First cause: December 2007

Sunday, December 30, 2007

On denoting and the laws of thought

In perception we have acquaintance with objects of perception, and in thought we have acquaintance with objects of a more abstract logical character; but we do not necessarily have acquaintance with the objects denoted by phrases composed of words with whose meanings we are acquainted. ... All thinking has to start from acquaintance; but it succeeds in thinking about many things with which we have no acquaintance.

One aim of Russell’s efforts is to resolve the problem of non-referring expressions or negative existentials. His concern is expressed (1905, n.p.)

By the law of the excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either ‘the present King of France is bald’ or ‘the present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.

Russell sought to address the problem by introducing a complicated (by his admission) application of the Laws of Thought. Another solution presents if one recognises that the problem of denoting may not stem from denoting, but from making a method of denotation that conforms to the Laws of Thought, evident in Russell’s consideration of the present King of France. While Russell applies the Laws of Thought, to bring sense, he has introduced a kind of modal aspect, by providing three options: always, sometimes, and never. My contribution will be to shift the onus onto the ontology.

Russell considers the proposition ‘A differs from B’ (1905, n.p.), explaining that if this is true, then there is a difference between A and B. In terms of the meditator’s system, this implies a difference in assets. He says that this may be expressed as ‘the difference of A and B subsists’. Otherwise, there is no difference, the statement is false, which may be expressed ‘the difference between A and B does not subsist’, (1905, n.p.). He asks, ‘...how can a non-entity be the subject of a proposition?’ (1905, n.p.) because if so,

‘I think, therefore I am’ is no more evident than ‘I am the subject of a proposition, therefore I am’; provided ‘I am’ is taken to assert subsistence or being, not existence.

As such, he argues, it is always self-contradictory to deny the being of anything; but this in itself leads to contradictions. If A and B do not differ, a supposition that either there is, or there is not, such an object as ‘the difference between A and B’ seems equally impossible (1905, n.p.).
Russell asks that meditators not make up their minds against the argument until they have attempted to construct a theory of their own on the subject of denotation. In the light of the current effort, it is not my intention to critique Russell’s efforts. Instead, I want to describe the nature of denotation from a holistic perspective, in the light of my arguments regarding the nature of ideas and perceptions as these sit in relation to omnets, assets and the General Principle of Equivalence.

To do so, I will begin by describing denoting from a Cartesian perspective. Then I will discuss the Laws of Thought that to my mind are at the heart of the problem. I believe that sufficient development of these early concepts may provide a meaning for the action of denoting that informs knowledge. In so doing, this will provide a tool kit and a better understanding of logic to enable further consideration of the Cartesian world.

Denoting presupposes a bi-condition
One of Russell’s (1905) concerns is that while thinking begins with acquaintance (by his determination), we use words founded in acquaintance to create denoting phrases for meanings that are intended to refer to that with which we are not acquainted, for example the present King of France. If terms are grounded in the Cartesian method, a distinction can be made between a reference to supposed existing omnets, such as the present King of France, and omnets that have a well-founded ontology. I believe that this alters the role of acquaintance in denotation. To me the use of each denoting term presupposes two actualities. The meditator presupposes
1. That there is a well-founded omnet, to which the term refers; and
2. That the meaning of the term in the mind of the meditator corresponds to the omnet under consideration.
For this to work for Russell, the copy principle must hold properly, such that the idea referred to has some referent in the world other than the idea itself. However, this is not verifiable, by Russell’s own standards (1967), essentially due to the Epistemological to Ontological divide (the difference between how we think the world to be and the way it actually is).

The Cartesian meditator has already limited the world to assets having a positive ontology by accepting/letting in only that which is indubitable, into the actual ontology (as opposed to possible ontology). So the idea of the existence of a negative existential is not a valid mode of thought. This is not particularly problematic for denoting the present King of France in the light of the above bi-condition, because, while the meditator may have no knowledge either way as to the existence of the supposed king, he may have well defined parameters that he deems to be the assets of a king of France. Then the statement, ‘The present King of France is bald’ either has a referent and this matches with the intent of the meditator (other people’s minds being irrelevant due to internalism) or it has no referent and so cannot match with the meditator’s idea, and so is a false denotation. To make this clearer, a proposition, viewed with respect to the General Principle of Equivalence, is a denotation of an omnet. In the present example, ‘The King of France is bald’ is a reference to a person for which hair is not one of his assets. If there is no King of France, then there is no such omnet in the world beyond the idea itself, so the second condition fails.

The Law of Excluded Middle (hereinafter the ‘LEM’), for example that the King of France either is or is not bald, that was a central motivator for Russell’s (1905) efforts, does not enter into the equation, as will be implicit in the work on logic that I will now pursue.

On the Laws of Thought
If I denote a big ginger cat as being a big red cat, it is easy to see that the cat is red, yet not red. It may be big in one sense, but not in another. Also, what is the maximum height of a short man? We need a system that brings sense to such duality.

Priest & Tanaka (2004) provide an analogy that suggests a useful mental stance, for the meditator in his considerations of logic, through Bohr's theory of the atom. By this account, an electron orbits the nucleus of the atom without radiating energy. Yet Maxwell's equations – an integral part of the theory – requires that an electron which is accelerating in orbit must radiate energy, and so should spiral in toward the nucleus. This seems to imply that Bohr's account is inconsistent. Priest and Tanaka explain that the inconsistency can be resolved if the two apparently inconsistent views are seen as paraconsistent. Logic is ‘paraconsistent’ if and only if its relation of logical consequence is not explosive; where ‘explosive’ means that a proposition and its negation (A,~A) implies that the proposition ‘B’ is true for any B (Priest 2004). The notation used here is the common form, as it presents in Priest (2004). Paraconsistent logic exists to accommodate inconsistent but non-trivial theories (trivial meaning that A, ~A is always true). Essentially, paraconsistent logic denies, qualifies, or makes conditional the Law of Non-Contradiction (hereinafter the ‘LNC’). As such, LNC is not a law at all. Then another sieve would be useful to make sense of propositions.

Stepping back from Priest and Tanaka’s description, consider that if, say, both Bohr’s description and Maxwell’s equations have an actual foundation in a well-founded omnet, both describe the same condition, then these prescribe boundary conditions upon the system, and the dichotomy is more properly viewed as a duality. The scientist (as opposed to the meditator for the sake of simplicity) is placed in a position where she or he ought to recognize that there is some underlying reality which anchors the model. Normally, one is not in a position to assign necessity to apparently dichotomous propositions, because one cannot be certain of the truth of either, for the reasons discussed in Chapter 2. But this is not the case for the world of the Cartesian meditator. In that world, two well-founded propositions can only be consistent, even if seemingly inconsistent.

Then, if there are two boundary conditions, and these are apparently contradictory, the problem lies in the way the meditator is conceiving the propositions, because the statements are paraconsistent. It may be that the Laws of Thought have reached the end of their proper domain.

It then lies with the meditator to pursue an interpretation of the system that brings meaning to terms used. For surely there can only be a singular Totality, else it would not be the Totality, which follows from the founding discussion and from the General Principle of Equivalence. It is this sense in which I consider the Totality, and wonder what interpretation of the concept enables evolution of the system while not contradicting the idea of there being a Totality omnet. The epistemology needs to account for such apparent contradictions as a feature of the Cartesian system.

I am not arguing that paraconsistency be employed, as it is for empiricism, until the more general view which accommodates the apparent contradiction is discovered, as was, strictly speaking the case for the atom. I am saying that, for the Cartesian meditator, the nature of omnets and assets begins as a windowless view, so terms essentially stand in for whatever is the case. As such the meaning of these terms is illuminated by an understanding of the system as a whole. Then, if all possibilities imply a singular result, then there is no contradiction and paraconsistency becomes consistency by our deeper understanding of the conditions that the terms were provided to denote.

For empiricism the normal method is to condition or limit previously held theories as soon as a more consistent view presents. Such theories are limited to truthlikeness (Oddie 2001). Consider the case of Bohr’s atom. The electron simply does not crash into the nucleus. The empirically based solution presents in the form of quantum mechanics. One might argue that this replaces Bohr’s view. Another interpretation, the one that I am advocating, is that quantum mechanics better informs the idea of an orbit (in the context of an electron) in terms of energy levels. Then one is justified to argue that the term ‘electron orbit’ (in context) and the ‘electron energy level’ denote the same state. Another example is the wave particle duality of quanta. We no longer consider this to be a dichotomy, for which either one or the other is incorrect. Rather, we accept that the idea is paraconsistent. The reason I discuss Bohr’s atom is because of my concerns regarding the meaning of the Totality, meaning ‘what is’.

Now turning to the Totality, I see a similarity of concept between the apparent duality of the idea of Totality, and Heraclitus’ claim: ‘We step and do not step into the same rivers; we are and we are not,’ (Robinson in Priest 2004). The contradiction is absorbed if one recognizes that the ontology includes a distinction between the river as omnet at a particular time, and the river as omnet over an extended period. Such a resolution might interpret the Totality as including all states of the world over all of time, or more simply, all states of the world, which equates to all assets (as world states) that go to make up the omnet that I refer to as Totality.

However this suggests a creation of new assets without limit, for if there is a continuity, then one might expect a whole new set of assets for each change of the universe, one more pure asset for every connection between the previous state and the next (whether this be a continuous change or not). Of course such a solution is just a guess, and is not, strictly speaking, accessible to the Cartesian meditator, for whom the particulars of the world are not properly informed by empiricist acquaintance.

For the Cartesian meditator, at this point in the discussion, there is a Totality in which he must be embedded (but this has only vague meaning at present), there is one or more pure assets, whether empty or not, and there is the General Principle of Equivalence. How this can accommodate change, in fact why one should expect change, will become evident in due course.

On the nature of truth and logic, a Cartesian perspective.
The Principle of Identity can be replaced under the General Principle of Equivalence with the condition of having all and only one’s assets in compresence as distinct from non-compresence. Identity then is a term that focuses on compresent assets, which was central to Leibniz’s (1995a) consideration of the Principle of Identity of Indiscernibles, in that he assumes compresence implicitly in properties going to make up an object as a unity – that is, being ‘in esse’.

Under the General Principle of Equivalence there is no foundation for an actual contradiction in the ontology, because the system is founded on there only ever being one omnet that can have all and only it assets. This is consistent with the view that there can be no two true statements (meaning statements that describe a reality), that are contradictory (see Glanzberg 2006 for an explanation of the central stances relating to idea of truth). An apparent contradiction springs from the epistemology when one describes an omnet using two propositions and finds that there is at least one asset (in the predicate) supposed of the omnet (the subject) referred to in one proposition, say A, and at least one asset supposed of the omnet by another proposition that is ‘not A’ or ‘other than A’.

The issue is informed by the ontology of the world as implied by the General Principle of Equivalence. Firstly I want to make a distinction between ‘not’ and ‘other than’, which has the same assets if the Law of the Excluded Middle (LEM) is necessarily true. Of course the LEM was banished to doubt hood by the Cartesian method.

‘Not A’ may be taken as representing the negation of A. What does this mean in the Cartesian world for which all assets have a positive ontological status? The meaning of words returns us to issues of denotation. Two interpretations present. Firstly, the meditator might be presupposing an asset A that an omnet (say B) with positive ontological status does not have or cannot have. This interpretation does not assume a proper ontological foundation for that asset A at all, given the positive ontology. It will be useful to denote interpretation symbolically as /A, meaning ‘there is no such asset A (in B)’. Alternatively, a reference by the meditator to ‘Not A’ may refer to some omnet of the Totality other than A. This interpretation might be denoted symbolically ~A (meaning ‘an asset of the Totality other than A’). So the first supposes the absence of an asset ‘in esse’, the second supposes the existence of an asset ‘ex esse’.

A further distinction may be made between the condition ~A referring to a particular B of the Totality and the general form of ~A referring to more than one B of the Totality, up to the limit case of all ~A of the Totality. For this thesis the simplest solution for the present is to ensure the intended target of the denotation is made clear in the description of system under consideration. While this may seem burdensome, in reality it expresses a very simple ontology, that there is a Totality, it has its assets and no two assets have exactly the same pure assets, which is just what the General Principle of Equivalence expresses.

My sense is that this is not a case against the LNC or the LEM, for they are an extension of ideas of equivalence and inequivalence. Rather, my concern is that the LNC and LEM are somewhat opaque to the meditator until these are considered and moderated by the meditator using the General Principle of Equivalence in the Cartesian system. As such, I feel that the LNC and the LEM may be treacherous at this stage due to the problems of denotation that I have just described. Then it is better to apply Ockham’s razor, which is essentially the effect of Cartesian doubt. This is not to be mourned. The LNC and LEM have long been a source of contention in philosophy, which is evident in concerns over denoting phrases. Other serious concerns are identified by Priest (2004). For these reasons, accounting for the notion of negative existentials through denotation in terms of assets and omnets assists the meditator in understanding the world.

Boundary conditions of the world – the Cartesian view.

From nothing, or anything, comes a unique origin for structure

On the structure available to possible worlds.

To prevent the intrusion of superfluous entities, one might demand that metaphysicians start with the empty world and admit only those entities that have credentials. This is the regime imposed by Rene Descartes. He clears everything out and then only lets back in what can be proved to exist.

So the expectation of an empty world, underpinned by the method of doubt is a valid consideration. The onus of proof is incumbent upon those who would have that there is something. But we must be very careful here by what we mean empty. We have already shown that the minimal ontology includes at least the condition that the GPE models and the Meditator.

But the world may once have been empty. More formally, there is no support for the idea that the Meditator has any special relevance to the existence of the world. While the formal GPE statement relies on a Meditator to consider it, for it to have meaning, because the GPE noumenon applies to everything at every level, it exists independent of there being a Meditator to think about its existence. That is, and this is important, the condition the GPE models, necessarily exists, no matter what other actual states might be.

References:
Sorensen, R 2003, 'Vagueness', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Fall 2003 edn, http://plato.stanford.edu/archives/fall2003/entries/vagueness/.

---- 2004, 'Nothingness', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Spring 2004 edn, http://plato.stanford.edu/archives/spr2004/entries/nothingness/.

The cataclysm that attends the General Principle of Equivalence

Page Navigator>>
1. On First Cause
2. First steps: The General Principle of Equivalence
3. Building a sturdy ontology.
4. The cataclysm that attends the General Principle of Equivalence
5. On the structure available to possible worlds.
6. Boundary conditions of the world - the Cartesian view.
7. On denoting and the laws of thought.
8. Something for nothing, and why this is not absurd.

4. The cataclysm that attends the General Principle of Equivalence.

On pure/minimal assets
By the General Principle of Equivalence, assets are what omnets have. Because assets are also omnets under the initial construct, then by symmetry if there is an internal difference within an asset or omnet, that implies a difference in assets. This implies directly that all omnets are composed of (possibly finite, possibly uncountably many) minimal assets for which further segregation has no proper ontological foundation. That is, such base assets are indivisible. Let's call these 'pure' assets. That all omnets are a compresence of such follows from the nature of the principle.

The number of these assets is irrelevant to the argument. This is not an iterative process where one divides an omnet into two or more assets then does so again and again. If it were, then the argument would be invalid. Rather, it follows from the GPE because it is just a recognition that an asset is an omnet and any two assets differ in some way, else they would be the same. Also it doesn't matter whether assets are properties, or tropes, or relations or some other more metaphysically bamboozling element. The beauty of the Cartesian view is that we aren't in a position to even consider such fine detail yet, for everything but the GPE and our own existence in the Totality is suspect.

For example, if there is a line, it might be made up of a finite number of line segments, or an infinity or transfinite number of points, or infinitesimals or perhaps something else. None of this matters, for it is made up of what it is made up of, and any difference along the line is due to a difference in assets, and any internal difference within such asset is likewise based on different assets immediately, not iteratively. So at the base level the elements are pure assets.

No matter what we suppose to be the case from the comfort of the World-of-Seeming, whether nothingness or anything else, each omnet is no more than pure assets. In this context, every complex omnet is a bundle of indivisible assets, where ‘bundle’ means pure assets in compresence (exactly the term that refers to the ontological condition implied by there being complex omnets).

This is parallel in meaning to the ‘bundle’ of bundle theory (see Armstrong 1978b), for which four central themes are evident, as these might apply to substances (Robinson 2004). The themes are
1. The concept of substance can be analysed in terms of some relation between properties conceived as universals.
2. The concept of substance can be analysed in terms of properties conceived of as individuals, e.g., as property-instances or tropes.
3. Substances are in fact no more than bundles of properties conceived of as universals.
4. Substances are in fact no more than bundles of properties conceived of as individuals.
Here substance is that which ‘stands under or grounds things’ (Robinson 2004, n.p.). For the Cartesian meditator, the idea of substance might equate to assets, but also may be an unnecessary layer of presupposed structure. The Pyrrhonian sceptic would argue that all these options reduce to opinion, for there is no clear determinant for any particular choice. Fortunately the meditator has no need to judge which might be the case, for all are suspect. To hold these concepts in abeyance is the right path for the Cartesian meditator, for strictly speaking, one cannot be sure that there are such complex omnets. The challenge is for the meditator to find some basis to re-admit such complexes into the actual ontology, through further consideration of universal conditions.

Why things can't hold together unless they are built from the GPE as constructor.
The difficulty comes when the Meditator looks for a basis for this bundling to rescue complex omnets from a sea of minimal (pure) assets. One needs to find a means of association but, prima facie, all such associations are themselves composed of minimal assets. To explain the current concerns with respect to this, I will consider a measure of recent philosophical commentary.

On compresence and bundling
Armstrong (2005) hints at a problem for bundle theories when he favours universals against tropes. A universal is a property that is essentially shared by whatever has it. For example all red things share the same red property. Tropes apply to individuals alone. A particular red ball has that red, but does not share it. He is prepared to forego the simplicity of tropes because identities across particulars (that is, universals) seem to be necessary to hold the world together.
Bundle theories, considered in detail in Armstrong (1978a), have ‘great difficulty with the metaphysics of the uniting principle or principle of bundling,’ (Armstrong 2005, p. 311) but he admits that a similar problem applies to the alternative view of properties as attributes of particulars.
Further, he wonders what might bundle ‘dispositions’, and expresses that this problem is one of the most confounding for metaphysics. For this reason, he likes the idea that every property should bestow power, presumably because this would provide some connection between cause and effect. It is not clear, however, how properties might achieve such power within themselves, given that they, being different from other properties, are not directly connected to other properties, and so require to be bundled by something other than themselves.
But compresence, according to Grupp (2004) must be a special bundle itself. He holds that this leads to an infinite regress, with respect to finding what bundles the special bundle. This is no different to the result just shown to follow from the General Principle of Equivalence, that all possible worlds are founded on minimal assets, but such assets have separate identity, otherwise they would be the same, which is essentially the argument of Heidegger (1969).

The problem is not with the possibility of assets, for we see evidence of such everywhere through the differences that must have some basis (such differences being differences in assets for this is all that omnets have). The problem is in the understanding of how these assets find a means of association. The existence of assets does not in itself say anything about these assets in some way forming an omnet at any level more complex than pure assets. For example, assets of bigness, redness, catness, or being two metres from another cat (should any of these be well-founded assets), are different to each other and different to the omnet in which they are compresent, they do not in themselves imply the existence of a big red cat with its relations, bundled in some way, making them 'in esse' to complete a big red cat resting in space.
An appeal to universals does not in itself rescue the omnets as they present to us, for they too have no ability to hold the world together, because if there are omnets, they reduce to minimal assets. The question that then attends the development is how such assets can form complex omnets, meaning omnets with more than one pure asset.
Our initial adventure showed that the General Principle of Equivalence is necessarily true, and reflects a global tautology. As such it should be relatively innocuous. However, taken to its natural end, pure assets constrained by the General Principle of Equivalence noumenon (meaning the condition of the world that the GPE models) are all that an omnet has, and the means of association is likewise composed of pure assets. As such there is a challenge as to what holds the world together.

To put this pointedly, because the GPE applies to all that is, it implies that everything in the world (energy, matter, words, ideas) should collapse to simples, unless there is some necessary truth that cannot collapse. But of course this is the GPE itself, for it is indefeasible, whatever is, even if the world is empty, relies on the GPE.

In my next post I will show that this implies that there is a unique origin for the world and that its origin is inescapable.

Building a sturdy ontology

Page Navigator>>
1. On First Cause
2. First steps: The General Principle of Equivalence
3. Building a sturdy ontology.
4. The cataclysm that attends the General Principle of Equivalence
5. On the structure available to possible worlds.
6. Boundary conditions of the world - the Cartesian view.
7. On denoting and the laws of thought.
8. Something for nothing, and why this is not absurd.

3. Building a sturdy ontology.

The subject of this post is to set out a basic ontology (see below for explanation of this term) as a metaphysical system that is capable of dealing with the concepts and constructions that develop under the action of the General Principle of Equivalence

WHAT IS ONTOLOGY?

Ontology is a spooky word and philosophers use and abuse it in many ways. Ontology can be seen as having four parts (Hofweber 2005):
(O1) the study of ontological commitment, i.e. what we or others are committed to,
(O2) the study of what there is,
(O3) the study of the most general features of what there is, and how the things there are relate to each other in the metaphysically most general ways,
(O4) the study of meta-ontology, i.e. saying what task the discipline of ontology should aim to accomplish, how the question it aims to answer should be understood, and with what methodology they can be answered.
According to Hofweber:
(O4) will have to say how the other three are supposed to be understood. If (O1) has the result that the beliefs we share commit us to a certain kind of entity then this requires us either to accept an answer to a question about what there is in the sense of (O2) or to revise our beliefs. If we accept that there is such an entity in (O2) then this invites questions in (O3) about its nature and the general relations it has to other things we also accept.

ONTOLOGY: THE VIEW OF THE CARTESIAN MEDITATOR

Let's look at the view of the Cartesian Meditator (one who accepts only that which is transcendent of doubt - see my post on the General Principle of Equivalence and Broughton's interpretation of this) as it relates to O1 to O4.
A NOTE FOR HARDCORE PHILOSOPHERS (to be ignored by everyone else): First recall that the Meditator I adopt here is the Meditator who sticks rigorously to Descartes' Method of Doubt as interpreted by Broughton (2002), but not the one that later drops this method for a softer view of a non-deceiving God. To complicated and long winded to talk about that here.

On O1: The Cartesian Meditator commits only to that which is indefeasible - meaning that which cannot be doubted. But this means directly that if there is something which is transcendent of doubt, one is obliged to accept it. One cannot say 'Oh that's all very good, but here is a counterexample' unless one can show that the counterexample is transcendent of doubt. If this were properly shown then my thesis fails, but there can't be two truths that disagree in reality, so I feel quite safe as Cartesian Meditator.

On O2: Virtually all that presents to the Cartesian Meditator is suspect - an illusion. It can't be trusted because one might be dreaming or tricked by an evil genius (see Descartes work or that of Newman in the Stanford Encyclopedia of Philosophy ('Descartes Epistemology') for more on this). Two things must be brought into the 'actual' ontology, from the 'possible' ontology (see Fine (1991), and that is the Meditator himself or herself, and the General Principle of Equivalence (seem my posting on this). Actually, everything else is suspect.

On O3: What are the general features of what there is? This concept is to my mind monumentally dangerous. We talk about properties, relations, tropes, space, things and no end of other aspects of what there is or might be. The Cartesian Meditator is very concerned about these. Kant looked at these in detail and showed that all these are essentially concepts manufactured in the mind, any or none of which might be a proper term for what is. No matter what we think of properties and so forth, we have no way of properly supposing that such notions are any proper basis to create a system that relates to the World-as-it-is-in-itself. If this is perfectly obvious to you, you can skip the next few paragraphs.

Swinburne (1995) investigates various kinds of properties, providing notions of hard and soft properties, general relational properties, general properties, particular relational properties, soft past-related properties and other variations, and then enunciates six different versions of the Principle of Identity of Indiscernibles (Leibniz - look up Wikipedia or the Stanford Encyclopedia of Philosophy on this if you are interested) relating to these definitions. For example (p. 390): ‘Any two individuals which have all the same general hard and past-related soft properties are the same individual.’ He then explores the implications of adopting each form of the principle. His purpose in doing so is to investigate which individuals might have ‘thisness’.
Armstrong (2005) takes a different tack. Rather than supposing various categories of properties, he compares and contrasts properties from the majority views, asking (p.309)
1. ‘Are properties universals or tropes?’
2. ‘Are properties attributes of particulars or are particulars just bundles of properties?’
3. ‘Are properties categorical (qualitative) in nature, or are they powers?’
4. ‘If a property attaches to a particular, is this predication contingent or is it necessary?’

I will consider Armstrong’s paper in some detail because this thesis provides terms under which these questions may be addressed, using a principle of equivalence. In particular, the question is not whether universals are properties or tropes, or categorical in nature or powers, but how properties, or whatever there is, can form unified structures having complexity any greater than a simple.
Armstrong supports universals rather than tropes. He is prepared to forego the simplicity of tropes, because identities across particulars (that is, universals) seem to be necessary to hold the world together. I will later argue that universals are not imbued with this characteristic, whether property or trope, or anything else.
He asks (p. 311) ‘How do properties stand to the particulars that have the properties?’ and finds that bundle theories have (p. 311) ‘great difficulty with the metaphysics of the uniting principle or principle of bundling,’ but admits that a similar problem applies to the alternative view (which he later addresses). He wonders what might bundle ‘dispositions’. Again he implies that all things may be expected to fall apart, and he infers that this is one of the most confounding metaphysical problems. Later he expresses the view that he likes the idea that every property should bestow power, presumably because this would provide some connection between cause and effect. This would be consistent with his adherence to the Eleatic Principle (Colyvan 2004).
Armstrong explains (p. 317) that
Baxter had wrestled with the problem of the ‘fundamental tie’ that is supposed to hold together particular and universal. It is the great difficulty that is regularly raised against universals. It apparently relates particular and universal, but it seems to be more fundamental than a relation. Philosophers sympathetic to universals have said apparently desperate things such as ‘non-relational’ tie’. Baxter came up with the idea that the particular and its universal actually overlapped, were partially identical. A thing’s properties, the universals it instantiates, go to make up a thing, and the things that a universal is instantiated by go to make up a universal. [my emphasis]
I have quoted this at length, because this is very similar to the solution that will derive in this work. However, to achieve this unity I have to drop the idea of universals, particulars and things. This is a tack that Armstrong warns against, for to remove any universal could have unwanted results. ‘The damage might ripple on further. So beware!’ (Armstrong 2005, p. 318).
I say 'rubbish'. If that is what removing universals does, then so be it. Let's not presume that such a fragile system would be a proper model of the world. The universe has been here since the beginning, so it is a bit stronger than all that.

By adopting the terms omnet and asset as described in The General Principle of Equivalence there is no presupposition about the way the world is, the terms are purely nominal. One might argue that merely referring to an omnet or asset presupposes the existence of such but this is not so. For whether there is just nothing or a singular something or a plural something, which exhausts the possibilities, these are nominally omnets. Similarly for assets, and if each omnet has only itself and is otherwise indivisible then the asset is the omnet. The GPE in this respect is just a global tautology that says what is, is what it is, has what it has.

On O4: This was said to be the study of meta-ontology, i.e. saying what task the discipline of ontology should aim to accomplish, how the question it aims to answer should be understood, and with what methodology they can be answered.
Ontology for this Meditator would ideally be able to answer all physics, mathematics and philosophical questions about the world, at least in principle. This is a big ask, but there are reasons for thinking this should be possible. The principle reason I have to thinking this, is that the GPE will be shown to imply that the only complex structure that can exist, must be constructed in reality as an effect of the condition of the world that the GPE statement mirrors. Pause for a moment and consider what this means. ALL complex structure. Then, if one can properly understand its implications, one can properly model the world, at least in principle. This is why I adopted the constructional ontology as a suitable model. Actually the constructional ontology is just the framework implied to be the right kind by the GPE itself - start with the Meditator and the constructor (GPE) and watch what happens.

HOW THE ONTOLOGY LOOKS TO THE MEDITATOR

Now we have a sturdy ontology. The ontology that the Meditator adopts is very much simplified in its early stages, for there is only a very sparse universe that might be admitted into the ontology, as will shortly be shown. One simply places all that might be into a possible ontology. This is just a construct in which all that might be is quarantined for consideration. No ontological commitment is given to any of what might be other than the meta-ontology itself, which is validated by the method of doubt. Then the only constructs that are carried into the actual ontology are those that are transcendent of doubt, namely the Meditator and the GPE. From there we can test possible omnets (meaning omnets that might have a Cartesian basis in reality) as candidates to enter the actual ontology.

I carry out this test in my upcoming post: The cataclysm that attends the General Principle of Equivalence. Then we get to see what is left in the system.

References:
Armstrong, DM 1978a, Nominalism and realism, vol. 1, Universals and scientific realism, Cambridge University Press, Melbourne.

---- 1978b, A theory of universals, vol. 2, Universals and scientific realism, Cambridge University Press, Melbourne.

---- 2005, 'Four disputes about properties', Synthese, no. 144, pp. 309-20.

Broughton, J 2002, Descartes’s method of doubt, Princeton University Press, Princeton.

Fine, K 1991, The Study of Ontology, Noûs, Vol. 25, No. 3 (Jun., 1991), pp. 263-294

Swinburne, R 1995, 'Thisness', Australasian Journal of Philosophy, vol. 73 no. 3, pp. 389-400.

First cause