Forthcoming in R. Casati, B. Smith and G. White, eds., Philosophy and the Cognitive Sciences. Proceedings of the 16th International Wittgenstein Symposium, Vienna: Hölder-Pichler-Tempsky, 1994.
1. Psychoontology is the ontology of the psyche and of related matters. Hence, by definition, it is a case of particular and applied ontology.
2. Here, following Leibniz’s idea, ontology is defined  by its characteristic question: How is possible? More exactly: How is x possible?
Now, the level of generality of a given ontology depends on the generality of its characteristic question, i.e. on the scope of the variable x. If it is the most general of all, we obtain the general ontology, which is the study of the following, most general, version of the ontological question: How is what is possible, possible?
To answer it we must provide a reason for being possible as well as a framework for the study of the ontological space of all possibilities. 
3. Particularizations follow by specification of the range of x.
For example, by asking: How are facts possible? or How is the world possible?, i.e. by searching for reasons for the existence of the world, its mechanism and basic principles, for sources of its regularity, we define metaphysics which, by definition, is the ontology of reality.
To be clear, description and investigation of the world is a business of science, whereas investigation of its basic and the most general principles is a subject of metaphysics.
4. Psychoontology is even more specific. It concerns the specifically human part of the world, the realm of human beings understood as wholes composed of, inter alia, their psyche and body.
The following questions are therefore characteristic for psychoontology: How is a psyche possible? How is cognition possible? How are soul-body or mind-brain connections possible? How is consciousness possible?, and so on. What, however, do these questions mean?
Leibnizian questions, to be sure, sound strange to laymen.
5. Take, for example, the second question on our list : How is cognition possible?
To understood it we need, first of all, categorization. Cognition is: 1. a relation (of which arity?, which objects are related?); 2. a process (of what type?); 3. a transfer or processing of information. What more?
Now it is clear that a proper framework for the investigation of cognition must include at least all the above items: relations, their arguments, i.e. subjects and co-subjects (things? situations? facts? persons? institutions?), processes, transfer itself, and information.
By such a descriptive and conceptual analysis we obtain a quite complicated domain which is organized in some way. Its investigation is a business of the cognitive sciences, including a suitable applied ontology.
To illustrate: In science we are interested in laws governing information transfer, in technology – in rules enabling us to transfer information economically, whereas in ontology we search for these components and features of the world which makes such transfer possible.
The psychoontology of cognition deals therefore with the most basic part of this investigation, i.e., with the mechanism of the field under investigation, with that which makes cognition possible, with the most primitive components and the most general principles of the cognitive universe.
6. Psychoontology is not a new subject. It has an at least three-hundred year old tradition starting with the Cartesian problem of psycho-physical connection and growing through the great contributions of Descartes himself, of Spinoza, Leibniz and Kant, and in the last two centuries through the works of many philosophers and scientists.
The paper’s title seems thereby to be misleading, producing the false impression. Why Towards?, if psychoontology is, in a sense, already flourishing?
The reason is simple: For further progress we need an exact, formal, complex and sophisticated psychoontology. But, unfortunately, contemporary psychoontology is not sufficiently developed for this to be achieved.
7. We are still in need of a general ontological framework in which the basic notions of psychology and of the other cognitive sciences can be defined clearly and rigorously, thus enabling a formal machinery in which psychic phenomena emerge in a natural and clear way.
Expressing our task by means of an example: we should be prepared for formal discussion and development of the ontological content of standard books in the field, like K. Popper’s and J. C. Eccles’ „The Self and Its Brain”.
8. Usually, such an apparatus is borrowed either from physics and from the other natural sciences, or from mathematics, logic and informatics, or from humanities, and then applied to questions of psychoontology.
Such a starting point was, however, produced for other domains, with different reasons in mind. In most cases it is too narrow, and hence improper. For example, use of the ontological apparatus prepared for the ontology of physics, which is a part of metaphysics, usually ends with the well-known and notorious difficulties of physicalism.
9. To overcome these difficulties and similar shortcomings we must rethink ontological questions of psychology, find a more general and hence more natural and proper formal apparatus, and next develop, step by step, logical psychoontology.
This should not be done against tradition. On the contrary, we should borrow, as much as is reasonable from the ideas of the old masters, reshaping them to meet the present standards.
10. The above task can be realized in many different ways, which in extremis even seem to be incoherent. The reason is simple: There is a large number of types of ontology, which are so different that they must produce differences in description and explication.
In what follows, I will try to outline several clues leading to combination psychoontology, i.e. psychoontology based on combination ontology.
11. Let’s start with a remark concerning what is likely the most popular post-Aristotelian ontology of things and properties. Clearly, it is a descriptive ontology. In its way of looking at the world, everything is classified with respect to the basic relation connecting things with their properties. Therefore, everything is either such-and-such a thing or such-and-such a property or, in some cases, both.
Therefore, for post-Aristotelian (or, more specifically, post-Brentanian) psychoontology the basic question is to find an adequate definition of psychological properties (and things). Basic psychological and cognitive notions have also be defined in this framework.
Take, for example, a mind.  Is it a thing? Which one? Or, is it a property? Again, which one? In general: which properties (things) are psychological? 
Quite a lot of obscure questions. Difficult to answer even for the most serious Aristotelians, like R. Chisholm.
12. Consider now an example taken from Wittgenstein’s Tractatus. A thought is defined there twice:
in thesis 2: A logical picture of facts is a thought; and
in thesis 3: A thought is a proposition with a sense.
One conclusion is immediate:
(1) A logical picture of facts is (or equals to) a proposition with a sense.
What more? If we really want to catch Wittgenstein’s idea we must answer several fundamental questions concerning Tractatus: What is a fact? What is a picture? What is a proposition? What is a sense? What is a configuration? What is its structure? What is its form? What is form in general? What is logical form?, and so on.
In the Tractatus they are explained informally in terms of the Tractarian version of combination ontology, which is rather obscure. Its clarification and full understanding needs therefore a formal development of the general combination ontology with a discussion of its Tractarian peculiarities.
13. Assume that with respect to the primitive relation simpler than all objects are divided into two families: simple objects, called elements, and non-simple objects, called complexes. The chief idea of combination ontology  is that complexes are combinations built up from simpler objects according to their internal traits, determiners.
The traits of an object constitute its form. By the fundamental idea of the combination ontology everything goes because of form. In particular, form determines all possible combinations in which an item can be involved, and – in the case of a complex – form determines the net of bonds fusing its components into one in such a way as to form a whole.
14. Combination ontology is a rather complex enterprise. It is, in fact, an advanced and complex theory of analysis and synthesis.
Its starting part is therefore a general theory of analysis and synthesis, in which the ontological universe of all objects OB is treated as ordered by two conjugate relations: an analytical one – simpler than : < and a synthetical one – to be a component of: Ě . Two associate operators: the analysator a and the synthetisator s are also considered. The ontological universe of analysis and synthesis can thereby be understood as the quintuple: <OB, .
The general theory of analysis and synthesis considers interconnections between the two relations introduced above and suitable operators. Its basic observation is that analysis and synthesis are dual but not invertible in a simple way.
15. They also differ from a methodological point of view. The theory of analysis is rather straightforward and immediate, whereas the theory of synthesis is more complex and subtle.
Difficulties concerning synthesis are connected with the characterization of wholes, their unification and with different types of synthesis. To meet these difficulties two approaches are introduced: the first, external and purely relational, and the second, internal and deeply modal.
The relational approach has itself two editions: one, which is simply the general theory of analysis and synthesis outlined above, and another, locative and connectional, which starts with a very basic reflection on the nature of combination.
16. What is a combination? Clearly, it is a complex of a special type. It is any natural configuration of objects, i.e., each collection of correlated and connected objects.
Each combination has thereby five primitive correlates: its stuff (i.e. the class of all its parts), its substance (i.e. the class of all its simples), its structure (i.e. the way in which its components are related), its form (anything which makes its structure possible), and its network (i.e. the net of bonds fusing its components together).
Several secondary correlates are also present.
17. The idea of combination can therefore be decomposed into three more primitive ideas: location, correlation and connection.
combination = location + correlation + connection
To be in a combination means to be located in it, and to be correlated and connected with other components.
Two ideas – that of location and that of correlation – are purely relational, whereas the idea of connection is more dynamic and modal.
Now, if we like to have a really general combination ontology, sufficient to cover both the realm of psyche and the realm of matter, we must have suitably general ontologies of location, correlation and connection.
And this is our task here.
18. Correlation ontology is immediate. It is the general ontology (or calculus) of relations  , for correlation simply means relation.
Its algebraic version, made under a special proviso, is the lattice theory of G. Birkhoff  , which presently is the best description the structures of combinations which we have.
19. The ontology of location is also at hand.  It formalizes location in any given relational frame via the thesis: an item x is located in y iff each part of x is related to y.
20. This idea can be expressed formally in the following way:
Fix a nonempty set U and a binary relation E on U. Next consider all derivative binary relations defined in this framework by means of composition of the universal quantifier and implication.
20.1 In this way we obtain at least two parthood relations:
xPy := „z(zEx ® zEy), Leśniewski’s parthood relation
x is a part of y iff each item which is E-related to x is also E-related to y,
or in a more familiar way:
x is a part of y iff everything in x is also in y
xCy := „z(yEz ® xEz), the covering relation dual to Leśniewskian one
x is covered by y iff each container of y also contains x
As a matter of fact, two further relations of this sort can also be introduced.
20.2 Extending the above procedure further we reach the following two formulas expressing the idea of location:
xLy := „z(zPx ® zEy); x is located in y iff any part of x is related to y
xAy := „z(yCz ® xEz); x is allocated in y iff it is related to any cover of y
Again two further locative relations can be considered.
21. We can check that the above definitions formalize basic intuitions concerning location. Among other things we can prove that
(2) Both location and allocation are logically stronger than the starting relation: L, A Ł E
Hence the proper locative structures are those in which the starting relation E is equal to its locative counterparts L and A:
IL E = L To be is to be located in, or
EL E = A To be is to be allocated in.
22. Now it is only a question of routine calculation to see that locative spaces satisfying at least one of the above axioms are quite similar to the usual preorders, hence they are regular and rich structures.
They indeed offer a very natural framework to study location, which is defined for any starting relational frame.
Therefore, the relational location is not limited to the usual cases of space-time, physical location and it is general enough to be used as a basis for studying cases of extra-physical location. 
23. The characterization of connection is more difficult, for it is not a purely relational matter.
Now we are interested in questions concerning the internal structure of a given combination, which is treated here as a whole. We are looking for a mechanism for its unification and therefore we search after determiners forming the combination from its components, i.e., for its form.
24. There are several approaches to the investigation of a given object’s form.
A standard mathematical technique is to choose a group of transformations and characterize its invariants, whereas a logical method  proceeds by treating suitable determiners or traits as ontological modalities which are subjects of logical treatment.
25. To this end, let’s use the most primitive pair of ontological modalities: making possible MP( , ) and making impossible MI( , ).
Take a given combination x and its two arbitrary components y and z . We can think of the latter as connected if each of them can be combined with the other.
I.e., y and z are both connected in a combination x iff there is the smallest part of x containing both y and z , say yČz, such that each of them make yČz possible:
C(x; y, z) := yPxŮzPxŮ$yČz(yPyČzŮzPyČzŮ”u(yPuŮzPu ® yČzPu)ŮMP(y, yČz)ŮMP(z, yČz)
Clearly, properties of the connection operator C depends on properties of the ontological modality making possible, the theory of which is known  to be complex and rich.
26. Any production is by analysis and synthesis.
The basic product of a given synthesis is, of course, combination itself. There are also secondary products, including properties of the combination and some phenomena caused by the synthesis and connected with the combination’s occurrence.
For our purposes some secondary products are even more important than the basic one. They include, inter alia, the usual properties of things, their determiners, traits and other qualities, several types of fields including physical ones, and several dynamical characters and states, like propensities, homeostasis, equilibrium and stabilization.
27. Restrictive syntheses, in which only combinations are produced, should be distinguished from nonrestrictive ones.
28. Emergent syntheses are special cases of nonrestrictive ones, in the course of which the rules for the process of synthesis itself are changed.
They are like games during which we not only produce game-situations, but sometimes also change rules of the game itself.
The most important case of an emergent synthesis we know is, for sure, emergent evolution. 
29. Now, the basic question concerning emergence is the ontological question: How is it possible?
In the framework of combination ontology the answer is rather straightforward. Emergence occurs by means of a nonrestrictive synthesis in which new qualities are produced.
Qualities form the combination’s form which, we remember, fully determines its synthesis. When new qualities are in play then the process of synthesis can, and usually is, changed by something which sometimes seems to be a case of downward causation. 
30. There is nothing mysterious in either the idea of emergent evolution (synthesis) or in that of downward causation, if a suitable theory of qualities is provided.
Such a theory is a chapter of the logic of qualities, which since the fundamental insight of Leibniz is the crux of combination ontology, i.e., the general theory of analysis and synthesis.
31. Certainly, existence is among the most important products of a special kind of synthesis.
The following conditions are necessary for the existence of an object x :
i) x must be a combination, and so a fortiori it must be a complex;
ii) x must be coherent, i.e. possible;
iii) x must be condensed and stable; and, according to Leibniz:
iv) x must be compatible with the maximal number of other possibilities.
32. The idea of existence is therefore quite complex and can be decomposed  into at least eight more primitive ideas:
existence = combination+coherence+condensation+stabilization+maximalization+…. or
existence = location+ correlation+connection+coherence+condensation+stabilization
33. The justification of all research, like any enterprise, is by its fruits.
Our ontological machinery is so developed that, if reasonable, it should offer us an adequate and natural way to deal with the basic cognitive notions.
Is our ontological framework correct and useful? To see the point, let’s return to an example of thoughts, discussed previously in §12 in the ontological terms of Wittgenstein’s Tractatus.
34. First of all, thoughts are (logical) pictures of facts, hence facts, hence existing combinations.
Notice that by §§ 17, 31 and 32 we now have a much more developed and sophisticated apparatus to study combinations.
On the other hand, the theory of synthesis and its subtheory of qualities (cf. §§ 16, 23-25, 28-29) are prepared especially to deal with the notion of form which, as any true Wittgensteinian scholar knows, is the crucial notion of the Tractatus.
35. Observe also that by §§ 19-22 we can speak, without any metaphor involved, about the location of thoughts both as pieces of the ontological space and as inhabitants of mine, yours, or his/her/its mind.
As a matter of fact, in the present framework we can define a mind either as any container of thoughts, i.e., an item locating the maximal number of co-located thoughts, or as the minimal combination of thoughts.
Instead of a conclusion
35. Combination ontology indeed offers room for advanced psychoontological research.
This is not a solution but an opportunity, which can and should be taken.
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 Perzanowski J., Badania Onto – Logiczne (Onto – Logical Investigations), work in progress
 Popper K. and Eccles J. C., The Self and Its Brain, 1977, Berlin, Springer Vlg.
 Schröder E., Vorlesungen über die Algebra der Logik, vol. 3, Algebra und Logik der Relative, 1895, Leipzig, B. G. Taubner
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 Wittgenstein L., Tractatus Logico – Philosophicus, 1922, London, Routledge and Kegan Paul
 For a discussion of general ontology in comparison with particular ones cf. Perzanowski .
 This is what Wittgenstein in the Tractatus named the logical space.
 Mine, or yours, if you like.
 Cf. a lecture „The Marks of the Purely Psychological” read by R. M. Chisholm at the 9th International Wittgenstein Symposium, 1984. Cf. Chisholm  –  .
 For more details see Perzanowski ,  and  .
 Cf. Schröder  and Tarski  .
 Cf. Birkhoff  and Grätzer  .
 Cf. Perzanowski  and  .
 For example the location of my thoughts when writing this essay.
 They are used in my ,  and  .
 Cf. Perzanowski  and  .
 Cf. Popper & Eccles  .
[13 Cf. again Popper & Eccles  .
 Like the idea of combination, cf. §17 .
Chair of Logic, N. Copernicus University
Fosa Staromiejska 3, 87-100 Toruń, Poland
Department of Logic, Jagiellonian University
Grodzka 52, 31-044 Kraków, Poland