An overview of Bradley's metaphysics and epistemology, which had much of the basic structure of quantum mechanics, but was all but ignored in the years following the formal quantum theories discovered by Heisenberg and Schrödinger. Bradley's version of absolute idealism was infected with the mentalism that was generally associated with idealism in the late nineteenth century. I develop his ideas from a standpoint somewhat more friendly to modern formal methods, although this is not much of a stretch, as Bradley had already taken absolute idealism strongly in that direction, if not all the way.
Bradley's Absolute Idealism [Bradley 1994] is characterized throughout by an inherent scepticism and belief in the limitations of knowledge. Truth as we apply it in practise is not an absolute concept, but is relative to our own perspective on the universe. Truth consists in the coherence of a system of ideas and judgements. While it is popular today to say that the justification for knowing something is a matter of coherence [Bonjour 1993], Bradley was more extreme than this. It is not just our knowledge that depends on coherence, but Truth itself. Truth in this sense is relative and probabilistic--there are degrees of truth and falsehood. Yet, can this really be truth? Can truth really be truth any more if we take away its absolute character?
We will see that for Bradley, coherence is, in another sense, truly absolute; for it is not the mere internal coherence of a belief system that is taken as truth. It is the coherence of this internal system with an external reality. In this sense, our beliefs and judgements must correspond with reality to be true. This seems like a correspondence theory of truth, rather than a coherence theory. Indeed, Bradley scholars disagree on the extent to which he held one view or the other. In fact, Bradley meshed together correspondence and coherence. To understand this requires an understanding of Bradley's metaphysics. He believed that every possible world, merely by being possible, was objectively as real as our own. So, although in one sense, my internal belief system must correspond to the "real world" of my experience in order to be true, this is only a provisional understanding of what is going on. Since my "real world" is just one aspect of the full Reality, my ideas need to correspond to it only because I fall short of knowledge of the full absolute reality, which includes all possible worlds. If I could know Absolute Reality, correspondence would be there only in the trivial sense of identity: the knower would be that-which-is-known, so in a way there would no longer be any need to correspond with it. Yet, according to Bradley, the idea of an Absolute Knower is nonsensical and impossible. To know something presupposes a distinction between knower and what-is-known. It is impossible to both be the Absolute and know it.
Bradley's Place in History
Bradley's metaphysics, which cannot really be disentangled from his epistemology, is a bridge between the Absolute Idealism of the nineteenth century and the Analytic philosophy of the twentieth [Manser 1983, pp. 1-24]. In his youth, the great Analytic philosopher Bertrand Russell was an avid fan of Bradley, but was to become his most serious critic in later years. Nonetheless, the logic-based approach of Russell and the Analytics was highly influenced by Bradley, and there are close ties between the two approaches. Bradley's philosophy itself is both highly logical and highly informal. He uses an informal logical reasoning with only a smattering of logical notation. While in less able hands, this might lead to superficial conclusions that lack the rigor of formalized logic, Bradley seems to have essentially recognized many of the limitations discovered in later years by formal metalogicians like Gödel, Church and Turing [Gödel 1931] [Hofstadter 1979].
Russell complained that Bradley and other Absolute Idealists (such as Fichte, Hegel and Schelling) tried to reduce metaphysics to mere logic--see [Bradley 1994, pp. ix-x]. For Russell, that may have been a condemnation, but I do not think Bradley would have had a problem with it. Bradley was working in a tradition that recognizes any possibility as an existing thing. The mere fact that it is possible is enough for it to exist. If we assume that logic and mathematics are capable of describing any possibility, then, indeed metaphysics becomes merely logic and mathematics.
I will not spend much time justifying this view, or exploring its subtleties, but will assume it along with Bradley . If it seems just too absurd, I urge the reader to view it for now as a thought experiment--what if all possibilities were real? Could we still have a notion of truth that accounts for our everyday experience? Bradley believes that we can, and that indeed any notion of truth that excludes any of the possible worlds from Reality is inherently inconsistent. This basic argument is not new with Bradley; it goes right back to the ancient Greek father of metaphysics, Parmenides of Elea [Parmenides c475 BC]. In a sense, metaphysics comes full circle with Bradley, back to its roots in Ancient Greece (Bradley's nineteenth century version of the argument is, of course, much more conceptually sophisticated than Parmenides').
After Bradley's death, Absolute Idealism suffered a setback, but similar ideas are becoming popular once again. David Lewis expounds an absolute idealist view essentially the same as Bradley's, but calls it "modal realism" [Lewis 1986]. There is also a striking similarity between Bradley's metaphysics and the "many-worlds" interpretation of quantum mechanics [Everett 1957], particularly versions that employ the Anthropic Principle [Barrow 1986] [Randall 1996a]. In fact, the mathematics of quantum mechanics could be viewed, without much exaggeration, as a formalization of Bradley's metaphysics.
Crucial to Bradley's whole metaphysical argument is his denial of categorical (subject-predicate) propositions, which he splits into three aspects: (1) the abstract idea, (2) the external reality to which the abstract idea refers, and (3) a judgement that evaluates the idea as referred to reality [Bradley 1883]. The abstract idea all by itself may simply be a statement such as "Bob is tall." We will assume for now that the external reality is our everyday world of experience. The judgement somehow applies "Bob is tall" to the real world and determines that it is true or false. "Yes," we say after thinking about it, "Bob is tall, isn't he?" We have made a judgement.
Now it may seem that this is undeniably a categorical judgement. It states that "Bob", a something in the world, is "tall", a feature in the world that Bob has. But Bradley says no, in fact, all judgments are conditional, not categorical. If we say "A is B", it is only because we are being imprecise. "Bob" and "tall" are universals, not particular things in the world [Bradley 1883, ch. 2, sect. 62]. We may like to think that, while "tall" is universal and applies to more than one thing, "Bob" surely is particular. But in fact, "Bob" as an object separate from the rest of the world, maintaining his identity through time, is an abstraction; it takes part of reality and ignores the rest. So judgement brings abstract ideas together into a conditional: If "Bob" Then "Tall".
But this isn't quite right either. For we mean by Bob, the Bob we know in this everyday world of our experience. So the "Bob" universal is highly underspecified. What we really mean is more like "Bob, in this world of experience around us, which we can only partially specify". We are judging that this includes "Tallness". So how do we determine that this underspecified idea of "Bob" includes "Tallness"? We perform a thought experiment. This is the judgement. The conditional part of the judgement--"If Bob in this world, Then"--is more than just a static idea of what Bob is. As an abstraction (and this is crucial to Bradley's entire system), it is necessarily a description of a process. Ideas are not like mental images, static data structures to be manipulated by the mind, which alone is capable of process. Rather, process is abstraction and abstraction is process. "This world" is part of the abstract idea "Bob". Yet, it cannot be a complete, static description of the world, since we cannot possibly know the world so completely. It is an abstraction. In more modern terms, it is a kind of model of the world we contain in our heads, like a computer program , a simulation of the world we can use to test further ideas that we would like to add to it, such as "Bob is tall". The act of bringing together the ideas "my real world" and "Bob is tall" is itself not simply a logical conjunction, but an active process, being itself an idea. In this synthesis, we create a new program, or model, out of the two existing ones. The judgement is the result of evaluating or running the program.
This is clearer for a judgement that is more obviously conditional and causal, rather than categorical, such as "If I drop the egg, it will break." This is obviously causal, involving a kind of mental experiment. But Bradley claims this is what we are doing with all judgements. "I drop this egg" seems obviously hypothetical, because we don't consider it necessary that an egg be dropped. "Bob in this world", however, seems like a simple fact. He is, after all, in the world, is he not? But Bradley would contend that the fact of Bob's existence is as hypothetical, in an absolute sense, as whether or not you drop the egg. It takes much careful analysis to realize what an apparently categorical statement is really saying. "If `Bob in this world' Then `Tall Bob'" is really still not quite right, either. After all, a simple modelling of "Bob in this world" will never tell us that he is tall. Our conditional must contain a test for whether he is tall. So what we really have is something like: "If `Bob in this world' and `Test-for-tall' Then `Tall Bob'". A more formal functional notation might look something like: Test-for-tall(In(world,Bob)) -> Tall(Bob).
Of course, this still isn't really an adequate expression of the ideas in our mind. If we kept filling this in more exactly and rigorously, presumably we would eventually get something like a computer program that could perform inferences based on an internal world model. A judgement, then, is an inference, combining existing ideas to produce new ideas . But the relegation of seemingly "foundational" empirical observations ("obviously" categorical) to mere conditionals, leaves the ontological status of our real world of experience in grave jeopardy. If all our statements about the real world are really simply asking "What if this was the real world...?", then we can never actually judge the real world to exist at all.
Bradley is reducing metaphysics to logic, in the tradition of the Absolute Idealists. Given this philosophical program, we cannot take as given that Bob is in the world, or that our "real world", which is after all an abstract idea, is the one true reality. For the "Bob" example, the condition is what we normally take as given: the real world of experience. But the world of experience, from a purely logical point of view, is contingent, not necessary. Even for a more obviously conditional judgement, like the egg example, the condition being tested is really only a little bit more than the real world as we know it: the "real world" plus the dropping of the egg. The dropping of the egg is a trivial modification to an already hypothetical idea.
One might argue that Bradley is just playing word games, and that his judgements are really still categorical. After all, if "my real world of experience" is hypothesized in every conditional judgement, then are they not by virtue of this fact, really categorical after all? Not really. I can hypothesize something in an imaginary world different from "my real world". In fact, strictly speaking, the case of the egg is just such an example, so long as I decide not to actually break the egg. Here, the external reality that the idea "I drop this egg" refers to is not the real world of my experience, but a hypothetical possible world where the egg is indeed dropped. An idea can hypothesize worlds much more divergent from our own than that. I can judge that "If Hitler had won the war, we'd all be speaking German." According to Bradley, the idea "Hitler won the war" actually refers to a different world than our own--one where the Germans won World War II. Or, I could judge that "Sherlock Holmes played the violin." This refers to the world where a man named Sherlock Holmes, a private detective, plays the violin and has a friend named Dr. Watson. The judgement may seem categorical, but it is a conditional based on the hypothetical world of Sherlock Holmes, for which we have an abstract internal model, built up from having read many Arthur Conan Doyle stories. In fact, most of us would be willing to admit all the above judgements as in some sense true (or false, which is equally to admit their reference to an external reality--if they did not refer at all to a reality, they could be neither true nor false).
But, one might counter, my judgement that Sherlock Holmes plays the violin is true only because my idea of him refers to stories written in "my real world". For the Hitler example, one could argue that Hitler actually existed so my judgement is about "my real world". I am saying that Hitler, in "my real world", had the potential to cause us all to be speaking German, even though it did not actually go that way. I am still categorically attributing this potential to the real world. If the statement was instead about a thoroughly fictitious world, with no prior existence even as fiction in "my real world", I could as easily say the statement was false as to say it was true. For instance, consider an obviously conditional judgement within the Sherlock Holmes world: "If Sherlock Holmes had married, he would have become an artist." Or better yet, consider a completely imaginary world made up on the spot with little resemblance to our own (call it Otherworld): "In Otherworld, things fall up." "In Otherworld, if I drop this egg, it goes into orbit." Surely these judgements, if any, are neither true nor false. Surely the idea "Otherworld" does not refer to any external reality, but only to an idea of imagination in my own mind.
Bradley would see this sort of thinking as totally misguided. If I have an idea "Otherworld", it is necessarily abstract. That means I do not have the particular thing in my mind. I have an abstraction that describes something external to my mind (something possibly much more complicated than my mind). The idea "Otherworld" automatically refers to an external reality, simply because it is an idea, an abstraction. When I think of Otherworld, the world I refer to may be far more underspecified than when I think of "my real world", but there surely are possible worlds that correspond to it. The set of all such possible worlds  that fit my internal description, is the "reality" that my idea refers to. In Essays on Truth and Reality, Bradley puts it this way:
"Every possible idea therefore may be said to be used existentially, for every possible idea qualifies and is true of a real world. And the number of real worlds, in a word, is indefinite. Every idea therefore in a sense is true, and is true of reality. The question with every idea is how far and in what sense is it true. The question is always whether, qualifying reality in one sense, the idea qualifies reality in another sense also. For, true in one world, an idea may be false in another world..." [Bradley 1914, ch. 3, pg. 42]Of course, since all judgements refer to possible worlds that have equal absolute status, the only absolute reality is the totality of all possibilities. The essence, however, of a judgement is to abstract from this absolute reality a part of it--something we take for the real world for the purposes of a thought experiment, though for it actually to be absolute reality would be logically absurd.
Since Absolute Reality includes all possibilities, there should be "worlds" that are not even spatially or temporally extended. A mathematical equation, for instance, is a conditional that assumes as reality whatever mathematical system it is expressed in (such as number theory or differential calculus, for instance).
So let us take stock by looking at the judgements we have considered so far, in order of increasing hypotheticalness  (relative to "our real world"):
"Bob in my world." → "Tall Bob in my world."The arrow represents the "execution" or "running" of the "abstract idea", "thought experiment", or (in more modern terms) "computer program" on the left hand side. On the right hand side is the new abstract idea produced by this process. This procedural aspect of abstraction is of immense importance to Bradley. He was adamant that a view of ideas, such as that of Berkeley and Hume, that sees them as static images before the mind's eye, is untenable [Bradley 1883, ch. 2, sect. 64]. It is process that gives a so-called static mental image meaning and reference. Without a procedure with which to perform a thought experiment, we have no right to say that the idea refers to anything at all. In fact, such a "floating idea" is an impossibility [Bradley 1914, pp. 229-247].
"Drop this egg in my world." → "Broken egg in my world."
"Holmes in Doyleworld." → "Holmes playing the violin in Doyleworld."
"Holmes in Doyleworld gets married." → "Holmes in Doyleworld becomes an artist."
"Drop this egg in Otherworld." → "Orbiting egg in Otherworld."
"2+2 in number theory ." → "4 in number theory."
But Bradley insisted that relations were not atomic, not real "in themselves". A relational structure is static. Objects connected by relations are illusory. You need a process of abstraction to unite two objects into a relation, otherwise, they suffer what Bradley called "fission". Without abstraction, or process, there is really nothing to connect two "related" objects, and we might as well just say we have a single object. For what is the relation, if not another object? But then we need another relation to connect the first relation to the objects it supposedly connected. But then that relation is another object and we need another relation, and so on, ad infinitum. This is "Bradley's Regress" and is a variation on the ancient Eleatic paradoxes of Parmenides and Zeno, [Parmenides c475 BC] applied to relational structures, rather than objects in space-time.
Bradley maintains that relational structures are not "real". They are not ideas . When we look at a relational diagram on a piece of paper it makes sense because the symbols on the paper really represent abstractions, processes, in our minds. We apply meaning from the outside. The diagram below illustrates the "fission to unreality" that Bradley talked about.
Why Relations are Unreal. What is the Difference between a and g?
We start with the relational structure in (a): "Loves(John, Mary)". But of course the words "John", "loves" and "Mary" are not really part of the relational structure, but are just there as reminders to us. So the relational structure, if it exists in the world "for real" apart from our own abstractions of it, might just as well be expressed as in (b): "b(a,c)". We can see that already, the meaning is slipping away. Still, the relational structure itself remains intact. Now, of course, "a", "b" and "c" are just arbitrary labels, as well. And in (b), there is really no reason to say that the relation has anything about it that makes it relational, as opposed to being just another object. So really, we just have three connected objects of different types, drawn in (c) as three objects of different shapes. But what is holding these objects together? If they are just three completely independent objects, then there is no relation anymore. Either we have no structure at all, or we need to say something like "Well, our original diagram was underspecified, so when you consider the relation as an object, you need to fill in more relations, as in (d)." But then, we can do the same thing and consider these as objects, as in (e). So we end up with a regress that gives us, in the limit, an infinite number of completely unconnected objects, as in (f). Of course, there is no point in continuing to draw different shapes, since the objects are now completely unconnected. In fact, if all we have is an infinite set of unconnected objects, why can we not say that there is really just one featureless objects, as in (g)? 
According to Bradley, relations exist only insofar as the objects within the relational structure get manipulated, used, or processed so as to form such relations. The static relations themselves fall apart unless viewed within some larger process. Without process, there is no meaning or reference, and hence no reality, since the complex system of "real" objects might as well be a single object. The Bradley regress is familiar to computer programmers who attempt to represent the world as a static system of related objects. One soon realizes in programming such a system, that there is really no justification for calling the "relations" relations rather than mere objects, unless the relation is used by some kind of procedure that describes how to manipulate the connected objects in a certain way. So a process is needed, or the relational structure will melt away to nothing. 
In a way, Bradley seems to be saying that particulars are not real, only abstract universals are real. But this cannot be the whole story, either, for as we make our concepts more and more abstract (i.e., our procedural model includes more and more possible worlds), finally including all possible worlds, we have then reached a state of complete knowledge. We would then know every possible thing about every possible world, indeed about every possible logical construction of any kind. This is the Absolute. In actual fact, Bradley would say that the progression to absolute knowledge I have just outlined is impossible. Complete knowledge is something we can only hope to approach as closely as possible. But the absolute itself nonetheless exists complete in itself. The fact that no knower within it can ever fully know it says nothing about its existence (see the next section on Bradley's epistemology). In one sense, it seems like the Absolute is the most abstract thing, since it includes all possible things. Yet, since nothing has been left out, it is now actually a particular thing! So here is one particular thing that Bradley is willing to admit as real. Yet, paradoxically, this particular thing seems to be the very height of abstraction. One might say that it is abstraction, as a particular. So it is not particularity per se that Bradley claims is unreal. In fact, the only world that is absolutely real is particular. It is only when we imagine an idea to refer to a restricted aspect of the Absolute, instead of the entire Absolute, that we are talking about something that is not real.
One must be careful in interpreting Bradley's epistemology without considering his ultimate metaphysical position. The fact that I take as real "my real world", for the purposes of performing inferences, does not make it the only reality. In an absolute sense, it is just another world in the infinity of absolute possibility. It is this Absolute that is the truly Real world . So my knowledge of "my real world" is only partial knowledge of the true referent of all judgements, the Absolute. Since all worlds are existent in the Absolute, knowledge is necessarily partial, since we cannot know all the worlds--but not because we cannot know whether the world modelled in our minds really exists out there. Of course it exists out there. Anything at all that can be thought of exists in the Absolute. That is not the source of our uncertainty. We are uncertain because there is no absolute justification for extending our current conscious experience into one possible world and not another. Yes, "my real world" exists out there. So does the world of Sherlock Holmes. What I need to justify, in Bradley's system, is not that "my real world" is the one true world, and that Doyleworld is nonexistent. Rather, I must show that I am justified in inferring "my real world" from my conscious experience, rather than Doyleworld. Yet, I could infer any world, since they are all logical possibilities.
It almost seems like there is no truth at all in Bradley's epistemology, at least none having any bearing on the truth or falsity of judgements we actually make. All judgements are true relative to Absolute Reality. This is Bradley's first notion of Truth: truth as identity. It applies only to the Absolute. Only by restricting our focus to a partial reality is it even possible to make false judgements or be inconsistent. This is Bradley's second notion of Truth: truth as correspondence, or copying [Bradley 1914, ch. 5]. Bradley does not ultimately hold a correspondence theory of truth--he does not view Absolute Truth as correspondence with an external world. But truth can be understood in a restricted context as correspondence. We pretend that our world is the only real one, so truth for us is correspondence with that world, which is truly external to us in the Absolute. Bradley is thus both fully a realist and fully an idealist [Bradley 1893, pg. 485].
Truth as Correspondence approaches Truth as Identity in the limit.
The first notion of Truth, while absolute, lacks some features we normally associate with truth. There is no room for falsehood, negative judgement or contradiction. All judgements just are. There is nothing about them to make them true as opposed to false. We start with our immediate conscious experience, what Bradley calls our "finite centre", and we perform inferences to get a construction that we call the "real world" [Bradley 1914, ch. 6]. But, unless we take one world as special over the others, there is no negative judgement [Bradley 1883, ch. 3]. In negative judgement, we consider the world inferred from our finite centre as all there is. Then, we can say that a judgement is false. One of Bradley's key insights was that this second notion of truth/falsehood requires a "higher level of reflection" than the absolute notion of truth without falsehood. Since we are taking one world as real (true) and the others unreal (false), we must perform inferences--thought experiments--that have within them the high level idea of what is true as opposed to false: a theory of what correspondence is. The first notion of truth does not require this higher-level cognitive criterion--all judgements just are true. There is no correspondence; ideas just are what they are: part of the Absolute. Contradiction and falsehood are impossible. The first notion is an identity theory of truth, the second a correspondence theory.
So what is this "higher level of reflection" we use to judge truth? And, if imposed at a higher cognitive level, is it not therefore subjective and relative, and not absolute? How can a subjective standard possibly define "truth", when our very idea of "truth" is of something absolute?
Bradley solves this dilemma nicely. Truth, he says, is coherence. The ideas I infer from my finite centre correspond to a real external world. Which world? The one, says Bradley, that has the most coherence with our finite centre. For Bradley, coherence is much the same as it is for Bonjour: a consistent, highly interconnected set of inferences with predictive, explanatory power [Bonjour 1993]. Inconsistency is, of course, impossible in the Absolute, but for a partial world, it is important. But we must always keep in mind that, in Bradley's system, falsehood and inconsistencies exist only on a higher cognitive level. Our minds decide arbitrarily that the judgement carried out corresponds to things in a partial world. There is no inherent property within the system of judgements itself that makes this correspondence special. Correspondence, and degree of coherence, is "language-dependent", and hence ultimately as "unreal" as a relational structure. Only the total complete coherence of the Absolute is language-independent. The particular private language in which my ideas are expressed, determined by my finite centre, will determine the relative degree of coherence. The only truly coherent thing is all of Absolute Reality. So coherence, for Bradley, includes comprehensiveness. An inferred partial world is more coherent if it subsumes a larger segment of the Absolute.
Another way to look at it is that the most coherent world is the one whose parts are most successfully unified into a whole (i.e., the one that can best be represented by an abstraction, best modelled by a procedure). But any abstraction short of the Absolute will ultimately not be enough, since something will be left out of reality. Short of the Absolute, then, truth is relative (truth of the second kind), but the standard is still absolute (truth of the first kind). So it is impossible for anything in my mind to correspond to the totality of absolute reality. Only a partial reality can be represented in my head, since as the observer, I myself must (at least) be excluded from "reality". This is a fundamental point at which Bradley departs from his predecessor Hegel. Hegel believed that the Absolute was Absolute knowing, and that it could "know itself"--be the subject and the object of its own thought. According to Bradley, this is incoherent.
Knowledge requires more than truth, it requires a division between knower and that-which-is-known. This division is itself an abstraction, and is not ultimately real. The knower gets "swallowed up" in the Absolute. Such an observer would have to step outside the system and view the Absolute from a further, more objective stance (at a higher cognitive level). But there is no higher level at which to view the Absolute. If there were, the Absolute would be incomplete and would be Absolute no longer. As we go from partial reality towards total Reality, truth becomes less a matter of correspondence with an external world, and more a simple matter of identity: the truth just is. This is ultimately what truth is. The partial, correspondence theory of truth is a necessary, and useful, tool, but can only properly be defined as something that seeks to approach as closely as possible the unreachable limit of Absolute Truth .
Short of absolute knowledge, we seek to build from the arbitrary starting point of a finite centre, a highly coherent partial world--one that can be simply described in a procedural process, and, Bradley adds, is comprehensive, taking in as much as possible of the Absolute. Comprehensiveness must be included in coherence, since a well-modelled world is a comprehensive one [Bradley 1914, ch. 7]. Coherence and comprehensiveness--or system--is the test for perceived and remembered (i.e., partial) truth.
To get anywhere with the process of inferencing, posits a self and not-self. We must artificially split the world into real and imaginary. This truth--partial, but the only kind that can have anything to do with practical knowledge--is necessarily fallible. For who says that this world is the real one and the world of Sherlock Holmes is not? In fact, when I judge that "If Sherlock Holmes had married, he would have been an artist", I refer explicitly to a world with less coherence than my own. But it too, is external to my mind (and my contention that it is "less coherent" is dependant on my choice of language, which already assumes my real world of experience as a starting point). Bradley, while an idealist, was also an ardent realist. If I take all the facts that I "know" concerning Doyleworld, I can build a model in my mind, an abstraction, of this world. The more comprehensive I make it, the better it corresponds to the "real" Doyleworld. But, you may protest, since this is an imaginary world, how can I say there is an external standard by which my model can be judged? I think Bradley would say that, really, your model is not judged against the external standard; rather, the external partial reality is judged against your model. Doyleworld is not something in your head. It is the external world that best corresponds to the mental abstraction that is in your head. Such a world is as certainly beyond your grasp to fully know as the real world of experience. So, in a way, it makes sense after all to judge what would have happened if Holmes had married. Yet, Doyleworld is so underspecified, that it really corresponds to what we would more naturally think of as a whole set of equally coherent possibilities. The number of coherent worlds in which Holmes gets married and becomes an artist may equal the number in which he gets married and does not. But if there is a majority of Doyleworlds where our judgement is correct, we are justified (even if we cannot know that we are justified) in making the judgement. But our justification is partial and probabilistic. The judgement is true, perhaps, in 60% of Doyleworlds.
Even then, this 60% figure is again dependant on our choice of language, since judging these different particular Sherlocks as the same man is an arbitrary abstraction. Remember that, according to Bradley, only particulars are real-but the only particular that can exist on its own is abstraction as a particular (the Absolute). Any particular abstraction is, on its own, ultimately as unreal as a static relational structure. But since complete knowledge of the Absolute is unachievable, we use our finite centre to construct something that is, on our own terms, as close to the Absolute as we can get. But from an absolute perspective, there simply is nothing special about any of the worlds, nor any preferred way to group the worlds into classes (such as "worlds-with-Sherlock-in-them").
Anyone who has ever listened to a group of Star Trek fans discussing the Trek world knows the lengths to which some people will go to coherently and comprehensively model an imaginary world. Inconsistencies between shows are ironed out by positing further modification to the model of Trekworld. These fans are "world-building"--doing just what physical scientists do with our sensory world when they build theories. But no matter how hard the fans try to build a coherent model of it, Trekworld will almost certainly be far less comprehensive and coherent than our world of experience. Trek-judgements will have a more probabilistic nature than scientific statements about our "real word". But this is a relative standard, and by no means indicates that the Trek-world is "unreal". If it is thinkable in a clear and distinct way, it is real in an absolute sense. But Bradley recognizes the pragmatic necessity of partial truth. And from this point of view, we can, in everyday language, assume that the most coherent world is the real one, and so we are justified in speaking imprecisely and labelling Trekworld "unreal". From our point of view, it is "less real" than our world, since it subsumes less of Absolute Reality.
Our world and its neighbours.
My own view is more in line with the twentieth century notion of the mind as a computer program, an epiphenomenon of underlying mechanistic processes, themselves completely nonmental. But we have seen that mechanism, exemplified in the computational model, is fundamentally abstraction. Where Bradley would say that computation is thus already somehow mental (even if there is no particular mind involved), I would say it is purely mathematical and nonmental. Mental phenomena do not appear until we get to the higher cognitive level at which negative judgement is possible. Yet Bradley quite rightly points out that without this higher cognitive level, there is no justification for correspondence. So human finite centres, containing such a higher level, provide their own justification for their view on Reality and their standard for coherence. The higher cognitive level used to impose truth/falsity on a purely formal, nonmental system, must come from outside the system. Only a conscious, rational system provides its own internal coherence standard, or language. Even then, it is a purely subjective and relative standard. The absolute just is, requiring no standard of correspondence with something else.
My view is ultimately somewhat different than Bradley's. He views Experience as the fundamental stuff of existence. I view Computation as more fundamental. Under my view, the word "idea", as used throughout this article, is completely nonmental. It is "what can be thought", not "thought itself". Bradley would probably say "Perhaps, but computation, like all abstraction requires Experience first before it can make any sense." To this, I can only say that whether Experience or Computation is more fundamental, we cannot settle with certainty until we have a more complete theory of mind, but since Bradley means by Experience the principle of abstraction, and I mean by Computation the principle of abstraction, it is perhaps not that relevant which intuition is more correct, if either . In both cases, we must ultimately be sceptics and admit that abstraction is a first principle that we take on faith, because it appeals to the intellect. It is a principle, in short, that I just cannot help but feel in my gut encapsulates the essence of what it is to be possible--which is to say, for an Absolute Idealist, what it is to be.