According to phenomenology one can talk about two kinds of meaning analysis: the static-structural meaning analysis and the genetic analysis. 1. The aim of ...
Husserl Studies 8: 205-220, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands.
Phenomenology, possible worlds and negation * WOJCIECH K_RYSZTOFIAK University of Szczecin The explication of the framework for the phenomenological genetic analysis of negation is the main aim of this article. This task is motivated by Charles Harvey's, Jaakko Hintikka's, David Woodruff Smith's and Ronald McIntyre's results concerned with accomodating possible worlds semantics to phenomenological genetic analyses. First, the concept of genetic analysis will be explicated. Subsequently, the main statements of Harvey and Hintikka will be presented. Then, these will be compared with the Husserlian theory of consciousness. Finally, the phenomenological conception of negation - different from Hussed's original theory and its interpretation formulated by Harvey and Hintikka - will be discussed and expressed with the help of categories of possible worlds semantics.
1. The concept of genetic analysis According to phenomenology one can talk about two kinds of meaning analysis: the static-structural meaning analysis and the genetic analysis. 1 The aim of static-stnlctural meaning analyses is the formulation of normal definitions which are identity-definitions, or equivalence-definitions of concepts and propositions. Normal definitions are presupposed in every language and theory. That is why this type of meaning analysis is not the specific type of phenomenological procedure. Genetic meaning analyses are the pecular kind of methods employed in phenomenology. Describing the constitution of meanings is the aim of this type of meaning analysis. Hence, the results of genetic analyses are not definitions, but descriptions of the 'constituting subjectivity'. The question which motivates genetic phenomenological investigations is: What are the mechanisms for the constitution of concepts and propositions? Some phenomenologists here talk about transcendental reflection on the constitution of meanings. 2 * I would like to thank Charles W. Harvey from the University of Central Arkansas and Leon Gurnafiski from the University of Torufi in Poland for a number of useful criticisms of an earlier version of this paper.
206 The understanding of genetic meaning analysis, in phenomenological investigations, must be preceded by the presentation of Husserl's conception of meaning. According to Husserl meanings fall under the category of noemata. 3 Some interpreters of Husserl's works identify noemata with meanings. 4 The others do not venture an opinion as to whether meanings are identical to noemata. 5 The basic feature of cognitive acts is intentionality as a relation between the act and the object of this act. This relation may be comprehended as an act's direction toward some object. 6 Noemata are mediators between acts and their intentional objects. They enable a cognizing subject to be directed towards objects. 7 Hence, using Carnap's terminology, one can say that noemata are intensional entities. Meanings are noemata correlated with cognitive acts which are executed with the help of linguistic expressions. 8 In other words, meanings are noemata correlated with speech acts. That is why the conception of noemata is relevant to the theory of meaning. Since noemata have an internal structure, then meanings must also possess an internal structure. First of all, one must distinguish between the noematic contents and the form of noema within which contents are comprehended by a cognizing subject. 9 For example, a reference to Aristotle occurs in the cognitive act executed with the help of the sentence 'Aristotle was a teacher of Alexander'. This reference is made possible by noema related to the name 'Aristotle'. This noema has the form of an individual. The contents of this noema are determinated by such predicates as: 'the philosopher', 'the author of syllogistic' and 'the founder of the Peripatetic School'. The noema of the whole sentence has the form of a state of affairs, the form of a proposition. This form is filled by contents of such noemata as: 'Aristotle', 'Alexander' and 'to be a teacher'. One may say that the concept of the noematic form is similar to the notion of the logical form as a syntactical structure obtained by replacement of extralogical constants with appropriate variables. It may also be accepted that the concept of the noematic content is similar to the notion of connotation as a set of properties correlatd with a given name. Noemata and meanings may be simple or complex. The complexity of the content and the complexity of the form are both the criterion of the above distinction. For example, the noematic form of the sentential cognitive acts is more complex than the noematic form of the acts which are correlated with names used in sentential speech acts, because the form of a state of affairs is founded on the form of an individual. The noematic content correlated with the noema 'The World' is more complex than the noematic content of the noema 'The Earth' because the former includes the latter. One of the most important tasks of phenomenological genetic analyses is just to describe the founding of complex noemata on simple noemata. In accordance with the basic schema of Husserl's phenomenology,
207 consciousness is the field of noetic-noematic tensions. 1° Every phenomenon of consciousness may be comprehended as consisting of two corresponding extremes. The first extreme is a noetic moment and the other is a noema of a given cognitive act. For example, Husserl distinguishes such noetic moments as: assertions, questions, denials, conjectures, desires and others. I 1 It might be said that the notion of noetic moments is a generalisation of Searle's concept of illocutionary force of speech acts. 12 Searle talks merely about speech acts whereas Husserl talks about cognitive acts in general. Of course, acts of speech belong to the category of cognitive acts. Noetic moments may be simple or complex. For example, a moment of assertion is founded on predication and reference to some object. It is a fundamental theorem of phenomenology that there is an essential correspondence between noetic moments and noematic forms. 13 For example, the form of a state of affairs is correlated with the noetic moment of acts of judging. The very important purpose of genetic analyses is to describe the foundating of complex noetic moments on simple noetic moments. 14 This phenomenon may be comprehended as a couPle of which the first element is a noetic moment and the second element is a noema. So, phenomena may be more or less complex structures because of the complexity of their elements. Awareness may be treated as a stream of noeticnoematic couples, a stream of phenomena. The appearance of the phenomenon in the stream of consciousness is dependent on a special sort of cognitive activity. This activity is often called 'transcendental activity'. It may be metaphorically said that the transcendental activity produces phenomena. The processes of such a production are designated in phenomenology by the expression 'the constitution of phenomena'. The constitution of the phenomenon is a complex process. It is composed of the synthesis of a noema and the synthesis of the noetic moment which corresponds to a given noema. Syntheses of noemata divide themselves into two parts: the synthesis of complex contents and the synthesis of complex forms. It needs to be emphasised that the concept of constitution is different from the concept of foundation, though they are both related. The relations of foundations are the basis of the processes of constitution and syntheses of various types. These relations express the mechanisms for the constitution of phenonema. One can say that the noema A is constituted from noemata B 1.... B n by the transcendental activity of awareness if and only if the noema A is founded on noemata B1,...B n. The descriptions of the relation of foundations are also descriptions of the mechanisms for the constitution of noemata. So the main task of phenomenological genetic analyses is to describe the various types of processes involved in the constitution of noemata. Hence, genetic analyses must contain descriptions of different kinds of syntheses as
208 well as various types of foundation-relations. Since meanings belong to the category of noemata, the descriptions of the processes of meaning-constitution are also the aim of phenomenological genetic analyses. So phenomenological methods of analysis are also methods of meaning analysis.
2. Harvey's and Hintikka's conception of negation Charles Harvey and Jaakko Hintikka assert that "'possible worlds methods of meaning analysis can accomodate themselves to the restraint strictures of pure phenomenology.''15 Phenomenology narrows the notion of possibilities to motivated possibilities whereas possible worlds semantics uses the concept of logical possibilities. 16 These authors assert that "in a Husserlian horizon analysis not all purely logical possibilities are allowed. Usually, only motivated possibilites are admitted. ''17 Hence they modify the framework of possible worlds theory in order to make it compatible with some of Husserl's statements referring to the processes of the constitution of phenomena correlated with logical connectives such as disjunction and negation. These modifications can be presented with the help of the following theorems: 18 HH1. There is the actual world which is a counterpart of doxastic consciousness. HH2. The cognizing subject exists in the actual world. HH3. The cognizing subject produces the possibilities, understood as possible worlds. HH4. The production of possible worlds is determined by spots of indeterminacy within the actual world and the activity of the cognizing subject. HH5. Possible worlds as produced by the cognizing subject are contained in the actual world by virtue of the disjunctive activity of consciousness. HH6. The role of negation is elimination, cancellation, of the produced possible worlds from the actual world. HH7. This elimination is successful if and only if the eliminated possible world is incompatible with the actual world. HH8. The elimination of incompatible possible worlds from the actual world is at the same time a clarification and an explication of the actual world. The degree of determinacy increases if some possible world within the actual world is successfully eliminated. According to Harvey and Hintikka, the above theorems are interpretationally similar to Husserl's statements concerned with the genesis of negation and disjunction. The concept of doxastic consciousness is not explicated by Harvey and Hintikka. It seems that it should be understood as designating an ordinary
209 consciousness. Therefore, their conception cannot be applicable to scientific, cognitive activity. The concept of motivated possibilities is not defined by them either. However, it may be explicated as follows: According to phenomenology, it may be said that there are one-sided, inadequate and undetermined cognitive acts. For example, the acts of perception belong to this category of acts. A back side of a perceived object is always hidden in the perception Of the object's front. The cognizing subject perceives that, for example, a given object is made of wood. However, this state of affairs is merely given from the one side. It is given from the front of the object. That the back of this object is made of wood, is not perceived. This state of affairs is only conjectural. So in every act of perception there occur conjectures about various states of affairs which are not directly perceived, but are conjecturaUy comprehended in the act of perception by a cognizing subject. These conjectures are just motivated by seeing a side of an object which is in front of us within the field of perception. That the back of the given object is made of ice, cannot be motivated by seeing that the front of the object is made of wood. Therefore, one can say that propositions may be motivated by other propositions. Of course, the relation of motivation is an intensional relation rather than an extensional one. From the possible world semantics' point of view, one can imagine a possible world in which there are objects made of both wood and ice. This world might even be consistent. Thus, one can assert that motivated possibilities belong to the category of logical possibilities, but not every logical possbility is also a motivated possibility. It needs to be mentioned that the relation of motivation is not formally defmed by analytic phenomenologists.
3. Possible worlds phenomenology and Husserl's conception of negation Husserl distinguishes between pre-predicative and predicative consciousness. 19 The pre-predicative stratum of consciousness is the basis of the constitution of phenomena lodged within the predicative stratum of awareness. The predicative stratum of consciousness is composed of phenomena which are related to propositional noemata. The pre-predicative stratum of consciousness contains phenomena which are correlated with primitive meanings and pre-impressions, primitive sense-data. 2° One must assume that there are many kinds of pre-predicative noetic moments which correspond with pre-predicative noemata. The detection of the sources of negative phenomena in the pre-predicative stratum of consciousness and the mechanisms for the constitution of these phenomena is one of the aims of the phenomenological-genetic analysis of negation. Husserl's description of the constitution of negative phenomena may be
210 interpretationally summarized in the following w a y : 21 HI.
H2. H3.
Negative noetic moments, noetic moments of acts of denying, are directly founded on the affirmative noetic moments of conjectures - understood as opposed to acts of confirmation - and the noetic moments of disappointed fulfilments. When the fulfilment of a given conjecture falls, then negation of this conjecture arises, the negative judgment arises. Affirmative conjectures are founded on protentive moments of the pre-predicative stratum of consciousness. Protentive moments are pre-predicative anticipations. They are connected with any presenting intentional act of reference to some object. These prepredicative anticipations are not assertions.
In this case, the relation of foundating is a relation of motivation. Conjectures are motivated by protentive moments of any presenting intentional act of reference to some object. Hence these protentive moments may be comprehended as a special kind of moment of motivation. H4.
So the noetic moment of negation is founded in turn on an affirmative noetic moment of some conjecture, moments of disappointed fulfilment, protentive moments and moments of presenting reference to a given object which is then denied.
The above analysis might be complemented by a description of the structure of the protentive moments of awareness. This structure has a temporal nature. Hence, the above description of the mechanisms of the synthesis of denying, as a noetic moment, is not complete. Because there is a correlation between the noetic sphere and the noematic sphere of consciousness, one can formulate, on the basis of the foregoing points, the description of the foundational structure of negative noematic forms of phenomena. H5.
Negative noematic forms are directly founded on the noematic forms of conjectures and the noematic forms of disappointed fulfilments.
Noemata of conjectures have the form of conjectural states of affairs. Since conjectures require confirmation, and according to Husserl the concept of confirmation, intrinsic to the notion of judgment, presupposes some previous modalization in relation to that which is confn'med, 22 one must assert that conjectural noemata are modalized noemata. These noemata can be treated as the possible noemata which have the form of a state of affairs. Thus, the subsequent theorem follows: H6.
Conjectural noemata are possible states of affairs, possible noemata.
211 Disappointed fulfilments refer to the relations between conjectural noemata and presented noemata, which are fulfilments of other conjectures. These relations can be comprehended as incompatibility relations between possible noemata and presented, actual noemata. Thus, one may accept the following theorem: H7.
The noematic form of disappointed fulfilment is the relation of incompatibility between a given possible noema and some actual, presented noema.
Husserl asserts that every phenomenon of pre-predicative consciousness can be expressed at the predicative level of awareness. Thus, conjectures may be interpreted as expressions of pre-predicative protentive anticipations. Hence noemata of conjectures may be treated as having a noematic form similar to a form of noemata of protentive anticipations. However, there are essential differences between noemata of conjectures and noemata of protentive anticipations. These differences refer to the contents of these noemata, especially to their ways of givenness. The noema of a conjecture has a 'thetic character' whereas the noema of protentive anticipation does not contain this element. 23 So one may accept the following statement: H8.
The noematic form of the protentive anticipation is the same as the noematic form of a corresponding conjecture, whereas the contents of these two types of noemata are different, they are especially different in respect of their ways of givenness.
Protentive moments are a part of every presenting intentional act of reference because of the act's one-sidedness, inadequacy and indeterminacy. Noemata of protentive anticipations are motivated supplements of every actual presented noema. They are contained in the context of the presented noemata. This context is motivated by spots of indeterminacy of a given actual noema. Thus: H9.
Since noemata of protentive anticipations are motivated by spots of indeterminacy of a given actual noema, the form of noemata, correlated with protentive anticipations, is founded on these spots of indeterminacy.
It is difficult to define the noematic form of spots of indeterminacy. This task requires investigations devoted to the ontology of incomplete objects. Summarizing, one can assert that negative noematic forms are founded in turn on the form of possible states of affairs, the form of tile incompatibility-relation and the form of the spots of indeterminacy. The actual world and the possible worlds of Harvey's and Hintikka's conception are respectively interpretations of Hnsserlian notions of the
212 doxastically cognized world and possible states of affairs as conjectural noemata. And since conjectures are treated by the authors as contained in the doxastic consciousness, and possible states of affairs are noemata of these conjectures, then one must accept that possible states of affairs are contained in the actual world. That is why the theorems HH3 and HH5 interpretationally result from the statement H3 and H6. Harvey and Hintikka assert that "we carl understand possible worlds to be possible variations and happenings within the spatial and temporal spread of the actual world. ''24 This opinion suggests that the actual world is not merely composed of possible noemata, but it contains actual presented noemata as well. Since actual noemata have spots of indeterminacy and possess the feature of incompleteness, the set of possible worlds, which could be produced by every cognizing subject, must be limited. These limitations are motivated by spots of indeterminacy. Therefore the theorem HH4 is compatible with Husserl's thesis H9. The disjunctive activity of consciousness in HH5 may be treated as an activity motivated by protentive moments, a protentive horizon, of every presenting act of reference to some object. Conjectures are results of this cognitive activity, and furthermore they are joined together by this activity within the horizonal stratum of every act of consciousness. In this way all logical possibilities are not allowed to be at the same time possible worlds accessible from the actual world. Merely protentively motivated possible worlds, as the noemata of conjectures, are accessible from the actual world. One can thus accept that Harvey's and Hintikka's theses HI-I1 - HH5 are similar to the interpretation of Husserl's conception given in this article. The theorems HH7 and HH8 are simple consequences of the statement HH6 and the thesis H7. However, HH6 becomes confused by the following difficulty: If the role of negation is cancellation of produced possible worlds from the actual world, then the actual world must change from negation to negation. The actual world before execution of negation is not the same as the actual world after execution of this operation. The first actual world contains the possible world, which is negated, and the second actual world does not contain it. This is a difference between these actual worlds. That is why one can not accept that there is exactly one actual world. Harvey and Hintikka could assert that the identity between the first actual world and the second actual world is not a Leibnizian, logical identity. However, in this case it would be very difficult to express such non-classical identity. Furthermore, classical identity (x = y iff for every C, Cx iff Cy) is the most adequate identity to the phenomenological project of reduction and epoch6. From the phenomenological point of view, the statement that objects x and y are identical although they have different properties or elements and parts, must be explained and justified in accordance with transcendental rules of
213 reduction and epochS. The concept of exactly one actual world is the concept of common sense. The notion of the common actual world is the basic condition of monadologic intersubjectivity and intersubjectivity in general. That is why this notion cannot be used in a phenomenological theory of possible worlds. This concept is entangled in the metaphysical presumption that every act of consciousness is related to the same actual world. The employment of the common concept of the actual world would be incompatible with the project of Husserl's phenomenology. Therefore, the term 'the actual world' used in ordinary speech has not the same meaning as the term 'the actual world' used in phenomenological investigations. The noema of the first term must be genetically explained. A cognizing subject does not know after the reduction whether the world of a reduced act A and the world of a reduced act B are identical. These worlds are identified by the cognizing subject within the doxastic consciousness, and the phenomenologist must explain how this is possible. From the phenomenological point of view, it is possible to say that there is a transcendental space of many actual worlds. These worlds may be understood as representations of the world in itself. But this thesis is metaphysical, and hence it can not be treated as a theorem of phenomenology.25 Harvey and Hintikka do not distinguish between the doxastic noema 'the actual world' and the concept of actuality which refers to the noematic contexts of any cognitive acts. These contexts are understood as semantical or noematic correlates of cognitive acts. The context of every act is the set or the collection of the noemata within which it is embedded. Presented noemata, conjectural noemata, protentive noemata and horizonal noemata belong to the contexts of conscious acts. These contexts may be called 'the noematic fields of acts of awareness'. Therefore, one can say that the doxastic noema 'the actual world', which is a horizonal noema, belongs to every field of any act of consciousness. However, this noema is not identical with the noematic field of a given act of awareness. These fields change from act to act, whereas the doxastic noema 'the actual world' is always the same within any of these fields. The next difficulty of Harvey's and Hintikka's conception is connected with interpretation of the double negation. If the role of negation is the elimination or the cancellation of produced possible worlds from the actual world, then it is a question what kind of cancellation the double negation executes. One could assert that the role of the double negation is the 'cancellation of cancellation'. However, this procedure is not intuitive from the point of view of possible worlds semantics. An advantage of the above conception is that it makes negation a modal functor. It grasps one of the most basic properties of acts of denying, executed in the ordinary activity of cognizing subjects. Namely, in ordinary
214 cognitive activity, a cognizing subject does not deny something which is directly, presentationally comprehended by an awareness. If we are seeing that the tree in front of us has green leaves, then in this situation we will never say seriously that the tree in front of us does not have green leaves. If we said in all seriousness in this situation, that the tree in front of us does not have green leaves, we would be told that we do not speak English well or that we are terribly confused. In ordinary cognitive activity, we deny something that is not seen and directly presented, but what is merely conjectured.
4. The conception of negation as creation of possible worlds The above-mentioned difficulties compel modifications in Harvey's and Hintikka's phenomenological possible worlds theory. The proposal of such modifications falls under a phenomenological framework too. However, it is not an interpretation of Husserl's conception. Husserl's investigations are treated here as merely the source of our inspiration. Harvey's and Hintikka's inquiries are the starting-point of the proposed informal theory. The central idea of m y framework resolves itself into the statement that the main role of negation is the production, the creation, of possible worlds or possible states of affairs as entities outside of some actual worlds. Therefore, one can say that the role of negation is the cancellation of the possibilities from some actual world and subsequently the location of these possibilities in any possible world within the space of all worlds. This assumption expresses a fundamental difference between Harvey-Hintikka's framework and my conception. The most important theorems are the following: K1.
A cogrtizing subject, in his ordinary cognitive activity, entertains relations to many actual worlds. Every doxastic, ordinary cognitive act is executed by a cognizing subject within some actual world.
Justification: Cognitive acts of a cognizing subject consist in learning, correcting and losing various bits of information. If the actual world is treated as a set of information which is at a cognizing subject's disposal in a given moment of his activity, then the actual world before reading newspapers by a given cognizing subject will be different than the actual world of this subject after execution of this cognitive act. For example, in the second actual world there is an information that somebody killed Fidel Castro whereas there is no such information in the first actual world. The actual world, when I am in my home, is not the same actual world as when I am in a pub. There is no drunken crowd in the first actual world whereas
215 there are tipsy men in the second actual world. K2.
Every actual world is a set of noemata correlated with various types of convictions of a given cognizing subject in a given moment of his cognitive activity.
Justification; If every actual world is interpreted as a set of information which is known by a given cognitive subject, then in virtue of the command 'Say all information that you know about the world', he will express this information with the help of various statements. Statements may be treated as linguistic expressions of convictions. Meanings of the statements are, according to phenomenological terminology, just noemata. K3.
In every actual world one can distinguish three subsets of noemata, i. Noemata of the first subset belong to every actual world. These noemata can be interpreted as the primitive noemata, and the set of them may be called 'the primitive actual world', ii. Noemata of the second subset are presented noemata. These are correlated with presentational acts. The noemata of this kind are often defined by phenomenologists as the filled, or partly filled, or saturated noemata, iii. Noemata of the third subset are conjectural noemata. They are correlated with linguistic acts of re-presentation.
Justification: Conjectural noemata are related to convictions which refer to situations hidden from the direct cognizing subject's comprehension in a given moment of his ordinary cognitive activity. That a cognizing subject in a given moment fixes his attention on concrete objects appearing in front of him does not imply that he does not know that New York is in America. Furthermore, one can not imagine the situation in which a cognizing subject feels sensually nothing. A cognizing subject is always in some point in space and time. Hence, he lives always within the sphere of concretes which may be directly, sensually comprehended by him. An ordinary cognitive activity beyond the sphere of sensible concretes seems not to be possible. The acceptance of the category of primitive noemata seems to be the most controversial assumption. However, it is compatible with Husserlian phenomenology, with phenomenological foundationalism according to which there are primitive meanings and contents. The rejection of this assumption would be the negation of the conception of genetic analysis, of the whole program of phenomenological investigation. Thus, primitive noemata are meanings which may be metaphorically called 'semiotic atoms'. K4.
The set of all actual worlds related to the whole of an ordinary cognitive activity of a cognizing subject is the linearly ordered set in virtue of various transformation-operations. The transformation
216 of a given actual world into another world is caused by the execution of any cognitive act. i. The transformation may be the enrichment of a given actual world with new noemata. These new noemata may be presented or even conjectural noemata. For example, a cognizing subject learns some new information about his wife or he perceives something that he did not see earlier. In the first case, an actual world is enriched with some conjectural noemata, and in the second case, an actual world is enriched with some presented and filled or partly filled noema, ii. The transformarion may be the cancellation of some noemata from a given actual world. For example, a cognizing subject forgets about something, iii. The transformation may be simultaneously the cancellation of some noemata from a given actual world and the enrichment of it with new noemata, iv. The transformation may be the dislocation of conjectural noemata from the third stratum to the second stratum of an actual world. For example, a cognizing subject conjectures some information, and subsequently he verifies it by perception, v. The transformation may be the dislocation of presented noemata from the second stratum to the third stratum of an actual world. For example, a cognizing subject perceives something, and then he averts his eyes from it but he continues to know that perceived earlier object has such and such properties. Justification: The term 'transformation-operations', relative to its extension, may be identified with the term 'productive, cognitive acts'. The productive, cognitive acts are acts which contribute new informations or cancel needless and superflous old information. Of course, the terms, relative to their contents, are different. The former refers to cognitive acts in relation to all the information given to a cognizing subject in some moment of his cognitive activity, and the latter refers to cognitive acts in abstraction from information possessed by a cognizing subject. Since the usage of the term 'productive, cognitive acts' is not controversial, the employment of the term 'transformation-operations' should be uncontroversial either. K5.
There are various relations of compatibility and incompatibility between the noemata of every actual world.
Justification: Since the notion of a noema may be understood as an interpretation of the ordinary concept of information and since it is said that there are various types of compatibility-relations and incompatibilityrelations between informations, then it may be said too that these relations may occur between noemata. K6.
The role of negation is the elimination of the conjectural noemata from a given actual world and the production of possible worlds consisting of cancelled noemata. It is also the transformation of an
217 initial actual world, which contains negated noemata, into a modified actual world which contains the negative noemata related to given acts of denying but does not contain negated noemata. Justification: Since the forgetfulness of information is merely the cancellation of noemata from a given actual world and since acts of denying are not acts of forgetfulness, the role of acts of negation can not be merely the elimination of conjectural noemata from a given actual world. Furthermore, negative convictions expressed with the help of various kinds of negative sentences make a certain form of "an informational memory'. Hence, negated noemata must be encoded, in some changed form, in the actual world obtained in consequence of executing the act of denying. The form of encoding negated noemata is the form of negative noemata. A negative noema is different from a negated noema, for the former contains the latter, but not vice versa. Moreover, if a cognizing subject executes negation of some information, then he ascribes different semantical status to this information than the status of accepted information. If the semantical status of accepted information is that it belongs to an actual world in a given moment of a cognizing subject's activity, then the semantical status of negated information is that it does not belong to this actual world but belongs to another world which may be called 'a possible world'. Every negative noema may be comprehended as an ordered couple (n, wi), where n is a negated noema and w i is a corresponding possible world. K7.
One can define two relations between actual worlds and possible worlds. Let A1, .... A i be actual worlds. Let w 1..... wi be possible worlds and let n be a noema. Moreover, if n is a noema, then (n, wi) is also a noema, i. The possible world w i is accessible from the actual world ~ if and only if there is a noema n such, that n e w i and n ~ A i and (n, wi) ~ A i. ii. The possible world w i is produced on the ground of the actual world A 1 if and only if for every n, if n w i, then n ~ A l, and there is such an actual world A 2 that w i is accessible from A 2 and A 2 = (Al-Wi) u {/n,wi/: n e wi} (where '-' is a substraction of sets, ' u ' is an addition of sets and ' {...:... }' is an abstraction operator).
Assumptions K1 - K7 are not a closed set of axioms. However, they are sufficient to formulate the genetic analysis of negative statements. On the ground of some actual world A 1, a cognizing subject comprehends incompatibility between a given bit of conjectulal information and other information. Since information may be treated as noemata, then a cognizing subject comprehends incompatibility between a given conjectural noema and other noemata. Hence, a given conjectural noema as incompatible with other noemata, must be eliminated from the actual world A 1. This elimination is
218 executed with the help of negative assertion. It is the result of this elimination that a cognizing subject simultaneously produces the possible world w 1 and transforms the actual world A 1 into the actual world A e. The negated noema n belongs to the world A 1 and subsequently to the world w r There is not the noema n in the actual world A 2. This world contains the negative noema (n, wl). Hence, a cognizing subject is related to the actual world A e and the possible world w 1 after an execution of denying. The possible world w 1 is accessible from the actual world A 2. Subesequently, a cognizing subject can comprehend the incompatibility between the noema (n, Wl) and other noemata in the world A 2. Hence, the noema (n, wl) must be cancelled from the actual world A 2. Thus, a cognizing subject must execute a double negation. At the same time, he produces a possible world w E in which the noema (n, wl) is lodged. A cognizing subject also tranforms the actual world A 2 into the actual world A 3 within which the noema [(n, Wl), w2] appears. The noema [(n, wl), WE] is constituted within the act of double negation, the act of double denying, and hence it is a noematic correlate of statements with double negation. Of course, the above-presented description of the constitution of phenomena with single negation and double negation is merely an idealisation. And that is why my analysis is only a general schema of detailed explanations of the role of negation in various cognitive situations. Moreover, assumptions K1 - K7 should be complemented by axioms concerned with the roles and noematic structures of such functors as: implication, disjunction and conjunction. The subsequent task should be a formalisation of complemented assumptions with the help of formal categories of topology and set theory. Actual worlds signifying noematic fields of consciousness within the stream of awareness may be interpreted as topological spaces. The three subsets of noemata contained in every actual world may be comprehended as determining a topology of every actual world as a topological space. It should also be mentioned that my conception does not have a strictly semantical nature because some actual worlds can not be comprehended as semantical models. Since actual worlds may be incompatible, then sets of statements, correlated with convictions of a cognizing subject and referring to an incompatible actual world, may be also incompatible. In accordance with the theorem of model theory that if a set of formulae is inconsistent, then there is not a model of this set, one must accept that incompatible actual worlds can not be treated as semantical models because incompatibility is a special sort of inconsistency. Of course, this conclusion is merely valid in reference to classical model theory. However, there are semantical theories in which the concept of non-standard possible worlds is defined. Non-standard possible worlds are inconsistent or incomplete
219 possible worlds. 26 That is why the notion of actual worlds in my conception is similar to the notion of non-standard possible worlds. Hence, the concept of actual worlds, in the light of phenomenology, can not be translated into the notion of actual worlds in Kripke's semantics. Actual worlds as noematic worlds are rather similar to Kripke's possible worlds. On the other hand, possible worlds as the worlds produced by acts of negation do not have counterparts in the standard possible worlds semantics. Moreover, the possible worlds can be inconsistent worlds in the same sense as actual worlds are called inconsistent. Therefore one must remember that the terms 'possibility' and 'actuality' do not have traditional meanings in my conception. To conclude, one can apply my conception to Plato's problem of existential negative true propositions. According to Plato, existential negative propositions are meaningless because they are contradictory. The statement that Pegasus does not exist involves the existence of Pegasus. There are many proposals for solving this paradox: description theory, free logic, logic of fiction, etc. In light of my conception existential negative sentences are meaningful because their main role is the creation of possible worlds. With the help of the statement 'Pegasus does not exist', a cognizing subject produces a definite possible world accessible from the given actual world. This statement is asserted on the ground of this actual world by a cognizing subject. This proposed approach to Plato's famous problem is different from hitherto existing proposals. This example shows that Harvey's and Hintikka's manner of reading Husserl's phenomenology is worthy of developing. Notes
1. On this distinction, see Charles W. Harvey, "Husserl's phenomenology and possible worlds semantics: A reexamination", Husserl Studies 3 (1987): 191-207. 2. On the transcendental subjectivity and transcendental reflexion, see J.N. Mohanty, The Possibility of Transcendental Philosophy (Martinus Nijhoff: Dordrecht, 1985). 3. In Ideas I, §§ 89-94, Husserl distinguishes between the complete noema and 'a noematic Sinn' which is an element of the noema. The noematic Sinn is just a meaning-entity. Husserl asserts that the noema of judgment is the meaning of a sentence used within a given judgment. 4. See David Woodruff Smith and Ronald Mcintyre, "Husserl's Identification of Meaning and Noema", The Monist 59 (1975): 115-132. 5. In his "The World as Noema and as Referent", Journal of the British Society for Phenomenology 3 (1972): 15-26 Guido KiJng says that meanings are a special kind of noemata. Dagfmn F~llesdal asserts that noemata am a generalisation of the notion of meaning. See his "Husserl's Notion of the Noema", The Journal of Philosophy 66 (1969): 680--687. 6. See Ideas I, §§ 84-85.
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7. Cf. Ideas I §8 87-90 and 128. F01tesdal accepts this thesis, too. He writes: "The noematic Sinn is that in virtue of which consciousness relates to the object." ("Husserl's Notion of the Noema", ibid., p. 682). 8. Cf. Ideas I, 8 124. 9. On this distinction, cf. Ideas I, 88 10, 11 and 134. Husserl says that formal apophantics investigates various ontological forms and syntactical categories, such as states of affair, relation, property, quantity, quality, etc. On the concept of formal ontology, cf. N. B. Cocchiarella, "Formal Ontology", in Hans Burkhardt and Barry Smith (eds.), Handbook of Metaphysics and Ontology (Philosophia: Munich - Philadelphia - Vienna: 1991), Vol. 2: L-Z, 640--64% and Barry Smith, "An Essay in Formal Ontology", Grazer Philosophische Studien 6 (1978): 39--62. 10. In Cartesianische Meditationen, §§ 14 and 17, Husserl distinguishes between the stratum of the 'cogito' and the stratum of the 'cogitatum'. This is just another expression of the opposition between the noetic and the noematic stratum of consciousness. 11. Cf. Cartesianische Meditationen, 8 14. 12. The concept of illocutionary force was introduced by John Searle in his book Speech Acts: An Essay in the Philosophy of Language (Cambridge University Press: London, 1977), esp. chapter 3. 13. See Ideas I, 8 93. 14. The concept of foundation is not clear in Husserl's works. However, there are attempts at the formalisation of this notion. But one must notice that they are not sufficient. These formal definitions are only employable in the field of noematic contents. See Barry Smith and D. Murray, "Logic, Form, and Matter" Proceedings of the Aristotelian Society, Supplementary Volume LV (1981), pp. 47--63, and Barry Smith and Kevin Mulligan, "Framework for Formal Ontology", Topoi 2 (1983): 73-85. 15. See Charles Harvey and Jaakko Hintikka, "Modalization and Modalities", forthcoming in Phenomenology and the Formal Sciences (Kluwer: Dordrecht). 16. On the discussion of this question, see Ch. Harvey, "Husserl's phenomenology and possible worlds semantics", ibid. 17. See Harvey and Hintikka, "Modalization and Modalities'. 18. Ibid. 19. See Hua I, 52. Cf. Harvey and Hintikka, "Modalization and Modalities". 20. This is not explicitly asserted by Husserl. 21. Cf. Experience and Judgment, trans. J. S. Churchill and K. Ameriks (Northwestern University Press: Evanston, 1973), §8 17-21. 22. Ibid., p. 272. 23. Ideas I, esp. 8 133. 24. See Harvey and Hintikka, "Modalization and Modalities". 25. Mohanty accepts a similar conclusion. He writes: "The idea of pluralism of worlds has come to stay... The transcendental philosopher, therefore, cannot start with a preferred representation of the world." (The Possibility of Transcendental Philosophy, p. XXIV). 26. Nicolas Rescher and R. Brandom introduce this concept in their book The Logic of Inconsistency: A Study in Non-Standard Possible-Worlds Semantics and Ontology (BlackweU: Oxford, 1980).
