Post Number:#76 
May 5th, 2012, 8:16 am
There have been many contexts in western philosophy where ‘Infinity’ is an odious idea.
As ‘the boundless’ in early Greek philosophy the infinite was the original substance which comprised the chaos which was ordered into the Cosmos, and was thus first rendered intelligible. In its original condition, the infinite boundless was horrid – something for God to get to work on, rather than anything divine in itself. Logically, an infinite regress is deplorable. (Do the on/off neural firings from the retina form a ‘picture’ in the visual cortex? Do we have an inner eye in the cortex, with which to see the picture? Does that eye have a retina too? …)
Cantor’s work on ‘transfinite’ arithmetic seemed to some philosophers of mathematics to provide a delightful logical articulation of the enigma of infinite numbers. Russell added the logically embarrassing Axiom of Infinity to the foundations of Principia Mathematica to prevent the infinite set being the null class – as it would be according to his meta-mathematical theory if there weren’t an infinite number of things in the universe to count.
But Neo-Kantian philosophers of mathematics like Brouwer rejected Cantor’s work and Russell’s - and all attempts to bring infinite quantities within the pale of human reason.
Again, because infinite numbers make nonsense of factorization, astrophysicists like Hawking today abhor infinite values for variables in their equations...
*
If theists today call God ‘infinite’ they are likely to mean that no predication in language that makes clear sense to us can make literal sense of God’s being. God cannot be ‘bound’ as a logical variable is ‘bound’ in the predicate calculus so as to frame an assertion of His existence – a thought which some take to comprise an argument for atheism. We cannot encompass God in what we say. To say that God is ‘infinite’ in that sense is not to say that God is very big – the way huge things we understand, like galaxies, are ‘great.’ Nor is it to say that God is everlasting. It is to say that God is categorially beyond the reach of our normal cognitive closure.
The thought that God is in Himself beyond our ken is time-honoured – as when Yahweh says (Exodus 3: 14) ‘I am that I am’. ‘Apophatic’ theology is the kind written on the assumption that there is nothing we may say about God – nothing literal and positive, that is. But the device of speaking negatively of God – saying what God is not – is sometimes taken to provide a content for apophatic theology more effectively than actually saying nothing about God.
In the spirit of apophatic theology the expression ‘infinite’ may be taken to be a negative – in that it is used to say God is ‘not finite.’ Avoiding the irreverent vulgarity of taking the negation of the term ‘finite’ in ‘infinite’ to refer to God’s endlessly big extension through all the dimensions we can think of, we take ‘finite’ to mean: ‘such as can be understood in terms of the concepts whereby we know our world.’ ‘Infinite’ will now be used for what cannot be so understood.
*
When metaphysics or cosmology treat of drastic totalities – of categories, of dimensionality, of comprehension – our minds boggle and it’s hard to judge whether we’ve arrived at the limits of the scope of our imagination or whether we have already crossed them into a sublime domain - or into a ridiculous one. The bewilderment we undergo around the bounds of definite sense, where we meet scenes drastically other than what we know, can provide mystics with metaphors to use when they seek to describe their ineffable experience of God - when that experience comes more as an 'unknowing' than as a 'knowing.'
The semantics of negative theology may work better in heady domains than in prosaic ones. Like all predications negative predications are only true when they make sense; and they will only make sense where their positive counterparts will. (Actually, of course, an expression that makes no sense doesn’t comprise a 'predication.') Only of numbers may we say they are not arithmetically even. So if we say that God is ‘not even’ in that way, we would appear to presuppose that God were a number. We may say of a lizard that it is 'not a mammal', but we may not properly say that the quality of mercy is 'not a mammal.'
*
From a modern logical point of view, if we can make negative statements about God using predicates that make good mundane sense, then God has been semantically drawn into the world. However, this may be acceptable to a 21st century theology of the Incarnation.
Sentence (1) rings categorially mistaken to theists today:
Sitting on His throne, God the Father occasionally shifts his weight from one haunch to the other, to keep comfy. (1)
Therefore the negation of (1) is categorially mistaken too, and it is therefore neither true nor false. But for contemporary Christians there is a way in which sentence (2) could have made sense nearly 2 000 years ago:
God the Son is sitting in the upper room of that house, having supper. (2)
Insofar as (2) did make sense then, sentence (3) would have made sense too:
God the Son is not sitting in the upper room of that house, having supper; He’s doing so in the house next door. (3)
But we have to add that we look upon the state of affairs described in (3) as providing an example of a semantic miracle.
*
To say that the poetics of our incomprehension of this or that infinity feels like our incomprehension of God is not to say that we should identify infinity with God. I doubt that Christians should treat ‘God is love’ as a statement of identity. ‘Love is God’ doesn’t seem to mean quite the same as ‘God is love’ - and the relation of identity is logically symmetrical. Because the meaning of ‘infinite’ trails a long history of pejorative associations, to deify ‘infinity’ per se risks sounding blasphemous.
As ‘the boundless’ in early Greek philosophy the infinite was the original substance which comprised the chaos which was ordered into the Cosmos, and was thus first rendered intelligible. In its original condition, the infinite boundless was horrid – something for God to get to work on, rather than anything divine in itself. Logically, an infinite regress is deplorable. (Do the on/off neural firings from the retina form a ‘picture’ in the visual cortex? Do we have an inner eye in the cortex, with which to see the picture? Does that eye have a retina too? …)
Cantor’s work on ‘transfinite’ arithmetic seemed to some philosophers of mathematics to provide a delightful logical articulation of the enigma of infinite numbers. Russell added the logically embarrassing Axiom of Infinity to the foundations of Principia Mathematica to prevent the infinite set being the null class – as it would be according to his meta-mathematical theory if there weren’t an infinite number of things in the universe to count.
But Neo-Kantian philosophers of mathematics like Brouwer rejected Cantor’s work and Russell’s - and all attempts to bring infinite quantities within the pale of human reason.
Again, because infinite numbers make nonsense of factorization, astrophysicists like Hawking today abhor infinite values for variables in their equations...
*
If theists today call God ‘infinite’ they are likely to mean that no predication in language that makes clear sense to us can make literal sense of God’s being. God cannot be ‘bound’ as a logical variable is ‘bound’ in the predicate calculus so as to frame an assertion of His existence – a thought which some take to comprise an argument for atheism. We cannot encompass God in what we say. To say that God is ‘infinite’ in that sense is not to say that God is very big – the way huge things we understand, like galaxies, are ‘great.’ Nor is it to say that God is everlasting. It is to say that God is categorially beyond the reach of our normal cognitive closure.
The thought that God is in Himself beyond our ken is time-honoured – as when Yahweh says (Exodus 3: 14) ‘I am that I am’. ‘Apophatic’ theology is the kind written on the assumption that there is nothing we may say about God – nothing literal and positive, that is. But the device of speaking negatively of God – saying what God is not – is sometimes taken to provide a content for apophatic theology more effectively than actually saying nothing about God.
In the spirit of apophatic theology the expression ‘infinite’ may be taken to be a negative – in that it is used to say God is ‘not finite.’ Avoiding the irreverent vulgarity of taking the negation of the term ‘finite’ in ‘infinite’ to refer to God’s endlessly big extension through all the dimensions we can think of, we take ‘finite’ to mean: ‘such as can be understood in terms of the concepts whereby we know our world.’ ‘Infinite’ will now be used for what cannot be so understood.
*
When metaphysics or cosmology treat of drastic totalities – of categories, of dimensionality, of comprehension – our minds boggle and it’s hard to judge whether we’ve arrived at the limits of the scope of our imagination or whether we have already crossed them into a sublime domain - or into a ridiculous one. The bewilderment we undergo around the bounds of definite sense, where we meet scenes drastically other than what we know, can provide mystics with metaphors to use when they seek to describe their ineffable experience of God - when that experience comes more as an 'unknowing' than as a 'knowing.'
The semantics of negative theology may work better in heady domains than in prosaic ones. Like all predications negative predications are only true when they make sense; and they will only make sense where their positive counterparts will. (Actually, of course, an expression that makes no sense doesn’t comprise a 'predication.') Only of numbers may we say they are not arithmetically even. So if we say that God is ‘not even’ in that way, we would appear to presuppose that God were a number. We may say of a lizard that it is 'not a mammal', but we may not properly say that the quality of mercy is 'not a mammal.'
*
From a modern logical point of view, if we can make negative statements about God using predicates that make good mundane sense, then God has been semantically drawn into the world. However, this may be acceptable to a 21st century theology of the Incarnation.
Sentence (1) rings categorially mistaken to theists today:
Sitting on His throne, God the Father occasionally shifts his weight from one haunch to the other, to keep comfy. (1)
Therefore the negation of (1) is categorially mistaken too, and it is therefore neither true nor false. But for contemporary Christians there is a way in which sentence (2) could have made sense nearly 2 000 years ago:
God the Son is sitting in the upper room of that house, having supper. (2)
Insofar as (2) did make sense then, sentence (3) would have made sense too:
God the Son is not sitting in the upper room of that house, having supper; He’s doing so in the house next door. (3)
But we have to add that we look upon the state of affairs described in (3) as providing an example of a semantic miracle.
*
To say that the poetics of our incomprehension of this or that infinity feels like our incomprehension of God is not to say that we should identify infinity with God. I doubt that Christians should treat ‘God is love’ as a statement of identity. ‘Love is God’ doesn’t seem to mean quite the same as ‘God is love’ - and the relation of identity is logically symmetrical. Because the meaning of ‘infinite’ trails a long history of pejorative associations, to deify ‘infinity’ per se risks sounding blasphemous.
