The quest for objectivity in mathematics and science by only allowing a simple recursive procedure runs through the whole history of their development. Effectively, what Hilbert was arguing is that semantics could be completely replaced by formally describable syntactical operations that reduce to instructions on how to proceed from one symbol to another, and Church and Turing conjectured that all such operations could be performed by a simple, recursively functioning machine. The thesis in effect assures us that we never need to get outside again, that all referents have indeed been internalised in a purely syntactical form.
This is essentially what Newtonian mechanics amounts to, and this is what underlies and defines almost all subsequent science. Newton did not analyse the world into atoms, as had the ancient atomists, but simply took over their conclusions and presupposed atomism. He began with structureless particles and then devoted his work entirely to synthesis, asking what behaviour can be manifested by such particles, individually or collectively.
This procedure has remained unchanged in modern physics. A feature of the formalism he developed is that almost everything of importance in it is unentailed.
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The only entailment is a recursive rule governing state succession. In the world seen through this kind of model, causation is collapsed down to what can be encoded in a state transition sequence, as this is all the Newtonian language allows to be decoded back into causal language.
There are further strictures in this procedure associated with the assumption that the universe is composed of structureless particles. It cannot be freed of all referents and remain mathematics. More generally, whatever is modelled by a formal system in which all entailment is syntactic entailment, is different from, richer and more complex than its formal model. It is impossible to reduce quality to quantity, or equivalently, semantics to syntax. Rosen then pointed out the implications of this for science.
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To open the path to a more adequate biology, Rosen examined entailment, modelling and measurement. While entailment between propositions is relatively straightforward, the more problematic question is, Can we ascribe entailment between phenomena? Modelling, which Rosen took to be the essence of science, is bringing entailment patterns between a model and that which is modelled into congruence. Rosen used his own version of category theory to analyse what is involved in modelling.
As Rosen noted:. Category Theory comprises … the general theory of formal modelling, the comparison of different modes of inferential or entailment structures.
Moreover, it is a stratified or hierarchical structure without limit. The lowest level, which is familiarly understood by Category Theory, is … a comparison of different kinds of entailment in different formalisms. The next level is, roughly, the comparison of comparisons. The next level is the comparison of these, and so on. To relate what is to be modelled to a model is a matter of encoding, while relating the model to what is modelled is decoding.
Encoding and decoding is an art, and this is true of all modelling. If modelling is successful, then what is modelled is a realization of the model. While normally we regard a formal system as a model of a natural system, it is possible to regard the natural system as a model of the formal system, and to regard natural systems as models of each other. This is a relationship of analogy. Rosen argued that the mathematical machinery currently regarded as the only way to carry out this process is far too narrow.
What it allows us to capture about the world around us, necessarily misses most of what is really going on, and most importantly, misses out on life. To develop science adequate to life, Rosen showed how, by rejecting assumptions of traditional science, it becomes possible to give a place to functions and final causes and to ask Why? Essentially, he refurbished and defended an Aristotelian form of science giving a place to all the four causes, including final cause. While in mechanisms, such causes can be examined in abstraction from each other, in life the four causes are so intertwined that they cannot be treated in this way.
Rosen showed how to represent systems through synthetic models in which functional components are the direct products of the system. In such models the components are context dependent and cannot be reduced to parts without being destroyed. These are able to represent systems in which functional organization cuts across physical structures and physical structures are simultaneously involved in a variety of functional activities. These are modelled mathematically by sets in which addition of sets does not equate to the addition of the members of sets.
That is, in place of a science that focuses on identifying independent material parts and showing how they operate, but which then obliterates any appreciation of the organization of the whole, Rosen developed a science of organization in which organization could be treated independently of its material instantiation. For Rosen the use of genetic algorithms, Boolean networks, cellular automata, artificial neural networks and related approaches are merely implementations of the Newtonian paradigm made possible by modern computers.
This for Rosen is merely complication, not complexity. Rosen defined a complex system as a system that requires multiple formal descriptions, which are not derivable from each other, to adequately capture all its properties. That is, there is no ultimate model of a complex system from which the other models, which can be formally identified and abstracted from the system, can be deduced. Stephen Kercel explicated this:. These three maps in the M,R -system each have a peculiar property.
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Each map has one of the other two as a member of its co-domain, and is itself a member of the co-domain of the remaining map. Thus, the metabolism map is a member of the co-domain of the repair map, and the repair map is a member of the co-domain of the replication map… As can be seen, the three maps form a loop, but not just any loop. Note that the map does not merely entail the result; more resticively, it contains it.
The maps form a loop of mutual containment. In particular, he has pointed out the relevance of his work for the study of protein folding and morphogenesis, which have always been deeply troubling to physicists. Just as Kepler and Newton enabled us to see that circular motion is only one kind of regular motion approximated in rare cases, we can now see that the kind of order revealed by scientists working within the constraints of Newtonian assumptions is a very limited range of possible order approximated in rare cases, for instance in the solar system or in experimental situations where conditions are carefully controlled.
And as we no longer assume circular motion and motion as deviations from this, we no longer need to treat closed systems consisting of independent parts as a reference point for scientific explanation. It is much more reasonable to regard the closed system as an extremely degenerate case of open systems.
However, Rosen was doing more than this. As Einstein kept insisting, science involves a free creative act of their intellect; ultimately, it involves wisdom. It involves the ability to select what is important about a problem from what is irrelevant or incidental, and to follow that. There is no algorithm for this, just as there is no algorithm for making a model. By showing the impossibility of reducing semantics to syntax, Rosen allowed a place not only to life itself but to the creative acts of the intellect and to the wisdom of great thinkers. Granting a place to creative acts and wisdom does not equate to making these intelligible, however.
And while Rosen has made a convincing case that life itself cannot be understood by pasting together our understanding of the components of life, he has not shown how life itself could have come to be. Theoretical biology still needs philosophical biology, and the problem is: How can the insights of the philosophical biologists be integrated with theoretical biology? The way I have proceeded so far is to have presented philosophical biology as taking its starting point in the experiencing subject and striving to overcome the idealist tendencies of this by showing how organisms can be seen as experiencing meaning, and then to have presented theoretical biology as taking its starting point in the objective world and striving to overcome the reductionist tendencies of this by showing how it is possible to give a place to life in an objective world.
But despite moving towards the same end point, overcoming Cartesian dualism and reviving Aristotelian themes that had been dismissed with the rise of the mechanistic world view, there is still a gap between these two approaches. Recognizing this gap should indicate what needs to be done. It is necessary to recognize a realm more primordial than the division between the subjective and the objective from which these could have emerged.
This, essentially, is the path proposed by Friedrich Schelling although this has seldom been appreciated, as he continues to be classified as an Idealist. In pioneering this path, Schelling, reviving and advancing the evolutionary cosmology of Giordano Bruno and developing the philosophy of nature of Johann Herder and Goethe, began the modern tradition of process philosophy.
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Schelling began as an Idealist as a disciple of Fichte. Fichte argued that only through mutual recognition between people, whose thought emerges first in relation to action in a world which resists their will, could such self-consciousness be achieved. It is also necessary to conceive the ego as part of and within an independently existing nature to make intelligible the possibility of self-consciousness.
Instead, Schelling argued that our comprehension of human consciousness has to be based on the philosophy of nature, replacing the mechanistic conception of the physical world with a conception of nature as dynamic and creative within which humans as social, self-conscious, creative beings, could have evolved. To account for the emergence of subjects living in a world of objects Schelling argued that it is necessary to reject both the approach to nature which begins with the subject and then appends objective reality to it, and the approach which begins with the objective world and then appends subjective experience to it.
It is necessary to identify a more primordial realm from which subjects and objects could emerge.
His procedure was to subtract from self-consciousness to arrive at the lowest conceivable potential, and then construct the path upward through a successions of limits to show how the conscious self could emerge from this as its highest potential. Insofar as nature is productivity, it is subject; insofar as it is product, it is object.