagoras had no idea how deep his insight really was. Lakoff calls Pythagoras’s philosophical insight a ‘folk theory’, but it’s a folk theory that launched Western science as we know it, so I would call it a paradigm, and one that has had unparalleled success over a 2,500 year history.
Philosophers, since the time of Russell and Wittgenstein, have mostly argued that mathematics is a sub-branch of logic, but Godel, Turing and Church, have all demonstrated, in various ways, that one cannot create all mathematics from a set of known axioms (Godel’s famous incompleteness theorem). This is one point that Lakoff and I appear to agree upon.
What many people fail to understand, or take into account, is that mathematics is not so much about numbers but the relationship between numbers – just look at how much mathematics is written without numbers. Robyn Arionrhod, who teaches mathematics at Monash University, Melbourne, made a similar point in her book, Einstein’s Heroes (effectively, a well written exposition on Maxwell’s equations). If one looks at mathematics from this perspective, one can see that the relationships cannot be invented – they are discovered. Mathematics is essentially a problem-solving endeavour, and this begs the question: if one is looking for a solution to a puzzle, does the solution already exist before someone finds it, or only after it’s found? Think: Fermat's Last Theorem; solved by Andrew Wiles 357 years after it was proposed. Think: Poincare's Conjecture; proposed 1904 and solved in 2002 by Grigory Perelman (read Donal O'Shea's account). Think: The Reimann Hypothesis; proposed 1859, still unsolved. To answer that question, I suggest, is to answer the philosophical conundrum: is mathematics invented or discovered?
Footnote: I sent a copy of this to Professor Lakoff as soon as I posted it, offering him the right to reply.
For an alternative point of view, read Lakoff’s and Nunez’s book, Where Mathematics Comes From. For a physicist’s perspective, read Penrose’s The Emperor’s New Mind or Davies’ The Mind of God. Arionrhod’s Einstein’s Heroes is a good read that indirectly supports the physicist’s perspective.
See also my later posting, Jan. 08: Is mathematics evidence of a transcendental realm? Amongst other things, I discuss Gregory Chaitin's book, Thinking about Godel and Turing.
The short answer is that it’s a mixture of both invention and discovery. Mathematics requires creativity to achieve breakthrough discoveries as does any field of science. But I’m short-circuiting the argument. A good starting point is to reference a book I’ve read, Where Mathematics Comes From, by George Lakoff and Rafael E. Nunez. This is an excellent book on mathematics, covering all the basics and a number of esoteric topics like calculus, transfinite numbers and Euler’s famous equation: eiΠ + 1 = 0. This equation brings together such diverse fields as trigonometry, logarithms, calculus, complex algebra and power series into one simple relationship. The physicist, Richard Feynman, who discovered the equation a month before his 15th birthday, called it ‘the most remarkable formula in math’. Lakoff and Nunez provide a very accessible derivation of this equation as the crowning piece of exposition in their book. I must say at the outset that I have neither the expertise nor the ability to write a book like this. It is a very good book on mathematics. All my arguments and contentions deal with its philosophical content.
Lakoff and Nunez eschew any notion that mathematics is ‘discovered’, which is not an uncommon position. They argue, reasonably enough, that mathematics can only come from an ‘embodied mind’, therefore any suggestion that mathematics ‘already exists a priori’ is a conundrum that defies rational explanation. They argue that the only mathematics we know of comes from the human mind, therefore the onus of proof for any alternative view rests with the proponent of that view. In other words, the default point of view has to be that mathematics only exists as a product of the human mind. There is no evidence to support any other point of view.
Just to address that last point: all scientific discoveries are products of the human mind, nevertheless they exist independently of the human mind as well. The specific problem with giving mathematics the same status is that it doesn’t exist materially independently of the human mind. I will come back to this point later.
But my main problem with Lakoff’s and Nunez’s book is the assertion that all mathematics can be explained by ‘conceptual metaphor’. I’ve since learned that this particular philosophical premise is a brainchild of George Lakoff’s, who has written numerous books explaining the significance of metaphor in human endeavour, including philosophy, science, and, of course, mathematics. George Lakoff is Professor of Linguistics at Berkeley University, and I’ve since had correspondence with him. I’ve come to the conclusion that we agree to disagree, though he never responded to my last correspondence.
Many of my criticisms of Professor Lakoff’s philosophy addressed in this blog (though not all) have been made to him directly. In his book, Philosophy in the Flesh, which he co-wrote with Mark Johnson (not Nunez), Lakoff seems to find fault with every philosopher he’s acquainted with, both living and dead. He does this by employing his own 'philosophy of metaphor' (my terminology, not his) to give the reader his interpretation of their ideas. Much of this posting deals with Lakoff's use of the word metaphor. Its relevance to mathematical epistemology is explained in the next paragraph.
Basically, a conceptual metaphor ‘maps’ from a ‘source domain’ to a ‘target domain’ to use Lakoff’s own nomenclature. In the case of mathematics, the source domain is the grouping of objects, and activities that involve removal or combining elements of groups or complete groups in various ways. The target domain are the concepts inside our heads, which we call numbers, and how we manipulate them to represent events in the real world. Target domains can also be graphical representations like number lines and geometrical figures. This is not a verbatim representation of Lakoff’s and Nunez’s ideas, but my interpretation to ensure brevity of exposition without losing the gist of their philosophical premise. I have no problem with this aspect of their argument. I agree that mathematics is one of the most efficacious mediums we have for bridging the external world with our internal world. I have previously explained that the experiential concept of the external and internal world seems to be the starting point for many of my philosophical discourses. Where I disagree with Lakoff and Nunez is their assertion that this ‘bridge’ is strictly metaphorical.
According to The Oxford Companion to the Mind, metaphor is determined by context. This definition of a metaphor assumes that a word, phrase or term that is used in a metaphorical context must also have a literal context. In the case of Lakoff’s conceptual metaphors, that comprise all of mathematics, the metaphorical and literal contexts appear to be the same. I asked Professor Lakoff: ‘In what context is 2+2=4 metaphorical and in what context is it literal? If I say I want 3 of those, am I talking metaphorically and literally at the same time?’ The impression I got from his book is that mathematics has no literal context, only a metaphorical context. In other words, with ‘conceptual metaphors’, he has created a whole new field of metaphors that are permanently metaphorical. I can see no other interpretation and Lakoff has failed to enlighten me when I challenged him specifically on this. Assuming my interpretation is correct, this begs the question: they are metaphors for what? The obvious answer, going back to the original ideas set out in the ‘source domain’ and the ‘target domain’, is that they are metaphors for reality.
In Philosophy in the Flesh, Lakoff continually talks about metaphor as if it’s the progenitor of all ideas and concepts. He analyses a philosophical idea by reducing it to metaphor then presents it as if the metaphor came first. I will discuss an example that’s relevant to the topic: time and space. Lakoff rightly expounds on how we often use terms associated with distance to talk about time – it’s like we visualise time as distance. In relativity theory, this visualisation is real, due to a peculiar property of light. In ancient cultures and some indigenous cultures, however, the reverse is true: they refer to distance in terms of time. When Eratosthenes calculated the earth’s circumference around 230BC, he measured the distance he traveled from the well in Syene (Aswan) to Alexandria by the number of days he traveled by camel. If this was a metaphor and not literal then his whole enterprise would have failed. As it was, his calculation of the earth’s circumference was out by 15% according to modern measurements (ref: Encyclopaedia Britannica).
Everyone knows that there is a mathematical relationship between distance, time and speed, which is literal and not metaphorical. Now all physicists know that this relationship breaks down at sub-atomic speeds and astronomical distances due to relativity, so how can we say it’s true or literal or real? To add a further spoke in the works, when we have quantum tunneling the relationship ceases to exist altogether. But these anomalies are not resolved by saying that they are all metaphors and not real. They are resolved by finding the correct mathematical relationships that nature follows in these circumstances.
Physicists like Roger Penrose and Paul Davies have written extensively on the remarkable concordance we find between mathematics and the physical world. Lakoff claims that this concordance is purely metaphorical, and by his definition of metaphor (source domain: events in real world; target domain: concepts in our heads) I would agree. Using Lakoff’s own logic, mathematics is a metaphorical representation of the real world, but in this use of the term metaphor there is no distinction between metaphorical language and literal language – metaphor is a direct translation. Lakoff often uses the term metaphor where I would use the word definition. When he defines a concept in terms of other known concepts he calls it a conceptual metaphor or a conceptual blend. Conceptual blend is bringing 2 or more concepts together to form a new concept. Conceptual blend makes sense, but conceptual metaphor doesn’t if there are no distinct literal and metaphorical contexts in which to make it a metaphor. I’ve also argued that where there is a causal relationship between 2 concepts, one is not necessarily, by default, a metaphor for the other. An example of this is periodicity being a direct consequence of rotation; day and night resulting from the earth’s rotation is the best known example. In Where Mathematics Comes From, Lakoff implies that this relationship is metaphorical.
Personally, I call Lakoff’s conceptual metaphors literal metaphors, because if they were literal then my entire argument on this issue would evaporate, which, of course, would be preferable for both of us.
Lakoff also maintains that all theories (in physics at least) are metaphorical, which is not an issue I will pursue here. I did point out to him, however, that some of his metaphorical interpretations (of Einstein’s theories in particular) were incorrect or misleading. I referenced Roger Penrose, who is more knowledgeable on this subject than either of us.
Lakoff argues that physics is effectively mathematical modeling that happens to get very close to what we observe, and there are many who would agree with this interpretation. (Renowned physicist, Stephen Hawking, subscribes to this view.) But many physicists would say that the mathematical concordance we find in nature goes beyond modeling because there are too many cases where the mathematics provides an insight into nature that we didn’t expect to find (for example: Maxwell’s equations giving us the constant speed of light in a vacuum or Dirac’s equation giving us anti-matter). Irrespective of this argument, nature follows mathematical relationships at all observable levels of scale. Lakoff, by the way, argues that there are no ‘laws of nature’, which is another argument, though not altogether irrelevant, that I won’t pursue here.
This has been a lengthy detour, but it brings me back to the point I made about the status of mathematics existing independently of the human mind. Most people struggle with this notion – it’s like believing in God. It evokes the idea of an abstract realm independent of human abstract thought. People call this the Platonic realm after Plato’s fabled realm of perfect ‘forms’. The real world, in which we live, being a shadow of this perfect transcendental world. Roger Penrose calls himself a Platonist (refer The Emperor’s New Mind), mathematically speaking, because he believes the mathematics we discover already exists ‘out there’. Paul Davies eschews the idea of Platonism (refer The Goldilocks Enigma) but in The Mind of God, he devotes a whole chapter to what he calls ‘the mathematical secret’: the way the physical world is ‘shadowed’ by mathematics.
I call myself a Pythagorean because Pythagoras was the first (in Western philosophy at least) who seemed to appreciate that mathematics is an inherent aspect of the natural world, like a latent code waiting for someone like us to decipher it. As our knowledge of physics progresses, this realisation only seems to become more necessary to our comprehension of the universe. I can’t help but feel that Pythagoras had no idea how deep his insight really was. Lakoff calls Pythagoras’s philosophical insight a ‘folk theory’, but it’s a folk theory that launched Western science as we know it, so I would call it a paradigm, and one that has had unparalleled success over a 2,500 year history.
Philosophers, since the time of Russell and Wittgenstein, have mostly argued that mathematics is a sub-branch of logic, but Godel, Turing and Church, have all demonstrated, in various ways, that one cannot create all mathematics from a set of known axioms (Godel’s famous incompleteness theorem). This is one point that Lakoff and I appear to agree upon.
What many people fail to understand, or take into account, is that mathematics is not so much about numbers but the relationship between numbers – just look at how much mathematics is written without numbers. Robyn Arionrhod, who teaches mathematics at Monash University, Melbourne, made a similar point in her book, Einstein’s Heroes (effectively, a well written exposition on Maxwell’s equations). If one looks at mathematics from this perspective, one can see that the relationships cannot be invented – they are discovered. Mathematics is essentially a problem-solving endeavour, and this begs the question: if one is looking for a solution to a puzzle, does the solution already exist before someone finds it, or only after it’s found? Think: Fermat's Last Theorem; solved by Andrew Wiles 357 years after it was proposed. Think: Poincare's Conjecture; proposed 1904 and solved in 2002 by Grigory Perelman (read Donal O'Shea's account). Think: The Reimann Hypothesis; proposed 1859, still unsolved. To answer that question, I suggest, is to answer the philosophical conundrum: is mathematics invented or discovered?
Footnote: I sent a copy of this to Professor Lakoff as soon as I posted it, offering him the right to reply.
For an alternative point of view, read Lakoff’s and Nunez’s book, Where Mathematics Comes From. For a physicist’s perspective, read Penrose’s The Emperor’s New Mind or Davies’ The Mind of God. Arionrhod’s Einstein’s Heroes is a good read that indirectly supports the physicist’s perspective.
See also my later posting, Jan. 08: Is mathematics evidence of a transcendental realm? Amongst other things, I discuss Gregory Chaitin's book, Thinking about Godel and Turing.
Wednesday 29 August 2007
God, theism, atheism
This is a letter I wrote to Phillip Adams in April 2005 - I don't think he would mind me posting it as it's not really a critique of anything he's written. It covers my views on a subject that often polarises people, and has a history of extreme violence (see my posting on Evil).
The essays I refer to herein may be the subject of a future blog or blogs.
Dear Mr. Adams,
I admit that I don’t always read your column but I was intrigued by your dissertation on life after death, and it prompted me to send you a couple of essays I wrote last year. I’ve believed ever since my adolescence, in complete opposition to my education, that a belief in God is perhaps the least important issue in living one’s life. Nothing I have experienced or read since has changed that point of view, but I give equal respect to theists and atheists preferring to judge them according to their actions, their attitudes and their words, as I hope they would judge me.
My philosophy has always had to allow for atheists, because, as your own article points out, they probably have the most uncluttered approach to death. I recently (the same day) read an editorial in American Scientist, and to quote out of context: ‘Whether there is an afterlife or not, we must live as if this is all there is. Our lives, our families, our friends... (and how we treat others) are more meaningful.. Rather than meaningless forms before an eternal tomorrow, these entities have value in the here-and-now...’
This captures my own philosophy pretty well because I argue interminably that it’s our interaction with our fellow humans that really matters rather than a belief in God, even though I do believe in God, albeit an unorthodox concept of one.
I am one of those heretics of my time that believes in a transcendental purpose but I don’t claim to be able to explain it or even claim that it is the ‘truth’. But what I do believe is that such a transcendental purpose is achieved in the way one lives one’s life rather than what one believes, so those who believe in nothing are arguably at an advantage because they are not prejudiced by preconceived ideas.
At the risk of sounding self-righteous, I don’t expect people to believe in God if they’ve never experienced it, and I know that for some reason, not everyone does.
If I lived in another time I would have been a shaman because I have experienced some strange things that the modern world and the scientific community (that I admire) claim are illusions, and they may be right. But our only experience of God is in our minds and therefore I agree with Augustine that God, or a relationship with God, is an internal journey, which has more in common with Buddhism (and even Sufism) than Christianity. But if you read my accompanying essays, you will see that I see God as the projection of the ideal self and therefore is unique for every person.
As an addendum to this post, I would like to comment on the polarity that seems inevitable to a discussion on this subject. Some well known atheists (I don't include Adams), have a fundamentalist zeal about their atheism, which I suspect they see as a necessary response to religious fundamentalism; Dawkins and Dennett are amongst the best known. They exhibit an intellectual superiority towards theists in the same way that some theists exhibit a moral superiority towards atheists. It is my position that both these positions are as false as each other.
See also my later posting on Religion.
Saturday 25 August 2007
The Meaning of Life
This is a submission I made to the magazine, Philosophy Now, in response to their 'Question of the month' last February. The entries had a strict word limit, which I incorporated exactly.
This blog has similar themes to my very first posting on Self, unsurprisingly, as the meaning of life is a purely subjective concept. One can also see a similar perspective to Victor Frankl's philosophy (Man's Search for Meaning and The Unconscious God). I think it's fair to say that we came to similar conclusions via different paths. When I read Frankl over 20 years ago, I couldn't have written this treatise; it's only in hindsight that I can see the connection.
For each and every one of us there exists an internal and external world. Some argue that only the external world can be discussed with any definition, and besides, the internal world is completely dependent on the external world, even to the extent that we think. This is because we all think in a language, and, for all of us, our language was gained from the external world. If we took this at face value then it could be argued that the internal world is irrelevant. However, this ignores the undeniable sense, we all have, that the internal world is the Self, and therefore has a significance that belies this simple analysis.
There is another argument put forward by some evolutionary psychologists that the only reason we have a self is so we wouldn’t become automatons. This leads to the plausible hypothesis that nature doesn’t really require us to have a sense of self at all; it’s sole purpose, from a biological perspective, is that it provides an effective conscious compulsion for us to survive and propagate our genes.
But both these arguments suffer from an examination of the internal and external world as if they are independent entities.
They ignore the interaction that we all experience, and how, through our responses to the external world over a lifetime, we develop and grow into complex psychological beings. No one passes through life without experiencing pain or emotional hardship at some level. The Buddha, according to legend, lived a sheltered and unscarred life until he went outside his palace walls and witnessed poverty, illness and death for the first time. The allegorical and truly insightful aspect of this story, is not the four noble truths that apparently arose from his observations, but that pain and suffering at some level are unavoidable for each of us.
We all yearn for stories, both fictional and biographical, that deal with the overcoming of adversity; it’s universal. Wisdom does not come from an extensive education, nor does it come from high achievements. Wisdom comes from dealing with all the adversities and misfortunes that fate throws in our path. Ultimately, it is how we respond and deal with life’s misfortunes that leads us to becoming someone we are happy to be or someone we inwardly despise. Adversity is the universal means through which we all gain wisdom and self-knowledge, and that is the meaning of life.
This subject is also touched upon in a later posting: Does the Universe have a Purpose? (Oct.07)
Intelligent Design
Evolution is nature’s design methodology, so replacing evolution with something else called 'design' is a non sequitur if it includes evolution and is meaningless if it doesn’t.
What does one mean by intelligent design? Its proponents say it’s the only explanation for the inherent complexity one sees in evolution. In fact, there are 3 possible interpretations of intelligent design; all of them inconsequential to science.
Firstly, the official interpretation, given above, effectively says there are aspects of evolution we don’t understand, therefore we can only explain it by invoking a ‘Designer’, otherwise known as God. But any lack of understanding of evolution, is a clear result of our ignorance rather than a need to invoke Divine intervention.
History shows that many of the gaps in our knowledge in the past were successfully uncovered in that past’s future. What’s more, history would suggest that there will always be gaps in our knowledge, so we should not be alarmed, nor afraid, to admit our ignorance of nature’s mysteries in the present, of which there are countless many. One of my favourite aphorisms is that only future generations can tell us how ignorant the current generation is. We always think, or claim, to know more than we do.
The second interpretation is that we acknowledge evolutionary design as hugely successful, albeit imperfect, and that it was designed from the outset by God. Another way of looking at this, is that we acknowledge evolution as nature’s design methodology, and the only remaining argument is whether it’s blind or teleological.
From a theological perspective, it can be argued to be part of God’s plan. But from a scientific perspective, bringing God into the picture explains nothing (see below). And this is why I always contend that science and religion are separate: they can’t answer each other’s questions.
The third interpretation is that intelligent design is really a case of ‘wedge politics’: to introduce ‘creationism’ into American schools. Creationism is another argument altogether, which replaces evolution with a fairy tale scenario of spontaneous creation. Not only is this completely, and obviously, unscientific, but all evidence suggests that the universe is a dynamic entity that has never stopped creating. In other words, in nature, creation is a continuous process.
In reference to the last paragraph, I would like to provide a further commentary based on an ABC radio interview I heard online in 2006.
I would like to add an insight provided by Margaret Wertheim (author of Pythagoras’s Trousers and The Pearly Gates of Cyberspace) in an interview on ABC Radio National (Australia). Wertheim made the pertinent point that both ID and ‘Creationism’ are the result of wedge politics to overcome the American Constitution’s requirement that religious teachings can’t be taught in State Schools. Therefore ‘believers’ attempt to introduce religion as science as an explicit Trojan horse.
Her implied point is that, if the Constitution allowed religion to be discussed in State schools, the strategy and the controversy wouldn’t exist.
This view is concordant with a quote in New Scientist, 9 September 2006, p.13 by Joseph Fessio, provost of Ave Maria University in Florida: ‘There’s a controversy in the United States because there is a lack of awareness of a thing called philosophy.’ This has been an argument I have used against proponents of ID ever since it raised its head. If people want to discuss this issue in an educational forum then it should be in a philosophy class, not a science class. People engage in this debate without being aware that they are discussing philosophy and not science. (See my March 08 posting, What is Philosophy?)
A belief in God neither hinders nor supports science, unless you're a fundamentalist. Bringing God into science to explain natural phenomena is a 'science-stopper'. You've stopped doing science, because you are effectively saying: I don't understand this, so I will invoke God and stop any further scientific investigation.
On the other side of the same coin, you cannot use science to prove or disprove the existence of God (though Richard Dawkins argues otherwise).
There is no physical evidence of God; the only evidence is what people feel and experience internally, so it's outside the realms of science which studies natural phenomena only. (See my later posting on Religion.)
See also my postings on Evolution and Does the Universe have a Purpose?
For a more detailed argument on this same topic, see my later posting in Nov.07: Is evolution fact? Is creationism myth?
On the question of 'complexity' and its role in describing life, Paul Davies provides an excellent exposition in his book, The Origin of Life.
Evolution
This is a letter I wrote to New Scientist recently, triggered by an article on 'Evolutionary design flaws' by Claire Ainsworth and Michael Le Page. It's not a critique of their article so much as a response.
I need to admit that I consider New Scientist the best periodical on the planet. The other reference is to Paul Davies, whom, along with John Gribbin, are probably the best science writers I have read. Having said that, I would vote Roger Penrose's The Emperor's New Mind, The Best science book for mine. Not only is it the best exposition on physics, without equations, one can read, Penrose's philosophical perspective on mathematics is very close to mine, as is Davies' (refer The Mind of God). See my blog posting: Is mathematics invented or discovered?
Reference: New Scientist, 11 August 2007, pp36-9.
What’s amazing about evolution is not the design flaws, but that, as a process, it can design so well at all. Nature’s designs, the result of an interaction of genes, environment and biochemistry can design the most amazing attributes, that not just provide survival, but outperform most of human inventions – take the human brain or the liver. I once saw a BBC documentary on testing the diving performance of peregrine falcons and it is designed to within the absolute limits of what is physically possible.
Evolution has no purpose, yet its strangest creation of all is imagination. It has evolved a species that can imagine a purpose where no purpose apparently exists. Einstein once said that the most incomprehensible thing about the universe is that it is comprehensible. The universe eventually created the means to comprehend itself. Evolution evolved a species that could eventually examine and decipher evolution. What sort of paradox is that?
I can’t help but find some agreement with Paul Davies’ thesis that he explores in The Goldilocks Enigma: 'it’s like the universe saw us coming' (quoting Freeman Dyson).
For those who are sceptical, be aware that evolution is used as a design methodology in industrial applications as well, using computer programmes that combine the 'most successful' of design 'offspring' in an iterative process.
This blog posting led me to write a companion blog on Intelligent Design. See also my later posting: Does the Universe have a Purpose?
In a later posting I provide a detailed argument on this entire subject: Is evolution fact? Is creationism myth?
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