Sunday, December 30, 2007

On denoting and the laws of thought

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.

7. On denoting

A note for the faint at heart.
The following section is not strictly necessary for the general reader. However the more hard bitten among you will be aware of a problem in denoting things. For example, Bertrand Russell noted that one might say that the present king of France is bald. Under our wonderful logic, he either is or is not bald. But of course, there is no present king of France. The GPE enables us to consider a more neutral view, for we know that it is infallible, where the laws of thought (laws of logic) hold merely the status of being self-evident. And self-evidence is no solid foundation. Not so long ago it was self evident that time was as steady as a rock - then came Einstein.

My aim is to show that implicit within a rationalist Cartesian view, the oddities of formal logic may be overcome.

Russell on denoting
The challenge of denoting properly is considered in depth by Russell (1905). Other theories of reference and contributions have been advanced by Meinong, Frege, Mill, Devitt, Kripke, Strawson, Putnam, Quine and others (Reimer 2006), and fall into three categories – descriptive theories, causal theories, and hybrid theories. This has led to a lively discourse that is not essential to this development. It has been argued that Russell’s theory is at best incomplete (Donnellan in Reimer 2006), but this is not an aspect that is important here. I select Russell because it provides a useful background to consider the problems of denoting to enable me to develop a form of denoting that permits the Cartesian meditator to refer to omnets in a way that is not reliant on presupposition for certain cases.

Russell (1905) holds that the subject is of importance in logic, mathematics and the theory of knowledge, because it is denoting that permits access to certain kinds of knowledge. He considers the example of a reference to the centre of mass of the solar system at a definite instant as a definite point. He identifies that while we can affirm propositions about it, we have no immediate acquaintance with the point, which is known only by description. He holds that the distinction between acquaintance and knowledge about something is ‘the distinction between the things we have presentations of, and the things we only reach by means of denoting phrases’, (1905, n.p.). I agree, and note that in the Cartesian system our denotation of omnets and assets is not founded on acquaintance with any particular, rather it is founded on knowledge of the system.

For the Cartesian meditator, acquaintance is cut off. Presentations cannot be trusted. Knowledge of the world is important rather than acquaintance. Certainly, there is no way to determine, from the World-of-Seeming, whether an idea is a proper copy of its subject, which is an expression of internalism and the E\O divide. Yet we can know about the General Principle of Equivalence noumenon, and its necessary existence.

For Russell (1905), certain phrases denote unambiguously, although we have no acquaintance with what they denote (their referents). In the idea of omnets and assets, we find an echo of this, in that we recognise that whatever we have under consideration denotes an omnet at some level, within the domain of discourse. For the Cartesian meditator, the nature of acquaintance is not trustworthy. It was this that reduced the problem of self reference in Section Examples exist all around us, yet the real nature of these omnets does not carry into empirical understanding. For Russell (1905, n.p., his emphasis),
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, ‘ 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.

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.

6. Boundary conditions of the world – the Cartesian view.

Given the problem of bundling previously mentioned, the meditator seeks to find a world that can hold together in some complex form. Is a complex form possible? One place to start is to consider boundary conditions, conditions that can only be the case, with which the domain of discourse (the world) must conform. We note several constraints that apply to the ontology necessarily.
1. Any variation in assets expresses a different omnet (by the General Principle of Equivalence).
2. There is only one Totality, because any variation would imply a difference in assets (follows from 1).
3. The Totality and everything within it complies with the General Principle of Equivalence at every level.
4. Only the General Principle of Equivalence has the power to bring compresence to pure assets, pure assets lack this power in and of themselves (previously shown through the problem of bundling).

Because these follow from the General Principle of Equivalence, they are not axioms. Rather, they are necessary truths, boundary conditions that may stand in for axioms.

As meditator, I am concerned about these truths. In the first instance, does not item 1 imply that the world cannot undergo change, as Parmenides and Zeno argued? I find myself flung into a state of empiricist denial. My refuge, as Cartesian meditator, is to say that the necessity of these truths suggests that my understanding of the Totality is not well formed. Regardless of the duality between the presenting world and Item 1, I cannot deny the truths so presented because they are as indubitable as the General Principle of Equivalence which gave rise to them. In the positive, the existence of this duality of interpretations is useful, because a logical theory may be tested by its capacity for dealing with puzzles (Russell 1905).

To explore the implications of the boundary conditions on the Cartesian system (the system of omnets and assets that present to the Cartesian meditator), I aim to develop a means of referring to the system of omnets, and a means to test supposed qualities of this system. If my terms do not properly denote, or are not constrained by the General Principle of Equivalence, further effort may founder on a lack of exactitude. The first task is to develop a system of denotation, the second to develop a form of logic to stand in for the Laws of Thought. I do this in the next blog.

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

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.

8. Something from nothing.

Can there be an empty world?

NOTE: THIS PAGE IS NOT QUITE FINISHED AS I NEED TO INSERT SOME SYMBOLS. Also, I am working to explain the abstractions better

To start at the very beginning, I use the ideas of denotation covered in the previous post. For those who found that heavy going, don't sweat it.

When I consider an empty world, I am presupposing that my idea of there being just nothingness and nothing else, corresponds to some omnet of the Cartesian system. If there is no such possibility for the existence of an empty world, by implication from the General Principle of Equivalence, then that denotation does not carry, it does not express an actuality of any world. That is, I can dismiss it as a candidate for acceptance as an element of my actual ontology. I might even have shown that it has no place in a possible ontology.

Under the General Principle of Equivalence, an empty world is still a possible world. Because it has all its assets, at least the asset of being itself or none other than itself, then should there be an empty world, it at least has unique identity. If there is an empty world, it certainly meets the criteria of being a pure asset, for it cannot be further reduced.

This concept of identity is non-vague in an ontological sense, because an omnet of nothingness has all its assets, which is a boundary condition that the General Principle of Equivalence expresses directly, and even the idea is bounded: one cannot conceive of it having a non boundary without first presupposing some form of dimensionality into which it could extend, but this would be wholly inconsistent with the idea of an empty world. This boundary need not be equated with a physical boundary. A boundary condition implies a boundary. Let the fact that it has identity be that boundary condition. If there are other boundary conditions such as a lack of extension, this does not add to or take from the concept.

I want the reader to re-read the above, for it is not an easy concept, but the concept applies to all omnets, not just nothingness. Only once this boundary concept is properly understood should one progress. Just as is done in mathematics, where we begin with a set of objects that might be counted, then get the idea of number, then remove the objects altogether and retain the idea of number, so is this boundary concept. One cannot properly gain a concrete idea of the boundary, and it is both unnecessary and dangerous to say that the boundary is like this or that. Rather, leave it as a term that refers to an asset of each omnet. Know only that every omnet has its assets, and this implies that it is whole, and as such it is complete. This completeness, no more than an expression and implication of the GPE, implies that there is a metaphysical point at which what a thing is, runs out. There need be no 'outside' the boundary, for indeed there is as yet no foundation shown for dimensions. But there is a boundary, and boundary is just the name given to this particular facet of the GPE as it acts on what is.

(A note for physicists: I am not talking about boundary and no-boundary conditions used in cosmology here, that is a wholly different idea that presupposes space, time and who knows what else. The idea is abstract, but the structure is an actuality of all omnets.)

(A note for philosophers: Some of you will hold that my idea of nothingness is wrong, for nothingness is the absence of any particular. Firstly consider the idea of omnets nominally, and hence that the term stands in for nothingness as much as anything. Secondly, apply your own brand of skepticism - this should lead you to see that making a distinction between nothing and something as being somehow different to the distinction between something and some other thing is a very odd supposition. The Cartesian meditator finds all are suspect, so none has the preferred view until it is tested by some strong principle. That principle is the GPE, which stands king.)

If the rules pressed on us by Sorensen’s metaphysician hold (see earlier posts), it rests with those who object to now show how there can be no boundary. Having such identity, the empty world is bounded, and together this forms the minimal possible world.

The boundary of a boundary.

Now, a boundary, simply being a boundary, without needing to know its ‘internal’ nature, knowing only that it has some positive existence, frees the meditator from the need to make comparisons with some presupposed meaning created in the World-of-Seeming. The meditator can assert that for the presupposition of there being an empty world, this is not possible, because there must be at least a boundary, as omnet. Hence we find no support for the supposition that there can be nothing and only nothing. Utilising our earlier symbolism, we can denote this absence as /nothing, meaning the denotation of the presupposed nothing does not express a reality.

Cause and effect
But now comes cause and effect. A boundary, being a boundary, and for which no understanding of its ‘internal’ nature is important, also has identity under the General Principle of Equivalence. So it too is bounded. This leads to an iterative generation of boundaries.
Let '>>>' be a relation of consequence following from the General Principle of Equivalence. Then


where N represents the number of iterations and {} represents a boundary. The idea of one dimensional space is not intended here, for space hasn't been shown to exist yet, just that there is a structure. I will return to the concept of number later and will discuss the meaning of the symbol 0, as well as what this symbol denotes, for reasons that will become clear later. In the interim, note only that the symbol 0 need not represent nothingness - it can represent any pure asset. The claim that the boundaries come into being is iterative, is supported by the recognition that a boundary cannot be bounded until it has some basis for existence, so in this way, each boundary has ontological priority over that which bounds it. However, a second view is available, that the converse is valid, meaning that for a boundary to have identity it must first be bounded. If so, then this implies an infinity of boundaries all at once. Which is the case? This matter reduces to ontological dependence, which I will discuss in my next post.

On the structure available to possible worlds.

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.

5. On the structure available to possible worlds.
Having set up an appropriate and sturdy ontology that conforms to the Method of Doubt, and identified that there is a challenge relating to the bundle view of properties, now the meditator is in a position to reconsider the Cartesian system, namely, the General Principle of Equivalence and other possible elements of the ontology. Let us note some aspects that we don’t yet know about the system.

Firstly, while we have identified a problem for bundling, this does not mean that there are no bundles. The system certainly may be bundled, and it may be bundled into a whole. Our challenge is to find how this bundling might be brought to the system, given that the Totality admits no change to the Totality. A trivial solution is that there is just one bundle, the bundle that is the General Principle of Equivalence. Of course this does not account for the meditator, except in the unusual solution that the Meditator is in some way an expression of the General Principle of Equivalence.

Also, we don’t know how many assets there are. The idea of none, one and many, a foundation for concepts of number, remain as supposed denotations (ie words that refer to supposed things) of a state of affairs in the Cartesian system, presently only a part of the possible ontology (see Building a Sturdy Ontology) . A hope is that with further investigation, this idea of none, one and many may gain better meaning. By anchoring terms in the system itself, as is implied by the conditions of denotation, what we seek is to find a synthesis of meaning that provides a singular understanding of each term in the context of the system.

In so doing, we will be in a position to determine some particulars about assets of the system, which for the Cartesian Meditator seem, at least at the outset, to be windowless. By ‘windowless’ I mean that to somehow actively sample a pure asset, as we might do with a chemical, is denied us. To do so would affect its status of pure/minimal asset, which is contradictory to the General Principle of Equivalence.

Lastly, we don’t know the position of the Meditator in this system. For surely there is a Meditator, as part of the Totality, and denial of the Meditator has been proven to be impossible under Cartesian doubt, as was argued by Descartes (Broughton 2002; Descartes 1995, 2003). This aspect must be left until last, and can only be answered in a simplistic form for the present. Loosely, here stated without proof, and only because I know where this blog is going, the answer is that the Meditator exists as an evolving part of the Totality. The Meditator is a finite and connected series of states, each iteration of which is driven by the action of the GPE noumenon (the condition of the world that the GPE models).

In essence, we don’t yet know any particulars of the world. A place to start is to consider the possibility that the world is in fact empty. I do so to examine whether the methodological principle that propels the empty world to the top of the agenda (Sorensen 2004) is valid.
Sorensen explains the idea (2004, n.p. his emphasis) :
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.

Sorensen, R 2003, 'Vagueness', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Fall 2003 edn,

---- 2004, 'Nothingness', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Spring 2004 edn,

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


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.


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.


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.

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.

Thursday, June 28, 2007

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.


Principles of equivalence are the most important to the disciplines of physics, mathematics and philosophy. In mathematics this is embodied by the Axiom of Identity: A = A. In philosophy it is represented by the first law of thought: what is, is. In physics to have an equation requires that there be an equivalence drawn. For example, one equation is that force equals mass times acceleration, or F = ma. What are we saying here? We are saying firstly that if we know a body's mass and its acceleration, given various units, then we will get a number with a composite unit (in this case Newtons) and the equation remains consistent for all masses and accelerations (let's leave Relativity aside for a while to keep things simple - the concept remains the same).

I am going to show that the most general principle of equivalence is also a model of First Cause. In advance I am going to name this principle the General Principle of Equivalence, and abbreviate it 'GPE'. By 'a model of First Cause' I mean that the proposition I am going to enunciate has a correspondence with a global condition of the world, that is it holds for everything in the world, at every level. By 'the world' I mean whatever there is.

Most importantly, if you want to be certain of your understanding, it is of highest importance that you assume nothing about the world beyond that which is certain in an absolute sense. Absolute knowledge of how the world is ('in itself') is not supposed to be possible according to present philosophy, so this is a rather cheeky supposition, but I'll leave to to decide.

So, for a while, set aside your expectations that there is a computer screen before you, that you have hands with which you type and so forth. Descartes dealt with this and I won't waste your reading time going over his work in detail here. Know only that he showed that one can be completely certain of one's own existence ('existence' being just that you are - which you will soon see follows from the GPE). Further, understand that the reason you can be certain of your existence is because you have no basis to doubt it.

Janet Broughton (2002) discusses this. She points out that the reason one can be certain of one's existence is because, to doubt, one must have a reason to doubt. It is not enough simply to say 'I doubt', for this is not justified, it is just a statement. Nevertheless, virtually everything can be doubted. One might be dreaming, or hooked up to The Matrix and deluded. By this hyperbolic doubt most of the propositions one might make about the world are suspect.

But one cannot doubt a proposition (meaning a set of words that proposes something about the world) if the doubt itself relies on the truth of the proposition for it to be a well-founded doubt. Otherwise the act of doubting undermines the doubt, and supports the initial proposition. So, in Descartes's case, 'I think, therefore I am,' is indubitable because to doubt this, I must exist, otherwise I could not be engaging in the act of doubt. Hence there is no proposition that I can utter that can undermine that proposition. This is good, because it gives me a place to stand, a place from which I cannot be shifted into oblivion.

Now 'I think, therefore I am' is the most particular proposition. It is the center of one's world, but says nothing of the world beyond oneself.

The other proposition is at the absolute other end of the spectrum. To write it with proper meaning requires that I take my perspectives out of the world. Kant talks about these perspectives, and took a long time to say it. In extreme precis what he said was that one cannot know the world-as-it-is-in-itself (as opposed to the world as it seems to be to us) because we see the world through the lens of the mind. For example, the way I see the world, interpret the world, is vastly different to the way an electron might see it. An electron has a more natural interpretation in reciprocal space or phase space and when I use equations to study its motion they are easier to work out in these other spaces. Which space is 'real'? Under the GPE it will become clear that all such spaces are just different interpretations and equally valid given certain conditions that apply under the GPE.

To get around this problem of the lens of the mind, one must take one's perceptions out of the system entirely. Simply this. If I talk about 'things' most people immediately tend to think of objects. You may have a broader view than just objects, and might be thinking mathematically, using 'elements' of sets. But there is no guarantee that this is a proper view. There may be things in this world that humans can never know of, and have no physical or mental condition to be able to be aware of them. Some (many) naturalist philosophers (for example Colyvan and Armstrong) argue that we should believe in only causally active entities, that is, if something has no action in the universe, it may be discarded. I understand why they might think this way, but philosophy has reduced to opinion these days and hasn't moved a half pace forward since Descartes.

To circumvent the problem of the lens of the mind, I introduce a new term:

Omnet - An omnet is a term that refers to anything at all, whether we have prescience of it or not. A soccer ball is an omnet, even if it is just my idea of a soccer ball. So does a flurgal. Now I have never heard of a flurgal, and have no knowledge of what it might refer to other than the term itself. Yet it is an omnet. The whole point is that I make no assumptions about what is. I may refer to 'omnets' (plural) in the future, but let omnet be singular or plural without judgment as to which applies. We don't have a basis for considering singular or plural as yet. Mathematics is as yet unsupported.

I want to make a cognitive distinction within omnets. That is that at present all omnets are just possible omnets, meaning omnets that possibly exist in some reality. Some of these may be found later to be well-founded omnets, meaning that there is well-founded reason for us to believe in certain omnets. Unfortunately, at present we can't know which are well-founded, because the evidence of the senses is not sufficient, for the reasons described by Descartes.

For those familiar with Descartes work, I wish to add a caveat. I do not accept all of his reasoning and especially the major body of his conclusions at all, for they were not well-founded. Rather, I accept only Broughton's interpretation of his method of doubt, and not her conclusions either.

So, the world is omnet(s). Let me add a further term:
Asset - An 'asset' is any omnet that an omnet has. So, if a chair is an omnet, it assets might be its legs, back, seat. Or it assets might be its color, mass, shape etc. The fact is that I have no basis for knowing what its assets are at this stage. Its assets might be its atoms; who knows? It doesn't matter because I again leave the term as wholly unspecified other than that asset are what omnets have.

I can now formulate the General Principle of Equivalence:

Every omnet that has all the assets of that omnet is that omnet.

The condition of having all and only one’s assets, then, holds implicitly that the identity of an omnet (what an omnet is) is founded on its assets (what an omnet has). As developed, ‘identity’ is the condition of having all one’s assets and none other than one’s assets. What it means ‘to have’ one’s assets, is based on the ontology (the study of what it means 'to be') of the system. I place a restriction on the terminology that what an omnet is, is conformal with what an omnet has, such that if there is some place where the two do not conform to the same place in the language, or one’s idea of it, that the meaning of ‘is’ and ‘has’, implies a different meaning not intended here. This paragraph may be confusing for some, and is not important if you can see what the statement means and that it captures all possible worlds.

I named the above proposition ‘The General Principle of Equivalence’ because it describes the basis for notions of equivalence and inequivalence, in so far as the complexity that ‘what is’ has, corresponds to equivalence and inequivalence (similarity or difference) of assets.

Why the GPE is immune to doubt.

As mentioned above, up to the limits of rational discourse, to doubt, one must have rational grounds for doubt, even if these are radical or ‘hyperbolic doubts’ (Broughton 2002; Newman, L. 2005). Such doubts include for example those put by Descartes: the dream argument, the evil genius argument, the lunacy argument and the fate or chance argument (Broughton 2002). However, even if one addresses each argument in turn, there is no guarantee that another basis for doubt will not be raised at some future time, unless all such arguments are struck down universally, so that there is no possibility of raising rational doubt.

The great value in Broughton’s interpretation of the foundation of Descartes’s method of doubt, whether this was what Descartes meant or not, lays in the recognition that one is not justified in holding a doubt about some proposition if that doubt relies on the truth of the proposition for the doubt to be valid. So, if there is a proposition upon which every possible act of doubting relies on the truth of that proposition, than that proposition is immune to doubt, and the Cartesian Meditator is honor bound to accept it as a necessary truth - a model of an actual condition of the world (see Building a Sturdy Ontology for rules of acceptance).

The indefeasibility of the General Principle of Equivalence follows directly from this. For any doubt to be valid, it must at least be internally consistent, which requires as a minimum that as an omnet the doubt must at least have all its assets, and only its assets and nothing different from the assets it has (which by the construction of the founding terms is all that such a doubt can be). In this way such doubts require that the General Principle of Equivalence be true. Then a doubt relies upon the General Principle of Equivalence and is self defeating. As such, the GPE is immune to Cartesian Doubt. It is transcendent of doubt for no doubt can be properly raised against it.

Further, because all that is, is an omnet, the idea holds globally - there is no 'outside the system'. It is a universal truth.

It is upon the GPE that I intend to build my case. The fundamental shift is effected by trading reasonably assigned, but not well-founded meanings, such as things and properties (as based on the evidence of the senses), for the global non-specific omnet and asset, that refer to all that is, but makes no supposition as to what the nature of the world is (for example the suppositions that attends the idea of substances and attributes) beyond that expressed in the statement itself.

Such universality and apparent triviality has been previously held to be blighted by the ‘fundamental ontological trade-off’ (Swoyer 2000, n.p.): that a simple but believable ontology (meaning proposed idea of what there is and how it is) seems to have a poor explanatory value, as compared with a rich ontology having great explanatory value, but in which it becomes difficult to believe in the ontological ‘machinery’. This trade-off falls away if a simple founding ontology has sufficiently broad implications. Then, by establishing the most global proposition – the General Principle of Equivalence – beyond Cartesian doubt, everything that follows from it may be rightly viewed as a reflection of the way the world is.

To continue further, we need to provide a system that is supported by the GPE. This will enable a sturdy ontology. Then we can consider the nature of the world, and will find that the world has a unique beginning.

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

Newman, L 2005, 'Descartes' Epistemology', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Summer 2005 edn,

Swoyer, C 2000, 'Properties', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Winter 2000 edn,