Copyright © 2014
Avello Publishing Journal
ISSN: 2049 - 498X
Issue 1 Volume 4:
The Paradox of Nietzschean Atheism
The quasi-ontology of “an sich”
Bernard Bolzano´s Theory of Science between Leibnitian Ars Combinatoria and the
Husserlian Idea of mathesis universalis
Fausto Fraisopi, Alexander von Humboldt Stiftung / Husserl-Archiv Freiburg, Germany
Abstract
Starting from the critical position that Husserl assumes against Bolzano and his idea of mathesis
universalis, this paper focuses and emphasizes Bolzano’s project for a mathesis and the
differences between this project and the Leibniz’s one. Putting into an historical perspective
these three forms of mathesis, by Leibniz, by Bolzano and finally by Husserl, open at the same
time a theoretical perspective concerning the non-ontological dimension of idealities they form
and articulate that mathesis as such. The an-ontological Combinatorics of propositions and of
ideas in themselves, suggests, by Bolzano, the possibility of a treatment of Combinatorics
independently from these ontological and metaphysical presuppositions that formed and
structured the Leibnitian ars combinatoria. In this sense, the philosophical position of a
“semantic Platonism”, assumed by Bolzano, open the perspective of a non metaphysical but
modular mathesis that we can articulate and widen beyond an ontological commitment
In the § 10 of the third book of Ideas pertaining a pure Phenomenology and a
phenomenological Philosophy, treating the relation between psychology and phenomenology,
Husserl sketch at the same time the dependence of the phenomenology from Bolzano´s theory
of propositions in themselves. Such digression depends essentially from many
misunderstandings that Husserl recognizes in the reception of his idea of Phenomenology:
“With the misunderstanding of the essence of phenomenology is connected the fact that
recently, and probably with regard to the impulses that I received from Lotze and
Bolzano and of which I am aware as always with the greatest gratitude, some have
called these great investigators founders of phenomenology and have done so in such
manner that it must simply seem as if the best way into phenomenology would be by
1
returning to their writings as the primal sources of the new science” [HUSSERL 1980,
49; Hua. 5, 57].
Following Husserl’s position, Bolzano’s logical conception must not be overestimated,
because Bolzano’s and Husserl’s Logic are very different, in the way that trey the place of a
non empiristic (i.e. transcendental) psychology and, in particular, the fundamental function of
eidetic intuition:
“But the great Logic of Bolzano has so little pertinence here that he had not even the
slightest inkling of phenomenology – of phenomenology in the sense that my writings
represents. From the idea of an eidetic investigation of Intuition, from that of an apriori
that arises there, a founding of philosophy and psychology upon eidetic cognition,
Bolzano is as far removed as Mill, since extreme empiricist utterances are found in his
works which are no less so than those of Mill” [Ibidem].
The gap between the phenomenological role of eidetic intuition and the position of subjective
acts in Bolzano could not be clearer. For this reason Husserl begins to describe the different
way of mathesis universalis that the phenomenology can build in opposition to the “naïve”
idea of a mathesis that can be founded (implicitly or explicitly) in the Theory of Science. The
difference between the sketch of mathesis given by Bolzano in his Works and the
phenomenological project of mathesis universalis, consists, for Husserl, in the radicalism by
which Phenomenology investigates the acts that grasp the idealities or truths in themselves.
For Husserl the gap could not be greater:
“My way to phenomenology was essentially determined by the mathesis universalis
(Bolzano did not see anything of this either), and for the conception of the idea of such a
mathesis, to which I was pushed by my studies on formal mathematics, the sketch by
Bolzano of a limited bit of this idea, a bit of the theory of propositions in themselves
and truths in themselves, was of inestimable value. Had I not already had the pure idea
in the mathematical sphere and not already had it also for the sphere of logical
mathematics, which in the most recent period has been worked out (independently of
Leibniz), then I would have seen the sense of Bolzano’s theory just a little as all those
have seen it who use and cite his Theory of Science”[Ibidem].
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We could at this point ask to us in which sense is possible that the theory of propositions and
truth in themselves can have an “inestimable value” without presenting, at the same time,
more than “a bit” of the idea of a mathesis universalis. And even if in Bolzano there is only “a
bit” of the idea of a mathesis universalis as such, what is the function of this “in themselves”?
It is a secondary or a determinant one? Husserl seems here no attribute to Bolzano’s theory
this Platonism that many interpreters claim to find in his Theory of Science:
“The extensive working out of a pure logic of ideas and propositions in themselves,
which in no way were recognized by Bolzano as ideal essentialities of the eidetic
Intuition in my Platonizing sense, gave me a firm substrate for reflection; with this,
as with the whole formal mathesis, are connected the problems that forced me to
progress from psychology to phenomenology. But even the problems were alien to
Bolzano. One can learn from him much formal logic, for he was a great
investigator in that […]; but phenomenology is just a little to be learned from him
as critique of reason” [HUSSERL 1980, 50-51; Hua. 5, 59].
Husserl divides also the challenge of developing a mathesis universalis into two different
tasks: the task of formal logic, and the task of critique of reason. Concerning the task of the
formal logic, we can attribute to Bolzano his important role; but concerning the task of the
critique of reason and phenomenology, that, as theory of transcendental subjectivity, the
phenomenology “is just a little to be learned” from the theory of propositions and ideas in
themselves. This theory, far to be acceptable for a phenomenology of acts representing
“eidetic intuition”, seems to be only a sketch of the method of Combinatorics in the pure
realm of “the formal”. We wouldn’t, at this point, discuss the exactness of Husserl’s
interpretation, but only try to understand the function, from a phenomenological and a
historical point of view, of the “an sich” for the construction of a mathesis universalis.
In Formal and Transcendental Logic, when Husserl discuss once more the question of the
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mathesis, and this time only with respect to the “formal”, in particular with respect to the
relation between formal ontology and pure apophantic, the Bolzano’s role seems to be minor
and Husserl’s criticism became stronger as it was in the third book of Ideas. But what is more
interesting here is the historical perspective where the theory of the “an sich” by Bolzano is
inserted, the perspective which begins with Viète and the algebraisation of calculus:
“The genuine discovery of the formal was first made, at the beginning of the modern
age, by way of Viete’s establishment of algebra – that is to say, by way of the reduction
of the theory of numbers and quantities to a deductive technique – and them attained its
pure sense through Leibniz, whose mathesis universalis obviously has thrust of
completely every restriction to even the highest materially filled universality”
[HUSSERL 1969, 80; Hua 17, 70].
The deep difficulty to think together the formal (formal ontology as formalized treatment of
“something”) and the apophantic, shows all the limits, in Husserl’s view, of the Theory of
Sciences and underlines the gap between a phenomenological development of the project of a
mathesis universalis and a non phenomenological one: “How hard it is to think the matter
through to the end and penetrate, in this manner, either from logical analytics into formal
mathematics or the reverse, and how highly Leibniz’s achievement in this respect is therefore
to be esteemed, on sees from the case of Bernard Bolzano” [HUSSERL 1969, 84; Hua 17,
74].
From the point of view of the apophantic, Bolzano develops a deep tentative in the
systematization and definition of the “formal” as such: “In his admirable Wissenschaftslehre
[Theory of Science], published in 1837, he has already gone far enough to project
systematically a theory of propositions in themselves and truths in themselves, as a selfcontained
apophantic analytics”.
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The defect of this sketch of a pure mathesis must be
found on the side of ontological treatment:
“On the other side, even in 1810, in his Beiträge zu einer begrundeten Darstellung der
Mathematik [Contributions to a More Grounded Exposition of Mathematics] he makes
an attempt at a fundamental definition of mathematics, which already approaches the
idea of a formal a priori theory of objects – to be sure, without penetrating to its actual
sense (as I shall show forthwith, at the close of this questions). And yet Bolzano does
not go far enough to think the two ideas, that of a analytics of propositions and that a
formal mathematical analytics, through to the end and discover their internal
equivalence, nor even far enough to take into consideration the possibility of an
algebraic theorization of the formation with which logic is concerned, parallel to that of
the formations with which formal mathematics, in the usual sense, is concerned. In short,
much as he learned from Leibniz, he falls short of Leibniz’s insights. […] In a word,
Bolzano did not attain the proper concept of the formal, the concept that defines formal
ontology; though in a certain manner he touched upon it” [HUSSERL 1969, 85; Hua 17,
75].
The reasons of this insufficient treatment of formal ontology resides in the indetermination of
the relation between the “empty form, anything-whatever, as the highest genus whose
subordinate differentiations are likewise empty forms”, and “the universal region “the
possibly factually existent (the real in the broadest sense) which is differentiated into
particular regions”. In this sense, left aside the determination of this difference, Bolzano left
aside, in Husserl’s conception, also the determination of the difference between the
subsumptions of forma particularizations under formal universalities and the subsumptions of
regional particularizations likewise under formal universalities on the other side. This bring to
a confusion in the relation between the apophantic and the formal (and formalized treatment)
of ontology in the perspective of a mathesis universalis as such.
5
Outside of the logic of besser verstehen adopted from the great philosophers in their
interpretations of the history of thought, seems important to try to understand, independently
from the great or the mall function that can have for a phenomenology as such, the role of
Bolzano attempt of Combinatoric for a post-Kantian and overall for a non onto-theo-logical
project of mathesis universalis [RUSNOCK 2000, 129 fww]. In every case, Husserl was right
to underline three aspect of Bolzano’s Theory of propositions and ideas in themselves: the
great importance of the statement of existence of this elements as such for the project of
mathesis, the character of indetermination of formal ontology by Bolzano, the placement of
Bolzano’s sketch of mathesis between Leibniz and the new Leibnitian projects of mathesis at
the beginning of twenty century. What Husserl don’t say, or he’s not interested to say, is in
which way that sketch of theory of science is decisive and determinant to release the project
of a mathesis universalis as such from the perspective of a onto-theo-logical metaphysics, by
which the Leibnitian project of mathesis did remain always limited.
Furthermore what Husserl doesn’t say is that the importance of Bolzano’s theory of
propositions and ideas in themselves stand out from the indetermination not only of the idea
of formal ontology as such, but of the ontological status of this “an sich” as well. If this “an
sich” is not a Platonistic entity as the “essence” grasped in eidetic intuition, is however
determined from a very interesting form of Platonism, that “semantic Platonism” that
precisely allow to liberate the project of mathesis universalis from the form (and the
metaphysical realm) of onto-theo-logy.
When first reading, in the Theory of science, the paragraphs concerning the theory of
propositions and representations, we do not necessarily notice their inherent ambiguity. The
ambiguity at issue has to do with ontological notions. Almost two centuries later, we could
agree that the source is to be found in “an sich”, the ontological-formal status that many
contemporary interpreters attribute to Bolzano. On the other hand, Bolzano’s ontology in
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itself, or better his fundamental meta-ontological thesis, prevents us from attributing to the
“an sich”, in its proper philosophical horizon, a status that may be properly called
“ontological”.
We could here attack the so-called “ontological-formalist” trend − almost always
superficial and false − that aims at attributing to the doctrine of “an sich” an essentially untrue
(incorrect) ontology: we lose not only the historical and exegetic adherence but also all the
speculative eloquence of the ontological ambiguity of “an sich” and the deep ontological
consequences that can come out of this theory.
What is, finally, this ambiguous “an sich”? How, after the theoretical position of “an sich”,
did it put down itself in the history of ontology? If we observe with more attention, the “an
sich” appeared at first as a “bad patch” of classical ontology, as a “passage at the limit” − as
an extenuation − of its fundamental categories. The approach of the Theory of Science at first
seems to be fundamentally an extension of Platonism. Following this position, it is impossible,
however, to define the theory of “an sich” as a kind of Platonism and, in particular, of logical
Platonism. Given that Plato introduces the ontological status of the idea as a warrant of the
stability of formal relations − that’s basically the issue of Phaidon − Bolzano, on the contrary,
presents the formal relations of “an sich”, those that simply give the ontological domain its
meaning, as devoid of any possible ontological status.
The position defined as “logical Platonism” appears indeed more as a bad extension of the
concepts of “Platonism” and “Realism” in the foundations of mathematics. Moreover,
independently from the question of the consistence of such a position, the latter appears more
and more projected on Bolzano ex post, from the problematic field of set theory, more than
intrinsically related to the position that Bolzano maintains in his main works. If we observe
with more attention, even if we acknowledge such a Platonism in Bolzano, such a link is
impossible in relation to the fundamental assumption (almost always implicit) of a Platonism
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assumed in relation to formal entities. Even in the most recent definitions of Platonism
[MADDY 1990, 20-36] the hypostatisation became possible in relation to mathematical
objects or sets of objects (by its canonical and traditional form). Bolzano was deeply aware of
this necessary assumption when he began to define the existential problem in the sense of
“propositions in themselves”:
“The underlying objective idea, however, the idea in itself, of which the subjective idea
is just the apprehension, is not, and cannot be, an existing thing. This is not because [...]
there are no golden mountains; rather because, were the ideas in themselves something
real, the propositions in themselves, of which they are the parts, would also have to be
real”[BOLZANO 2004, 41].
Now, there is a strong anti-Platonist assumption in relation to the possibility of
hypostatising a propositional form (simple or complex) as an existing entity. Bolzano poses
the awareness of this impossibility at the basis of his reasoning, because he is deeply aware
that when we have to operate with a formal and syntactical form, the hypostatisation becomes
more problematic (if not meaningless) than a simple hypostatisation of semantic entities.
Anyway, if a logical Platonism did exist, it would bring with it a strong ontological
assumption, i.e. an assumption explicitly expressed, an ontological commitment about the
formal entities which count as “objects”: a strong ontological assumption needs the
introduction of second order quantified variables. This is impossible and finds no occurrence
in Bolzano’s theory, or, at least, in the theory of “an sich” as proposed by the Theory of
science.
But the approach of the Theory of science is not only far from a Platonism, it is also far
from a certain Aristotelian perspective that has determined and oriented the late-scholastic
German metaphysics, particularly concerning logic.
In almost all logic handbooks of the Aetas kantiana − and even before, starting from Meier
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− there was no doubt in acknowledging the logical priority of concept, i.e. of the formal
representation of an object (thing), over proposition [Satz] or judgement [Urteil]: these, as a
whole, were mereologically dependent, from this speculative point of view, on their parts.
This logical scheme of construction of deductive chains from a single objectal
representation (the substance) starting from which, with the inherence of a predicate, a
judgement and hereafter a syllogism and syllogistic chains (epi- or pro-syllogisms) were
formed, basically determined the classical ontologies (and in the end the Leibnitian ontology,
which was to be grounded upon the assumption of the ontological nature of the relation of
inherence) [RUSSELL 2008, 12, 42-50].
But what seems more interesting for our purposes is that the logical scheme also
determines Bolzano’s ontology, following the articulation between effective being [wirkliches
Sein] and property [Beschaffenheit] : this sketches essentially the conceptual gap between the
ontology of things and the quasi-ontology of propositional forms in the Theory of science.
Nevertheless, what determines the innovative break of the Theory of science is exactly this
logical “propositionalism” that switches − in relation with the “an sich” and the logical realm
(das Logische) – the mereological order of dependence between representation (idea) and
proposition, therefore opening many new perspectives on the formation of deductive chains.
We cannot, for the moment, state that Bolzano definitely breaks this fundamental
symmetry between logic-formal relations (structured in relation to the conceptual pair
object/determination) and the ontological realm (structured in relation to the relation of
inherence). It is however doubtless that, whit this inversion, Bolzano can break, to begin with,
a symmetry that was almost natural in logical theories, as it relates to their epistemological
utility. This implies a refusal, even not definitive, of a naive theory of correspondence
[Korrespondenztheorie]:
9
“For precisely this reason I cannot grant the identity of the two expressions: “This
judgment is in accordance with truth” and “This judgment is in accordance with reality”;
even if the two are often confused, and can be confused, especially whenever the truth
in question concerns an existing object, as in the case of the apple tree” [BOLZANO
2004, 113].
In this act of breaking, or calling into question, the logical structures of late scholastic
metaphysics (in particular of the mereological priority of ideas upon the judgement) and,
consequently, in the calling into question of the fundamental and meta-ontological
assumptions of metaphysics, the ambiguous ontological status of the “an sich”, its “quasiontology”
finds its “natural place”. This quasi-ontology is forcefully embedded − assuming
the mereological dependence, in the realm of “an sich”, between proposition and
representation − already in the first definition of proposition in itself as such. This first
definition is basically a negative one, to which will follow a positive (but not very clarifying)
characterization:
I wish to show as clearly as possible what I mean by a proposition in itself. In order to
accomplish this, I want to define first what I mean by a spoken proposition or a
proposition which is expressed in words. With this name I wish to designate any speech
act, if through it anything is asserted or expressed; that is to say, whenever it is one of
the two, either true or false in the usual sense of these words; or, as one can also say, if
it either correct or incorrect. [...] Given that it is understood what I mean by a spoken
proposition, I should like to note that there are also propositions which are not presented
in words but which somebody merely thinks, and these I call mental propositions.
Obviously, in the expression ‘spoken proposition’, I differentiate the proposition itself
from this articulation. In same way I differentiate a proposition from the thoughts of it
in the expression ‘mental proposition’” [BOLZANO 1973, 20]
It’s at this point that Bolzano introduces the so-called “positive” definition of the
proposition in itself:
“A proposition in itself I call that particular entity which one must necessarily associate
with the word ‘proposition’ if he wants to follow me in the above distinction. It is that
10
very entity which one thinks of as being a proposition when one asks whether or not
somebody has articulated it, or whether or not somebody has thought it. The same entity
I mean by the word ‘proposition’ if, for brevity’s sake, I use it without the additional
phrase ‘in itself’. In other words, by proposition in itself I mean any assertion that
something is or not the case, regardless whether or not somebody has put it into words,
and regardless even whether or not it has been thought” [BOLZANO 1973, 20-21].
Another clarification of the quasi-ontological status of the “an sich” is presented by the
definition (again at first negative) of the representation in itself, or simply “representation”,
the mereologically dependent component of the proposition in itself. In the § 48. 2, Bolzano
states:
“Anything that can be part of a proposition in itself, without being in itself a proposition,
I wish to call an idea in itself, or simply an idea or objective idea. This will be the
quickest and easiest way of conveying my meaning to those who have understood what
I mean by a proposition in itself” [BOLZANO 1973, 61].
Why? Because, as a mereological component depending on the proposition in itself, the
representation in itself will be obtained from the same method. This mereological dependence
was used, at first, by Bolzano, to define not only categorematic but also and at the same time
syncategorematic terms 1 . Those terms, conceived as mereologically dependent on the
proposition in itself, are homogeneous with it, from the point of view of non-ontological,
quasi-ontological status. They have no (clearly assertible) ontological status: exactly like
propositions in themselves, they do not presuppose “a living being of whatever form as the
subject in which it is accomplished”. On the other hand, like a judgement or a statement, the
subjective representation (idea) or the simple expressed name, have a “real existence at the
time when they are present in a subject, just as they have certain effects”.
Exactly in the same way in which the proposition in itself is linked out of an “ontological”
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realm, from the one ontological realm of the judgement and statement, we have to divide the
effective state from the non effective state, i.e., on one hand, the subjective representation and
the expressed name and, on the other hand, the representation in itself. This latter corresponds
only to “every subjective representation” and, consequently, it cannot correspond to
something ontologically determined: “by objective idea I mean the certain something which
constitutes the immediate matter [Stoff] of a subjective idea, and which is not to be found in
the realm of the real”. “An objective idea − as Bolzano continues − does not require a subject
but subsists [bestehen], not indeed as something that exists, but as a certain something even
though no thinking being may have it; also, it is not multiplied when it is thought by one, two,
three, or more beings, unlike the corresponding subjective idea, which is present many times”
[BOLZANO 1973, 61].
This step of negative definition − where the mereological dependence leads to the
definition of the three syntactic components (representation-subject, representation-predicate
and the concept of connection) − induces this feeling of ontological ambiguity of the “an
sich”. The cause, as we will see (and as we have already sketched), is that the syntactical
structure of the proposition in itself (representation-subject, connexion, representationpredicate
or determination) isn’t so much a copy, a mirror image (therefore derivative) of the
ontological relation in the stronger sense we can find between substance and property
[Beschaffenheit]. [SIEBESTIK 1992, 33 fww]
This appears now − as Jan Sebestik says – to be an ontological difference. But, for us,
against Sebestik’s interpretation, this ontological difference does not correspond much to an
ontological dualism or, better, to an ontology (already a largely Meinongian one) whose
domain is articulated in two classes of objects: the objects for which we need to say that they
exist and, on the other side, the objects to which the ambiguous expression “there is” applies.
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It is precisely this aspect of the theory of the Wirklichkeit that represents the originality of the
meta-ontological approach of Theory of science and On the mathematical method. The very
same thesis was to become soon an essential point of discussion in the exchange with Exner.
The representation-subject’s “an sich” − which “subsists” [besteht] − doesn’t bring itself to
the “für sich” [for him] of the substance, of the wirkliches Sein (about which we must affirm
that it properly exists). This impossibility of superposing both comes from the unavailability
of a direct (automatic) superposition of the syntactical form to the underlying ontology.
This is a meta-ontological thesis which − as we will see soon in relation to Combinatorics,
of which it represents the speculative presupposition − is full of consequences. It is at first, as
Benoist says, “the liberation of the category of thing in relation to the canonical sense of
being”. Nevertheless, if we consider it more attentively, this main importance consists in the
fact that this thesis is presented for the first time (explicitly) as a meta-ontological thesis, even
if “ante litteram”. This “meta-” is justified precisely by an asymmetry that, for Bolzano, never
became an ontological dualism or, which amounts to the same thing, a logical Platonism. This
meta-ontological thesis affirms indeed an asymmetry, which had never been affirmed before,
neither by the critique of reason nor by the onto-theo-logy that it criticizes. This is because the
question was concerning essentially the possibility of affirming the existence of beings not
outside of the ontology as such but only outside of the horizon of perceptive experience.
The Kantian equivalence between “immanent ontology” and “analytic of pure
understanding”, in fact, from this point of view adopted the same speculative grammar of late
scholastic metaphysics, only inserting a limitation to perceptive impression in the possibility
of speaking about ontology as such. This introduction was decisive but was at the same time
co-essential, from a meta-logical point of view, to the onto-theo-logical thesis which we
would criticize.
The Kantian prohibition provided by immanent ontology concerns beings (roughly
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speaking, “objects”) like “soul”, “God” or a collection of objects like “world” and doesn’t
affect as such the possibility to speak of a subsistence [bestehen] concerning sense, or
concerning a formal structure, as the subsistence of a certain something [ein gewisses Etwas].
Here Bolzano seems to follow Kant’s strong epistemological realism, but only if we don’t
consider that quasi-ontological Aspect of the “an sich”. As a result, it is this Aspect that
correctly acknowledges the meta-ontological thesis in all its importance. This consists
precisely in that aside, in the opening of a thematic space where we can describe an
ontological horizon and where, at the same time, we can fix its exception as residual. This
residual field of that thematic and meta-ontological space, that represents the outside of the
ontological domain of wirkliches Sein, doesn’t contain many metaphysical beings − described
in themselves as Realities [Realitäten] − but only a-physical beings, completely different
from the thing with its properties (like a Kantian heritage) as well as from mental states, i.e.
the judgements or the subjective representation as paqeμata thV uchV. That meta12
ontological thesis is indeed so radical that it includes, in the domain of ontology, the mental
states – taken as acts of grasping the non-ontological, the quasi-ontological objects of “an
sich”:
“A truth in itself is not just a thought or recognized truth considered in abstracto, i.e.
wrenched from its psychological context. For even out of its psychological context (i.e.
without a consideration of this context), each recognized truth still has an existence as a
cognition or judgment in a certain individual at a certain time; further, it has a greater or
lesser intensity and vividness, and is made with a greater or lesser degree of coincidence:
all predicates than in no way apply to truths in themselves” [BOLZANO 2004, 113].
The thematic space described in the meta-ontological thesis of “an sich” contains
completely new objectivities [Gegenständlichkeiten], residual beings, other than physical
things or mental states. On the one hand, there is therefore the space of so called “semantic
objectivism” − that is not really logical Platonism − whose objectivities cannot be fully
individuated, and on the other hand there is the horizon of the effective, which is rendered
14
meaningful by the thesis of epistemological realism: without exception, objects have and must
denote a space-time individuation. Is there ontology without individuation i.e. independently
from the quantification of variables? In this case, can we also call it “ontology”? Should we
rather consider the place of this ontology in an ontological Neverland? Bolzano’s answer to
the two first questions is clearly and definitely negative. The answer to the third is, in terms of
Bolzano’s philosophy, uncertain: we must complete it with another theoretical step.
But why, at least, does the “an sich” appear to be provided with a quasi-ontological status
rather than affirmed as a flatus vocis? Has the kind of Platonism which allows us to speak
about propositions and representations in themselves in a non-nominalistic way finally been
excluded? This is the alternative Bolzano tries to avoid for his meta-ontological perspective,
as is sketched in § 51.
The element which removes this alternative is to be found in this same mereological
interlocking that brings from the whole of the proposition in itself to the objective
representations as parts and, then, to the syntactic articulation between representationsubject/
connexion/representation-predicate. This notion, meta-logical and meta-ontological at
the same time, is the “something” [Etwas], the thing [Ding] − which introduces the neutral
notion of “object” [Gegenstand] into Bolzano’s meta-ontology.
“Also, the question “what does the word ‘thing’ mean for me?” has been answered. For
me, it is equivalent to “something”, and accordingly the widest concept of all”
[BOLZANO 2004, 110/1].
The “something” (or object) plays precisely the role of relativizing the wirkliches Sein, and
is to present itself as a “general form” grounded upon the primitive character of the relation
between representation and what is represented. The “something” is such a general and
comprehensive that it cannot be defined by means of thought: a form that resides even above
the distinction between concrete and abstract. The mere fact of speaking about something in a
15
merely logical way, and therefore, in the perspective of Theory of science, upon the metaontological
aside from the Wirklichkeit, involves a proto-theory of the object that allows us to
“speak about-”. Bolzano states:
“Even an idea, since it too is something, and thus an object (in the widest sense of the
word), can have characteristics. Thus, for example, a certain idea might have the
characteristic of simplicity, another than of compositeness” [BOLZANO 2004, 43].
The “something”, that is described in the thematic opening of Bolzano’s meta-ontology −
exceeds also, so to speak, that quasi-ontology that oversteps the bounds of the horizon of
effectivity [Wirklichkeit] to grasp the objectivity of logical and formal structures: the meaning,
being impotent to constitute the form of the “an sich”, its structures, and to determine the
primitive relation between representation and what is represented, acknowledged in the
“something” − so that, because of this, even the non-objectual representation depends from
this relation − is “transcendental”.
It is precisely the “something”, as the general form of every grasping that describes the
thematic space of meta-ontology. Nevertheless, this sketch of a theory of object
[Gegenstandstheorie] not only extends our ontological outfit but, at the same time, allows us
to face a new form of Combinatorics. This describes a new way to think the essence of logic.
Indeed, this possibility infinitely Combinatorics of the “something”, i.e. of the
representations and propositions in its quasi-ontological autonomy, is so large as to overstep
the capacities [Fahigkeiten] of the subject, overstepping the domain of meaningful [cogitabile]
1) to consider the different sizes of ideas bring us to the idea of a representation which
size will be larger than that of all other representations. But after a deep reflection, we
must acknowledge that such a representation cannot exists.
“I mean nevertheless that they exists such ideas who are absolutely widest and highest.
And I mean that the idea of a certain something [Etwas] or that of an object in general is
16
already such a representation. Because we state of a idea, that she get an extension if
they are certain objects those are be represented by him. The extension of a idea cannot
consequently be wider than in the case of she contain any object that can be given.
That’s precisely what realise the representation of an object or a something in general.
Who agree with this will can easily find many other representations of the same size: i.
e. the idea what isn’t nothing like all the others who contain the concept of negation two
for two” [BOLZANO, 1929, §99, 53].
The possibility “of saying something meaningful”, determining not much the “something”
and the autonomy described from this general form, cannot determine the extension and the
release of the logical Combinatorics between representations and propositions in themselves.
Indeed the meaningful [cogitabile] appears already as a representative composition of the
“something” and the possibility (necessarily subjective) of meaning as such − therefore, the
possibility of grasping a proposition and an idea in themselves (modifier and not determining
predicate) − it appears also entirely different from the “something”. The meaningful is
constitutively contained in a ontology from an already necessarily “ontologized” form of
being.
By this assumption Bolzano can overtake all late scholastic tradition and, at the same time,
the Kantian theory of modality, according to which the possible was understood only as
“possible experience”, as functional to its inclusion in the domain of effectivity [Wirklichkeit].
Nevertheless this overtaking became possible only on the ground of the so called “revolution
of analyticity”. At first this overtaking is, so to speak, a parte ante − oriented to the Leibnitian
ideal of a universal logical language, which had been almost completely excluded from the
transcendental philosophy and that had completely lost its importance in the late-scholastic
metaphysical system of Wolff. But the import of this renovation of the Leibnitian project
17
needs full understanding. As Joëlle Proust says:
“Without undertaking the Leibnitian project of an universal characteristic, because of its
defiance in regard to symbolizing formalism, the Theory of science offers a speculative
equivalent: there is the ideal set of significations, decomposable in their element and
fixed. That’s not the symbolism who creates this precise and definitive determination of
sense, but its belonging to a set that is pure and separated from the variations linked to
individual existence and to the future of language” [PROUST 1987, 84].
Bolzano establishes, in his speculative perspective, the idea of a universal logical language
– one that cannot necessarily be formalized by symbols − radicalizing two basic Leibnitian
15
concepts: the idea, not explicit, of a substantial independence of eternal truths from divine
understanding, and the combinatoric idea of substitutivity salva veritate 2 .
The quasi-ontology of “an sich”, indeed, simply radicalizes the assumption on which
Leibniz was ambiguous in §§ 43-46 of Monadology, i.e., the radically anti-Cartesian thesis
about the impossibility of creation (or only modification) of eternal truths3. The prerogative
that the quasi-ontology of “an sich” can concede to God is only an infinitely more powerful
grasp of propositions and representations in themselves than men can ever obtain.
The proposition in itself, ontologically depending on no understanding, assembles men and
God in the same impossibility to effect in any way the “an sich”: neither men nor God create
the significations by which they obtain knowledge. Nevertheless, as we have already said,
there is another difference in relation to the Leibnitian onto-theo-logy, that makes it so that
the Bolzanian project in the Theory of science is oriented to a completely other epistemic
dimension. Indeed, in spite of the greatness of the Leibnitian project of mathesis universalis,
we must make the same remarks concerning the Leibnitian Combinatorics: it always and
constitutively develops itself in connection with a strong metaphysical presupposition; by this
presupposition, the proposition always represents, in a logical image, the relations and the
18
states between monads, of which God is the root (the source)4. Is it the same for Bolzano?
Exactly speaking, no, because the relation − as we will see − is inverted.
The quasi-ontology of “an sich” and the combinatorial nature that will be assigned to the
logical objectivity given the absolute neutrality of the something, describes a space entirely
and ontologically autonomous of the Combinatorics (in the sense of autonomy from an
ontology and not, like for logical Platonism, of an autonomous ontology!). Only after this
statement of the ontological autonomy − but only from an epistemological point of view −
must we try to establish the correspondence (indeed, the specularity) between a proposition in
itself, grasped in its completely self-subsistent objectivity, and a state of affairs. The
judgement of a transcendental ego is neutralized and, therefore, is also neutralized by the
Kantian prejudice against analytic judgement. A Combinatorics not oriented in a metaphysical
sense of the primitive notion − framed in an onto-theo-logic view5 − nor structured by a
2 For this principle, see the formalisation given by TARSKY 1994, 55. See also LEIBNIZ, 1988,
362 :
« Coincidit A ipsi B, si alterum in alterius locum substitui potest salva veritate, seu si resolvendo
utrumque per substitutionem valorum < (seu definitionem) > in locum terminorum, utrobique
prodeunt eadem, eadem inquam formaliter, ut si utrobique prodeat Salva enim veritate fiunt
mutationes quae fiunt substituendo definitionem in locum definiti vel contra. < Hinc sequitur, si A
coincidit ipsi B, etiam B coincidit ipsi A >”. LEIBNIZ , 1992, 260-261.
See also LEIBNIZ, 1988, 360 :« Termini primitivi simplices vel interim pro ipsis assumendi, sunto.
simply syntactical form, must reinstate the concept of analyticity and enlarge the notion of
truth. As Joëlle Proust says, “the new revolution that Bolzano creates concerning analyticity
consists in the fact that this analyticity is grounded more upon what the proposition of a same
family doesn’t says than on what it does say“. The research does not concern intentions or
concepts but references of which we must only compare the extension. We must not ask if a
19
predicate “belongs” to a concept, but if the individuals obtained from the predicate include
individuals that are indicated by the subject. Into Leibnitian syntactical criterion of truth, the
partial definition must prove that the predicate was as well contained in the subject. On the
contrary, Bolzano proposes a semantic criterion”. This criterion is at first semantic “because it
supposes the reference to an objective world where things can be enumerated and classified
following its properties”. It is at the same time, therefore, “extensional, because the models
contain classes of individuals respectively related by relations of inclusion”. “That’s also
inclusion both classes that explains what is the convenience between terms” [Proust 1987,
111]. In spite of the definition given in On the mathematical method, a definition clearly and
exclusively formal [Bolzano 2004, 47], the combinatorial possibility of substitution salva
veritate, far from presenting in itself only a senseless mechanical game, plays the rule of
sense-making. The method of variation, a mathematical model only of predicative logic
substitution, plays the most fundamental rule for science, i.e. that of grasping new
propositional entities ontologically autonomous and therefore new truths in themselves:
“I showed in the preceding that there are universally satisfable as well as non-satisfiable
propositions, given that certain of their parts are considered variable. It was also shown
that propositions which have either of these properties on the assumption that i,j....are
variable, do not retain this status if different or additional ideas are taken as variable. It
is particularly easy to see that no proposition could be formed so as to retain such a
property if all its ideas were considered variable. For if we could arbitrarily vary all
constituent ideas of a proposition, we could transform it into any other proposition
whatever, and thus could turn it into a true, as well as a false, proposition. But it would
be important enough to deserve notice if a proposition contained even a single idea
which could be arbitrarily changed without altering the truth or falsity of the proposition;
i. e. the propositions which could be obtained from it through the arbitrary alteration of
20
this one idea would either all be true or false, provided only they have reference.
Terminus (quo comprehendo tam Ens quam Non-Ens). Ens < seu possibile > (intelligo autem
semper concretum, quia abstacta tanquam non necessaria exclusi). Existens (licet revera reddi possit
causa existentiae, et definiri posset Existens, quod cum pluribus compatibile est quam quodlibet
aliud incompatibile cum ipso. Nos tamen his tanquam altioribus abstinemus). Individuum (Etsi enim
Ens omne revera sit individuum, nos tamen terminos definimus, qui designant, vel quodlibet
individuum determinatum, ut Home seu quilibet homo, significat quodlibet individuum naturae
humanae paticeps. At certum individuum est hic, quem designo vel monstrando
vel addendo notas distinguentes (quanquam < enim > perfecte distinguentes ab aliis individuis
occurentibus). Ego (est aliquid peculiare, et difficulter explicabile in hac notione, ideo cum
integralis sit, ponendam < hic > putavi) ».
Borrowing this expression from Kant, I allow myself to call propositions of this kind
analytic. All other propositions, i.e. all those which do not contain any ideas which can
be changed without altering their truth or falsity, I call synthetic” [BOLZANO 1973,
§148, 198].
This logical opening would be impossible without the quasi-ontology of “an sich”, which
keeps safe the value of propositional truth from the subjective dimension and renews − on the
basis of the method of variation − the meaning of analyticity. There is no more need to recur
to the conceptual pair implicit/explicit, as it happens, on the contrary, in Leibniz, Kant, and in
post-Kantian Logic too.
The conceptual component, endowed with an entirely different status, subsists “elsewhere”
− an elsewhere that is nowhere in the sense of spatial and temporal individuation, but that is
elsewhere only in the meta-ontological sense. It is elsewhere in relation to the implicit and
21
explicit, as in mental states, those that belong exclusively to the cogitatio possibilis, to the
meaningful and not to the autonomy of semantic entities. For this reason, the Bolzanian
concept of Combinatorics must rest unsatisfied by a simple explanation based upon the
conceptual pair implicit/explicit:
“Generally, it seems to me that none of these explications sufficiently emphasizes what
makes these propositions important. I believe that this importance lies in the fact that
their truth or falsity does not depend upon the concept of which they are composed, but
that it remains the same irrespective of the changes to which some of their concepts are
subjected, provided only that reference of the proposition is not destroyed” [BOLZANO
1973, § 148, 201].
Bolzano reaffirms here not only that postulate of mereological priority of the proposition
with respect to representation in itself as a fundamental thesis against the traditional
conception of analytic judgement – a conception which represents, finally, the presupposition
of a Platonic hypostatization of semantic entities. Bolzano affirms here, moreover, the
semantic (but non-ontological) importance of Combinatorics.
The proposition in its autonomous consistence already has its truth-value, and its truthvalue
doesn’t prejudge the importance of the variation or substitutivity salva veritate, in spite
of the adoption of a transcendental point of view. Indeed, from a transcendental point of view
(a logic that acknowledges to the judgement the function of revealing a new truth as synthetic
judgements), an analytic judgement is fully useless, because it hides already in itself,
implicitly, the truth.
The cognitive enrichment of the analytic lies clearly sic et simpliciter in the Combinatorics
of autonomous quasi-ontological entities: otherwise, as Bolzano states at the beginning of §
12, the value of the analytic judgement would be much too small. The cognitive richness of
analyticity must also be strongly stated because the variation is exactly not a question of a
22
banal logical operation. The variation does not just explicate what was only implicit, but also,
allows us to grasp new propositions in its quasi-ontological autonomy: new entities that,
belonging to the “same family”, come with a truth-value in themselves.
Is it true, then, that Bolzano comes back to a “pre-critical conception of truth”? It is true,
indeed, that he searches for the definition of truth not in the product of a judgment (as an
ontological event, or as a mental state) but only in the correspondence between a proposition
and a state of affairs. But this remark doesn’t do full justice to the radicalism of the Bolzanian
approach.
The ontological autonomy of propositions and the method of variation introduce in the
realm of conceptual a different complexity from those which characterized pre-Kantian logic
and ontology. Bolzano’s “ordo idearum”, so to speak, is not the “ordo idearum” that receives
its grip on reality as perfectly isomorphous to the concept God has of it. Bolzano enlarges our
ontological outfit via the introduction of the quasi-ontology of “an sich” in order to pursuit a
double speculative approach: 1) the negation of the naive symmetry between ordo rerum and
ordo idearum, found in late scholastic metaphysics, and of its foundation in the onto-theological
presupposition (i. e. Wolff’s divine understanding); 2) the enlargement of our sights
on the horizon of ideality of formal structures. This enlargement concerns precisely
mathematics; not, as it happened with Kant, just the pro-syllogistic chains of consecutio
rationum. Moreover, Bolzano develops , as the theoretical point we was searching for, an
essential and decisive dissymmetry from an epistemological point of view: a dissymmetry
between the realm of wirkliches sein, of ontology, whose opening is fixed and whose objects
are necessarily what they are, and the quasi-ontological field of an infinitely formal
Combinatorics that enlarges itself more and more.
The enrichment of the Bolzanian universe is therefore not to be found only in the
introduction of the quasi-ontology of “an sich”, as if this latter were an absolutely static
23
component, but precisely in its dynamism: this field of semantic objects (as horizon of speech)
can inflate and enlarge indefinitely, keeping safe formal consistence at the same time. This
change entirely results, in particular if we consider again that the reassignment of these
entities in the realm of knowledge of reality (necessarily structured by semantic ideality) is
grounded upon this dissymmetry between a ontology and a quasi-ontology.
Indeed, by the syntactical operations of substitution, which enlarge our semantical-formal
outfit, only our knowledge of reality is to become enriched (at least in its possibility). If the
quasi-ontology of “an sich” cannot become effectively productive in ontology, in the domain
of the wirkliches Sein; nevertheless, it has a real and massive productivity with respect of our
approach to reality, our approach to relational configurations of effective being. This is
fundamentally much more essential than simple, naive productivity. The “quasi-“ of ontology
of “an sich”, in its ambiguity, inserts precisely this dissymmetry in the epistemological
meaning and opens, at the same time, by means of Combinatorics, an enlarged possibility of a
conceptual (representational) grasp of reality: this was impossible for pre-critical and critical
conceptions of analyticity. But this ambiguity must face a dilemma, even if we don’t want to
accept it as an epistemological hypothesis as such. The dilemma consists in the decision that
we can make − from a speculative and meta-ontological point of view − about this “quasi-“.
We could pursue the enlargement to our ontological outfit admitting − why not? − one, two,
three, n other ontologies, or stating an ontological dualism where one of two ontological fields
are constructed from many classes (typologies) of formal objects, each enriching itself in
inflationist way. That’s the Meinongian way of ontology.
But we can nevertheless come back, more attentively, to the subjective modalities by
which the specular dissymmetry between formal idealities and ontological realm is articulated.
This is the phenomenological way of ontology. There are, essentially, two speculative projects
24
strictly related to two different concepts of the descriptive method. We must decide, at least,
which among these two projects contributes more deeply to define a mathesis universalis. The
mathesis, in this renewed sense, can only represent the same science that, as Bolzano states in
§ 1 of Theory of science, appears in all those treatises that we can compose starting from this
fundamental ambiguity of the quasi-ontology of “an sich”.
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