Monday, July 12, 2010

Foundation 3: A Constructional Ontology

Ontology - eh?
, is the study of reality. For historical (and somewhat odd reasons) an ontology is a chosen view of reality. So, for example, the physicist's ontology is a world of matter and energy. A psychologist's ontology is that there are people, and thoughts and feelings. For the modern Cartesian meditator none of these other ontologies are valid, in that people could be figments of our imagination (they aren't, but the strict Cartesian skeptic cannot accept them into the ontology because there may be no one there).

So, an ontology can be chosen based on how it is make up. A constructional ontology (the point of interest in this post) is one which serves to construct complexes from simples (Fine 1991). I want to show how the modern Cartesian stance (see here for a description of this stance) leads the modern meditator to adopt a constructional ontology. I also want to show how this ontology is constituted and to consider the primary items that populate the Meditator's world.

So this post develops framework from which the Meditator may begin to construct a world from an a priori principle (a principle that needs no reference to the world as it seems to be) rather than relying on Descartes’ non-deceiving God. Identification of this principle is outside the scope of this post.

The roots of a Cartesian ontology.
An ontology consists of all those items which are, in an appropriate sense, accepted (Fine 1991). The criterion of acceptance is that the item should be there (for good reason) not necessarily because someone puts it there. This presents a challenge to the modern meditator. While the Meditator can have—is obliged to hold—belief in those propositions that are immune to doubt (see my post on skeptical commitment) apart from one’s self, all other items that might populate the Meditator's world are initially suspect, so should not be there, at least at the outset of an enquiry.

As such, the Meditator begins with a very sparse world indeed. By comparison, where the physicist's world, or at least ontology, is immediately and densely populated by the evidence of the senses, and comes with a spacetime already built in, and within which measurements can be made as a basis for deriving laws and other theoretical constructs in any number of dimensions, the Meditator begins with only those propositions that are indefeasible, and they are the most abstract of propositions. For example, "I think, therefore I am" establishes that the Meditator exists, but says nothing of that existence. There is no body here, and the mind has no more than an innate idea of equivalence and difference (as argued in this post). All these other ideas come only later, after the other founding proposition is introduced (not in this post - later). But it is a start.

Beginning with some aspect or abstraction from the presenting world, as is done by the physicist, is a very useful way to develop an ontology. However, the challenge for the physicist is not in populating the ontology, but that all theories developed around such are limited to description rather than true explanation. For example, to attribute the attraction of one massive body to another, to gravity, does no more than name the apparent attraction. To then explain gravity as the effect of gravitons or the curvature of spacetime, or some other aspect simply moves the description one step to the left. As one approaches questions as to the actual nature or origin of things such as space or time, the physicist draws up short. Consider Richard Feynman (in Walding, Rapkins and Rossiter 2004, p. 6):
We physicists work with time every day but don't ask me what it is. It's just too difficult to think about.
In fact all the fundamental concepts of physics are similarly affected. Until a well-founded answer is available, the efforts of the physicist, and seemingly everyone else, is incomplete and may be just plain wrong. Certainly, as Popper identified, regardless of protestations by the physicist, no amount of data can verify a theory, but data can falsify the theory (Oddie 2008).

Is the mathematician any better off? While mathematicians mostly agree that mathematics is a discipline built on the a priori, its development is very closely linked with the natural sciences (von Neumann 1966, p. 181) in an empirical sense. Geometry, for example, previously argued by Kant to be a priori, von Neumann finds to have originated as a natural, empirical science. The problem of mathematics as it applies to the physical world is easy to spot. For example, π is found deeply embedded in our physical theories, from circular motion to quantum mechanics. But Heisenberg's Uncertainty Principle imposes strict limits to measurement. Then, under contemporary mathematics, there is an infinity of numbers sufficiently close to π that can be substituted for π in the equations of physics, from an empirical standpoint that would provide solutions experimentally indistinguishable from using that actual π. Consequently an infinity of theories that substitute other numbers for π in our trusted theories would work equally well. One need only consider the number of decimal points required. Around eighty decimal places might do it.

Then, if one ought to accept the simplest theory (Occam's razor) our present physical theories ought to be regarded as false: a rational number of around eighty digits is easier to compute than the irrational π. It may be that using π provides an over-description of the world that is inherently misleading. Indeed the same argument can be applied to the number e, which, through its association with the trigonometric identities would undermine the greater part of quantum theory.

While truth is the aim of inquiry, fallibilism affirms that, typically, our theories are false or very likely to be false, and when shown to be false they are replaced by other false theories (Oddie 2008). This cannot be the case for an ontology built on an indefeasible Cartesian ontology. This provides sufficient reason for the philosopher who seeks truth, to set aside, at least for a little while, the empiricist who demands that the world is as it appears to be, and to walk with the modern Cartesian rationalist.

Seeking to beat the fundamental ontological tradeoff.

Regardless of the near empty ontology that first presents, Descartes’ epistemology is attractive in that, being indefeasible, the items of the ontology cannot be falsified by presentations from a dubious world, so a Cartesian ontology ought to be pursued. Comparing the physicist’s ontology to that of the Meditator, we see what Swoyer (2009) calls the fundamental ontological trade-off: that a rich ontology with its promise of powerful explanatory power is fettered by increased epistemic risk, whereas a more rigorous ontology seems to have a lesser ability to explain our world.

Is this trade-off an illusion? For the first part, the promise of causal explanatory power (as contrasted with descriptive explanatory power) through an empiricist’s ontology is just that; a promise that cannot be realised. For the second part, insofar as the Meditator is obliged to accept indefeasible propositions as a model of an actuality, then, if indefeasible principles imply consequences, these too ought to be accepted into the ontology. This growth of accepted propositions characterises a constructional ontology, to which I shall return shortly.

Initial conditions, Fine’s possible ontology and actual ontology.
Fine (1991) says:
An ontology is actual; it includes everything that it is correct to accept. By contrast, we may talk of a possible ontology, which consists of everything that might be accepted (as the total ontology).
With respect to the idea of a possible ontology, Fine is not here talking about metaphysical possibility as it is usually used, but what might be true of an ontology, rather than what is true. This is exactly in tune with the Meditator's stance of holding no initial belief in any proposition or its negation. Then the Meditator is authorised to survey what might be true.

Fine notes that one might hold that there is no such thing as an actual, as opposed to a possible ontology for there is nothing which counts as the correct ontological stand; there are merely different, equally legitimate, stands. He investigates how absolutist notions might be avoided in the description of an ontology. But such avoidance is not a thing to which this Meditator would subscribe. The Meditator does not begin with absolutist notions, but that does not mean he or she might not end up with one.

The stance of the Meditator is to hold no belief either in the affirmative or the negative about the existence of conditions of the world unless and until propositions about supposed conditions are shown to be indefeasible (see [Author] 2009b). Then the Meditator is authorised and obligated to accept indefeasible propositions into the actual ontology as a matter of sceptical commitment (see [Author] 2009b) as models of actual conditions of the world. Rather than contrasting a chosen ontology with other possible ontologies, the Meditator begins with all possible ontologies bundled into one, and, through application of the Method of Doubt, sieves through all those available in the hope of finding propositions that must be accepted, due to their indefeasibility. So, rather than beginning with givens, the items of the ontology gradually come into view. Because something is possible if it is a possible view (Fine 1991, p. 268), the possible ontology encompasses the totality of what-is, and what-might-be (but isn’t). Then, the dialectical nature of the possible ontology is no more than an expression of the Meditator's idea of equivalence and difference, for in the possible ontology is every possible proposition and its negation, at least at the outset. The possible ontology is populated immediately through reference to what might be. However, for the Meditator, such reference is metaphysically vague: [T]he world of the modern Meditator begins as a sparse world of barely defined, essentially windowless objects, shrouded in doubt, about which we seek to determine laws that have ontological force, that bring these objects into some level of focus, in so far as each principle defines a characteristic of the system, to which the objects must comply, or they have no place in the system. ([Author] 2009b): From the possible ontology the actual ontology (see Fine 1991) may be populated by sieving through the possible ontology using the Method of Doubt, seeking trustworthy propositions as models of actual conditions of the real world. How one can consider dialectical possibilities, when the objects of the dialectic are initially windowless, is a challenge, but consideration of this must be left to another time. One must first consider the ontological framework, and it does not require objects. The Meditator’s Constructional Ontology. Fine studies how a discipline gets shaped by the positions which are adopted and the strategies that are pursued. The apparent absence of givens in a Cartesian ontology, brought by the Meditator’s position, restricts the Meditator’s strategies, and suggests that any world discoverable from a Cartesian stance might be a constructional ontology. A constructional ontology is an ontology where some, perhaps most, of the objects of the ontology are accepted on the grounds that they are constructed from other objects in the ontology (see Fine 1991). It is an ontology in which complexes are constructed from simples through the action of a constructor. Fine describes the nature of the constructional ontology in terms of givens, constructs, constructees, constructors, items and elements. Givens are those items that are just accepted into the actual ontology; a starting condition or origin of the ontology. Constructs are those objects constructed from constructees and constructors. Essentially, the constructor acts on constructees to create constructs, though, as Fine later notes, there is no rule to say that a constructor requires a constructee to operate on – the constructional ontology might arise ex nihilo. As an example of a constructional ontology, Fine provides the cumulative hierarchy of sets, in which the constructees of any set are its members and the constructor is the set-builder. Constructs and constructees are elements; elements and constructors are the items of the ontology. Fine describes three non-modal principles for a constructional ontology. These are: Inclusion: Each given is to be accepted (within the ontology).
Closure: If the elements el, e2, . . . and the constructor o are accepted and if o is applicable to el, e2, . . . , then the result of applying o to the elements el, e2, . . . is also to be accepted.
Foundation: Any element of the ontology can be constructed from the basic elements of the ontology by means of constructors in the ontology. For the Meditator's ontology, these principles fall away. The principle of inclusion is unnecessary. Strictly speaking, there are no givens in the actual ontology of the Meditator. For example, the Meditator is accepted from the possible ontology due to the indefeasibility of, 'I think therefore I am,' so is not a given. In the same way, the Meditator seeks an indefeasible proposition as constructor. Equally, the principle of closure is unnecessary also because constructors are not applied to elements, as the mathematician does to the null set to produce a hierarchy of sets. The Meditator has no authority to do so. Rather, if there is an indefeasible proposition that refers to some aspect of the ontology, for example to an element or the totality, and the proposition says something of that aspect, then the aspect shall comply. The new aspect exists. That is, the Meditator is obliged to accept that the condition of the world that an indefeasible proposition models has ontological force upon the ontology. Closure therefore is no more than recognition of Sceptical Commitment (see [Author] 2009b). The Principle of Foundation can also be dropped because, for the Meditator, conditions will be what they are, and the Meditator is in no position to create principles unless and until they arise naturally through Cartesian enquiry. In any case, Foundationalism is already part of the stance of the Meditator. If this idea is well-founded, the world will eventually come into view as an evolution brought by constructors. As an example, say there is an indefeasible proposition that says all that exists is bounded. Then each boundary is likewise bounded, and the ontology evolves automatically. Indefeasibility of a proposition that has implications for the actual ontology implies causal power in the real world of the item the proposition models. In the case of the fictitious example, such a proposition would mean that there is a condition of the world that in some way brings an iteration of boundaries into existence. The constructional ontology and foundationalism. Decartes' foundationalism features a foundation of unshakable first principles, and a superstructure of further propositions anchored to the foundation via unshakable inference (Newman 2008). One wonders at the number of first principles that might be needed. Descartes’ foundationalism, in the light of Aristotle’s expectation that a form of knowledge is accessible that establishes the first premises, that anchors demonstrations of other pieces of knowledge as justified truth worthy of belief (Smith 2004) supports the idea that there is some foundational statement upon which all other pieces of knowledge are built. If so, a constructional ontological framework, with indefeasible propositions organised in the manner of a well structured, architectural edifice, would permit the growth of knowledge about what is, independent of empiricism. The task of the modern Meditator is to discover sufficient items to act as constructees and constructors for a model of the world. If Aristotle is right, there might be just one first principle, and as such this would be a constructor acting on what is and what might be but isn’t; hence the possible ontology. This is not very different from the present state of physics. Gibbs (1995) and Wigner (1960) for example, observe that the history of theoretical physics has been a succession of reductions to lower levels: more fundamental, more unified, more symmetrical and ideally simpler. So the empiricist’s world and the rationalist’s world might coexist. First step to identifying Aristotle's foundational statement. Given that the actual ontology has accepted the Meditator, it also includes the Meditator's innate ideas of equivalence and difference (see [Author] 2009a). Consequently, because these ideas are epistemologically prior to all other ideas, while at the same time all impressions are dubious, it is from equivalence and difference alone that the Meditator must develop his or her understanding of the world. A natural step would be for the Meditator to express this idea of equivalence and difference as a singular proposition. Then this proposition ought to be the foundation of the Meditator's world. To do so, one needs to develop a lexicon free of Quinean circularity (see Quine 1960) by which proper, non-judgmental, non-anthropocentric reference might be made to the contents of the possible and the actual ontology, thereby enabling the Meditator to create propositions. Conclusion. Combined with past work (see [Author] 2009a, 2009b) the Meditator has made progress. Knowing of his/her own existence, the Meditator has found a position within the actual ontology from which to consider the possible ontology. Having identified that he/she has an innate idea of equivalence and difference, the Meditator has a basis for thinking about the world. Added to this, the Meditator now has an ontological framework within which a rich Cartesian ontology might be developed. Within this, the idea of equivalence and, by extension, difference, may provide a key to wider knowledge of the world. Reference: [Author] 2009a, Toward a Cartesian Ontology – Equivalence and Difference, Submitted to Nous, Forthcoming. [Author] 2009b, Toward a Cartesian Ontology – Sceptical Commitment, Ontological Force, and the Modern Meditator, Submitted to Nous, Forthcoming. Fine, K 1991, The Study of Ontology, Noûs, Vol. 25, No. 3 (Jun., 1991), pp. 263-294 Oddie, G 2008, 'Truthlikeness', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2008 edn, Quine, W.V.O. (1960), Word and Object, Cambridge MA: MIT Press.

Smith, R 2004, 'Aristotle's Logic', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2004 edn, Swoyer, C 2000, 'Properties', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Winter 2009 edn, von Neumann, J 1966, 'The mathematician', in RB Heywood (ed.), The works of the mind, University of Chicago Press, Chicago, pp. 180-96. Walding R, Rapkins G, Rossiter G 2004, New Century Senior Physics, Oxford University Press, South Melbourne.

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