James Knight, the Network Norwich columnist, asked me the following question. Posted below it is my reply.
Do you think the cosmos is platonic just in the mathematical sense or in another way too? I'm just making sure that when we speak of the cosmos we are both using platonic in the same terms. How are you using it?
Hi James,
The following answer to your question impinges upon some issues that I have been pondering for years: in particular why is that in our culture the “irreducible intuitive” is so often pitted against the “reducibility of mechanism?” This theme I see in almost everything: from H. G. Well’s “The Time Machine” where the Eloi are pitted against Morlocks, through the Cartesian ghost in the machine and ‘left brain’ versus ‘right brain’ traits, to charismatic verses non-charismatic. This seemingly irreconcilable dichotomy has now consumed my theoretical deliberations for many years and constantly makes unexpected appearances in my writings (See this link for example ). Here is my attempt to address this issue. It is in fact a very pressing matter because for many years I have been very alienated from evangelicalism. I have put that down to a swing in mainstream evangelicalism toward ‘right brain’ faith expressions and this has become the de-facto version of Christianity in some quarters. There has, in my view, been a consequent loss in authenticity and this has threatened my faith. So, the stakes here are very, very high and I find myself defending my faith from other people with faith. Paradoxically I don’t find atheists anywhere near as threatening!
The short answer to the question is: I use the word ‘platonic’ to refer to the world of mathematical constructions and models. These constructions are explored with the likes of number theory, geometry, set theory, computational theory etc. The most salient feature of this world is its debatable ontological status; it seems to be a world of possibility rather than actuality. Many (if not all?) objects in the cosmos can be modeled using a subset of platonic mathematical constructions isomorphic with them. Cosmic objects are platonic in as much as they may be isomorphic with mathematical objects. A much longer answer is probably necessary when one realizes that there are some tough conundrums here.
At first sight the fundamentals of mathematics are disarmingly minimal, undemanding of an elaborate physics to host them. Take for example the Turing machine: it seems to ask for little more than two discrete sequences (the tape and procedural steps) and a state transition diagram (=software). From this simple model the whole of mathematics seems to open up. Many versions of material reality could host such a simple machine and its computational equivalents and therefore there seems no lack of clarity or mystery in trying to conceive mathematics: it is devoid of that ‘right brain’ mystique; it is, seemingly, the progeny of the ‘left brain’, a paragon of mechanism.
But the self-referencing intricacies and enigmas come in thick and fast once we get reflexive. For a start if we allow the Turing machine to analyse its own mathematics (meta-mathematics) up pops Gödel’s theorem and Turing’s halting theorem. Also there is this question: Is the concept of mathematics intelligible without at least a minimal physical world able to host the mechanical reifications of its computations? Is there truly an independent platonic world that mathematics inhabits irrespective of the existence of a material ontology? And where does the mind fit in all this? Is the activity of an apparently ‘mindless’ mechanism of elementals, such as we find, in a Turing machine, the essence of mathematics? Or does mathematics only exist by virtue of a preexisting mind that can conceive it?
Mathematics appears to transcend a particular material instantiation of its objects whether that instantiation is a Turing machine or some other model of computation. The objects of mathematics can in principle be instantiated on a variety of media ranging from Searle’s beer cans to silicon chips. Therefore the essence of mathematics is to be found over and above material instantiation. Mathematics is about abstraction from material reification; it is about classes of activity and pattern and these things are not necessarily tied to a particular substantive realization. Abstraction, class and pattern are intelligible only as pure concepts inside an up and running mental context which can then handle.
These are difficult issues, but for a theist their resolution is likely to be bound up with the concept of Divine Aseity (see also your concept of absolute reason) Like you I favour the view that mathematics betrays the a-priori and primary place of mind; chiefly God’s mind. The alternative view is that gritty material elementals are the primary a-priori ontology and constitute the foundation of the cosmos and mathematics. But elementalism has no chance of satisfying the requirement of self explanation as the following consideration suggests: what is the most elementary elemental we can imagine? It would be an entity that could be described with a single bit of information. But a single bit of information has no degree of freedom and no chance that it could contain computations complex enough to be construed as self explanation. A single bit of information would simply have to be accepted as a brute fact. Aseity is therefore not to be found in an elemental ontology; elementals are just too simple.
In the search for Aseity elementalisation leads to an ontological dead end because elementals have a lower limit complexity of one bit, a limit beyond which there is no further room for logical maneuvering that could resemble anything close to self explanation. In contrast complexity has no upper limit and hence if Aseity is to be found at all, it must reside at the high end of logical complexity, perhaps at infinite measures of complexity with some kind of reflexive self affirming properties, such as we find in your “there is one true fact” example.
Like you James I’m attracted to Berklian idealism and/or a phenomenological philosophy, because taking sentient complexity as the fundamental given seems to provide a better chance of solving the philosophical conundrums over the nature of the mathematical abstractions, self explanation, and consciousness. However, I can find no necessary objection to the idea that sentience, particularly Divine sentience, may be able to engage in some kind of mathematically reductive self description; but in doing so such description would be no more than sentience describing itself in terms of its own ontology; something similar happens when a programming language is used to write its own compiler. As you say “…..personality is not something that we can turn on itself and identify outside of the layering we put in. I think personality is too big for such isolated imputations.”, If I understand that correctly then yes, personality cannot be described with something beyond itself; but in the final analysis personality, particularly God’s personality, may be big enough to cope with its self description in terms of its own ‘substance’. So sentience is at once both reducible and irreducible. Reducible because it may be mathematically reducible, but irreducible in that it cannot be reduced to an ontology other than itself. This may help satisfy the twin but seemingly contradictory intuitions of the reducibility and irreducibility of sentience.
There is often distaste for the idea that somehow reductive descriptions of sentience are possible. This distaste may result because our self-conscious first person ontology, something which is very sacred to each of us, is trivialized if a reductive description of sentience is used as Trojan horse to smuggle in a profane materialist ontology. It is one thing to attempt a reductive description of sentience in terms of the cognitive artifacts of sentience, but it is entirely another to surreptitiously swap a first person ontology for an elemental materialist ontology whilst attempting to carry out this reduction. A descriptive reduction is an entirely different thing from an ontological reduction. In any case I would question the intelligibility of the whole notion of a gritty “material” cosmos “out there”: if I am right then the fundamental particles of the cosmos are not solid little quarks or strings but cognita. Quarks and strings demand a complex mathematical context to be intelligible. The philosophical problems in this area seem to result of an attempt to relate incommensurables; mind and matter. My own opinion is that one or the other has to go and since ‘material’ noumena are far less real than the first person experience it is the former that has to go.
I have always had grave doubts about the intelligibility of an ontology of “material” elementa pictured to be lurking out there somewhere beyond sentience. It is surely ironic that many Christians are at one with many atheists in picturing such a conception. It is ironic that the default Christian folk philosophy is that of a “materialism plus” ontology – that is, a basic off the peg materialist ontology is supplemented with a “spiritual world” of demons, sprites, angels and of course God himself, all of which haunt the interstices of our gritty earthly reality in the manner that the human “spirit” is supposed to haunt the human body: the ghost in the machine. This is of course Cartesian dualism. For theists dualism actually leads to a tripartite reality: 1. God. 2. The Spiritual World 3. Matter. It all smacks of the classical Gnostic view of particles of spirit somehow trapped in a profane material world, a world that owes its creation to a demiurge; after all, the feeling goes, how could a perfect spiritual God have anything to do with a world of grimy matter? In the light of this default philosophy it is no surprise that Christians across the board are so utterly alienated from their world and are retreating into the mysteries of the “right brain” and the mysteries of the inner self where the unaccountable machinations of intuition replace mechanism. There follows the great Christian cop out from having to account for itself by simply declaring “It’s all in the heart”. In its more extreme expressions salvation for the Christian Gnostic is an escape from the ‘evil’ material world through states of altered consciousness.
Christian dualists are never far from atheism; they hover on the abyss of atheism. If for some reason their concept of a haunted reality should betray them and they react against it, they find a profane materialism purged of sacredness ready to welcome them. And the betrayals do happen: crises in leadership, failure of their religious paradigm to materialize in the form prophecies, blessings, healings and revivals, and the whole creaking show patched up by a bullying authoritarian leadership, well versed in spiritual spin.
I don’t accept a three substance or even a two substance cosmos: I am striving for an integrated vision, not the horribly fragmented vision of contemporary Christian Gnosticism that has lead to the incompatibilities between heart and mind, right and left brain, intuitive Christians and analytical Christians. But an integrated one substance vision is not the same as pantheism. Ultimately what distinguishes substances apart is differences in logical configuration, and configuration is about pattern, abstraction and classification and therefore about mathematics and therefore about mind. And so a one substance vision when looked at more closely is capable of resolving itself into a multi-category, multi-substance vision.
There is, in fact, one very fundamental category division to be found in this one substance vision. We are patterns of mind stuff, but of an entirely different genus to God himself. We and our cosmic context seem to be in that part of the mathematical spectrum that counts as mere possibility: we are too simple as logical constructions to possess the property of Aseity. Our patterns of sentience have no necessary existence and it is this that distinguishes us sharply from the substance of Deity and Aseity. So in one sense the greater cosmos is composed of two very different substances: God, the sentience that necessarily exists, and everything else created ex-nihilo and sustained at His pleasure.
Do you think the cosmos is platonic just in the mathematical sense or in another way too? I'm just making sure that when we speak of the cosmos we are both using platonic in the same terms. How are you using it?
Hi James,
The following answer to your question impinges upon some issues that I have been pondering for years: in particular why is that in our culture the “irreducible intuitive” is so often pitted against the “reducibility of mechanism?” This theme I see in almost everything: from H. G. Well’s “The Time Machine” where the Eloi are pitted against Morlocks, through the Cartesian ghost in the machine and ‘left brain’ versus ‘right brain’ traits, to charismatic verses non-charismatic. This seemingly irreconcilable dichotomy has now consumed my theoretical deliberations for many years and constantly makes unexpected appearances in my writings (See this link for example ). Here is my attempt to address this issue. It is in fact a very pressing matter because for many years I have been very alienated from evangelicalism. I have put that down to a swing in mainstream evangelicalism toward ‘right brain’ faith expressions and this has become the de-facto version of Christianity in some quarters. There has, in my view, been a consequent loss in authenticity and this has threatened my faith. So, the stakes here are very, very high and I find myself defending my faith from other people with faith. Paradoxically I don’t find atheists anywhere near as threatening!
The short answer to the question is: I use the word ‘platonic’ to refer to the world of mathematical constructions and models. These constructions are explored with the likes of number theory, geometry, set theory, computational theory etc. The most salient feature of this world is its debatable ontological status; it seems to be a world of possibility rather than actuality. Many (if not all?) objects in the cosmos can be modeled using a subset of platonic mathematical constructions isomorphic with them. Cosmic objects are platonic in as much as they may be isomorphic with mathematical objects. A much longer answer is probably necessary when one realizes that there are some tough conundrums here.
At first sight the fundamentals of mathematics are disarmingly minimal, undemanding of an elaborate physics to host them. Take for example the Turing machine: it seems to ask for little more than two discrete sequences (the tape and procedural steps) and a state transition diagram (=software). From this simple model the whole of mathematics seems to open up. Many versions of material reality could host such a simple machine and its computational equivalents and therefore there seems no lack of clarity or mystery in trying to conceive mathematics: it is devoid of that ‘right brain’ mystique; it is, seemingly, the progeny of the ‘left brain’, a paragon of mechanism.
But the self-referencing intricacies and enigmas come in thick and fast once we get reflexive. For a start if we allow the Turing machine to analyse its own mathematics (meta-mathematics) up pops Gödel’s theorem and Turing’s halting theorem. Also there is this question: Is the concept of mathematics intelligible without at least a minimal physical world able to host the mechanical reifications of its computations? Is there truly an independent platonic world that mathematics inhabits irrespective of the existence of a material ontology? And where does the mind fit in all this? Is the activity of an apparently ‘mindless’ mechanism of elementals, such as we find, in a Turing machine, the essence of mathematics? Or does mathematics only exist by virtue of a preexisting mind that can conceive it?
Mathematics appears to transcend a particular material instantiation of its objects whether that instantiation is a Turing machine or some other model of computation. The objects of mathematics can in principle be instantiated on a variety of media ranging from Searle’s beer cans to silicon chips. Therefore the essence of mathematics is to be found over and above material instantiation. Mathematics is about abstraction from material reification; it is about classes of activity and pattern and these things are not necessarily tied to a particular substantive realization. Abstraction, class and pattern are intelligible only as pure concepts inside an up and running mental context which can then handle.
These are difficult issues, but for a theist their resolution is likely to be bound up with the concept of Divine Aseity (see also your concept of absolute reason) Like you I favour the view that mathematics betrays the a-priori and primary place of mind; chiefly God’s mind. The alternative view is that gritty material elementals are the primary a-priori ontology and constitute the foundation of the cosmos and mathematics. But elementalism has no chance of satisfying the requirement of self explanation as the following consideration suggests: what is the most elementary elemental we can imagine? It would be an entity that could be described with a single bit of information. But a single bit of information has no degree of freedom and no chance that it could contain computations complex enough to be construed as self explanation. A single bit of information would simply have to be accepted as a brute fact. Aseity is therefore not to be found in an elemental ontology; elementals are just too simple.
In the search for Aseity elementalisation leads to an ontological dead end because elementals have a lower limit complexity of one bit, a limit beyond which there is no further room for logical maneuvering that could resemble anything close to self explanation. In contrast complexity has no upper limit and hence if Aseity is to be found at all, it must reside at the high end of logical complexity, perhaps at infinite measures of complexity with some kind of reflexive self affirming properties, such as we find in your “there is one true fact” example.
Like you James I’m attracted to Berklian idealism and/or a phenomenological philosophy, because taking sentient complexity as the fundamental given seems to provide a better chance of solving the philosophical conundrums over the nature of the mathematical abstractions, self explanation, and consciousness. However, I can find no necessary objection to the idea that sentience, particularly Divine sentience, may be able to engage in some kind of mathematically reductive self description; but in doing so such description would be no more than sentience describing itself in terms of its own ontology; something similar happens when a programming language is used to write its own compiler. As you say “…..personality is not something that we can turn on itself and identify outside of the layering we put in. I think personality is too big for such isolated imputations.”, If I understand that correctly then yes, personality cannot be described with something beyond itself; but in the final analysis personality, particularly God’s personality, may be big enough to cope with its self description in terms of its own ‘substance’. So sentience is at once both reducible and irreducible. Reducible because it may be mathematically reducible, but irreducible in that it cannot be reduced to an ontology other than itself. This may help satisfy the twin but seemingly contradictory intuitions of the reducibility and irreducibility of sentience.
There is often distaste for the idea that somehow reductive descriptions of sentience are possible. This distaste may result because our self-conscious first person ontology, something which is very sacred to each of us, is trivialized if a reductive description of sentience is used as Trojan horse to smuggle in a profane materialist ontology. It is one thing to attempt a reductive description of sentience in terms of the cognitive artifacts of sentience, but it is entirely another to surreptitiously swap a first person ontology for an elemental materialist ontology whilst attempting to carry out this reduction. A descriptive reduction is an entirely different thing from an ontological reduction. In any case I would question the intelligibility of the whole notion of a gritty “material” cosmos “out there”: if I am right then the fundamental particles of the cosmos are not solid little quarks or strings but cognita. Quarks and strings demand a complex mathematical context to be intelligible. The philosophical problems in this area seem to result of an attempt to relate incommensurables; mind and matter. My own opinion is that one or the other has to go and since ‘material’ noumena are far less real than the first person experience it is the former that has to go.
I have always had grave doubts about the intelligibility of an ontology of “material” elementa pictured to be lurking out there somewhere beyond sentience. It is surely ironic that many Christians are at one with many atheists in picturing such a conception. It is ironic that the default Christian folk philosophy is that of a “materialism plus” ontology – that is, a basic off the peg materialist ontology is supplemented with a “spiritual world” of demons, sprites, angels and of course God himself, all of which haunt the interstices of our gritty earthly reality in the manner that the human “spirit” is supposed to haunt the human body: the ghost in the machine. This is of course Cartesian dualism. For theists dualism actually leads to a tripartite reality: 1. God. 2. The Spiritual World 3. Matter. It all smacks of the classical Gnostic view of particles of spirit somehow trapped in a profane material world, a world that owes its creation to a demiurge; after all, the feeling goes, how could a perfect spiritual God have anything to do with a world of grimy matter? In the light of this default philosophy it is no surprise that Christians across the board are so utterly alienated from their world and are retreating into the mysteries of the “right brain” and the mysteries of the inner self where the unaccountable machinations of intuition replace mechanism. There follows the great Christian cop out from having to account for itself by simply declaring “It’s all in the heart”. In its more extreme expressions salvation for the Christian Gnostic is an escape from the ‘evil’ material world through states of altered consciousness.
Christian dualists are never far from atheism; they hover on the abyss of atheism. If for some reason their concept of a haunted reality should betray them and they react against it, they find a profane materialism purged of sacredness ready to welcome them. And the betrayals do happen: crises in leadership, failure of their religious paradigm to materialize in the form prophecies, blessings, healings and revivals, and the whole creaking show patched up by a bullying authoritarian leadership, well versed in spiritual spin.
I don’t accept a three substance or even a two substance cosmos: I am striving for an integrated vision, not the horribly fragmented vision of contemporary Christian Gnosticism that has lead to the incompatibilities between heart and mind, right and left brain, intuitive Christians and analytical Christians. But an integrated one substance vision is not the same as pantheism. Ultimately what distinguishes substances apart is differences in logical configuration, and configuration is about pattern, abstraction and classification and therefore about mathematics and therefore about mind. And so a one substance vision when looked at more closely is capable of resolving itself into a multi-category, multi-substance vision.
There is, in fact, one very fundamental category division to be found in this one substance vision. We are patterns of mind stuff, but of an entirely different genus to God himself. We and our cosmic context seem to be in that part of the mathematical spectrum that counts as mere possibility: we are too simple as logical constructions to possess the property of Aseity. Our patterns of sentience have no necessary existence and it is this that distinguishes us sharply from the substance of Deity and Aseity. So in one sense the greater cosmos is composed of two very different substances: God, the sentience that necessarily exists, and everything else created ex-nihilo and sustained at His pleasure.
