Bernard Bolzano: Study of science – Truths and consequences

 After propositions, Bolzano moves to discuss truths in themselves or objective truths that may or may not be known by anyone. He considers this a field not yet investigated by anyone and finds even his own results very preliminary.

Like with propositions, Bolzano begins with characteristics common to all truths, the first one being the familiar one that truths do not actually exist, making it thus incorrect to say that some truths exist eternally and some temporarily. He notes also that all truths deal with objects, so that their subject is a representation that refers to at least one object. Bolzano admits that some truths appear to have propositions as their subject, but thinks that the subject in these cases is actually a representation of a proposition. Similarly, he continues, truths with imaginary objects as their subject (e.g. round square does not exist) usually have a representation of an imaginary object as the real subject (in the example, the truth  is actually “the representation of a round square refers to no objects”). Sometimes, Bolzano adds, such truths are actually hypotheticals: “golden mountain is barren” means actually “if a mountain is golden, it would be barren”.

If the subject of a truth must be a representation referring to some object, Bolzano says, its predicate must be a representation referring to such a characteristic that every object referred to by the subject has. Furthermore, he continues, all truths must be compatible with one another (they are true at the same time), and every truth is derivable from infinitely many other truths, while infinitely many truths are derivable from every truth. Finally, every truth and every collection of truths is a part of another truth (at least the truth saying that all these propositions are true).

Just like with propositions, Bolzano goes on to describe different types of propositions. Actually he mentions only one possible division of truths, namely, that of analytical and synthetical truths. Analytical truth, Bolzano defines, has as its constituent at least one representation that can be switched with any other representation so that the proposition remains a truth, just as long as the proposition (that it, its subject) refers to an  object; any other truth is synthetical truth.

Evidently, Bolzano thinks, there are analytical truths (his example is “every A, which has b, has b”). Then again, he thinks, synthetical truths are a bit more difficult to find. Bolzano notes that there are characteristics that belong to all objects referred to by a representation without being constituents of that representation, but this is not enough to establish the existence of synthetical truths. For instance, the characteristic of the sum of the angles of a triangle equalling two right angles is something featured in all triangles, although this characteristic is not a constituent of the representation of a triangle. Still, Bolzano surmises, the truth “this triangle has angles equal to two right angles” is still analytical by his definition, because in switching the representation “this” with another representation that makes the subject objective (in other words, by changing the object referred to by the word “this” to some other triangle), the proposition remains always true. 

Bolzano notes that the problem just described can be circumvented, if we just pick a subject that is either simple or then of the type “something that has x”. The predicate of the synthetical truth we are searching for, he adds, should not be such that holds of all things when some of its constituents is changed (any characteristic of the type “being x or not-x” is of this kind. Bolzano suggests using either simple predicates or combinations of simple predicates of the kind “x and y and z…”. Finally, the constructed proposition must also be true – Bolzano’s own example is “A is actual” where A is meant to be some intuition. 

Bolzano thinks that there are clearly also negative synthetical truths (his example is “A has no b”, where A is intuition and b is a characteristic that A does not have). Furthermore, he notes, “representation of something, which has characteristics a, b and c, refers to an object” is always a synthetical truth, because if the characteristics are switched to such that are incompatible with one another, the result is not true. Finally, Bolzano points out that “representation of something, which has characteristics a and b, is imaginary” is synthetical, if it is true, because then a and b are incompatible, and when switched with compatible representations, make the resulting proposition untrue.

Bolzano considers it evident that there are both analytical and synthetical truths that are either intuitive propositions or conceptual propositions. Thus, “each triangle is a figure” is a conceptual analytical truth and “this triangle is a figure” is intuitive analytical truth. Similarly, the aforementioned “A is actual” is an intuitive synthetical truth, while Bolzano’s other examples of synthetical truths are conceptual.

The rest of Bolzano’s investigation of truths discusses what he considers the most remarkable relation between them, that is, the already mentioned relation of ground to its consequence relation. He again notes the example of a thermometer rising, which is at most a ground for us knowing that the summer is coming, but not an objective ground for the truth of the summer coming, where the consequence relation would hold independently of our thoughts. This example shows also that the consequence relation is not the same as the relation of derivability: “summer is coming” is derivable from “thermometer is rising”, but not its consequence.

Is consequence still always derivable from its ground? Bolzano thinks this is not so, because of the following example. All practical truths, he says, must be founded in a truth of the form “we should do A”, which with some propositions of the form “doing A requires doing X” is the ground of all practical truths. Now, Bolzano suggests, this highest law of ethics appears to be founded in the truth that A is something that we can do, but there seems to be no rule of inference that would account for this unique consequence relation, since they can prove obligations only from obligations.

As we already saw with the example of the ground of practical truths, the complete ground of a truth is usually a collection of truths, while the individual truths in that collection are then just partial grounds. Bolzano ponders the question whether the rules of inference used for deriving the consequence from this collection of truths should be regarded as part of the ground. He comes to the same conclusion as Lewis Carroll that this would lead to an infinite series of ever new rules of inference.

Bolzano then considers the question whether the consequence relation is the same as causality. No literally, he answers, because causes and effects are actual objects, while grounds and consequences are truths, which are not actual. This leaves still the possibility that causes and effects could still be constituents of grounds and consequences. Indeed, some consequence relations involve causes and effects (e.g. “God is” could be a partial ground of “world is”). Still, Bolzano thinks, not all consequence relations involve existing objects, such as consequence relations involved with mathematical truths. Thus, he concludes, concepts of cause and effect must be defined by concepts of ground and consequence, as he has already suggested, but the latter cannot be defined by the former.

Bolzano does not find ground and consequence to be simple concepts, because they are concrete and least have “something” as their constituent (that is, ground is something that “grounds” something else and consequence is something “grounded” by something else). He has no idea whether this abstract notion of “grounding” has a further definition. All the definitions suggested by earlier philosophers, Bolzano says, are either circular or then faulty – for instance, grounding cannot be defined as determining, because an equation determines a magnitude, but is not its ground.

Since we cannot define the consequence relation precisely, Bolzano suggests describing its features as much as possible, in order to distinguish it from other similar relations. Thus, he says, derivability holds between propositions, whether true or false, while consequence holds only between truths. Sometimes we do say that a consequence relation holds between falsities, Bolzano admits, but then we are actually speaking of derivability or then we consider cases where switching some representations in these false propositions and thus making them truths, creates also a consequence relation between them (Bolzano’s example is when we say that “monkey can speak” is a consequence of “monkey has distinct representations”).

Bolzano notes some other similar confusions. Sometimes we confuse causality with consequence and say e.g. that God is the ground of the existence of the world. Sometimes we speak as if mere representations could be grounds, for instance, when the ground of our fear of death should be our representation of it – actually, it is then not representations in themselves, but our thoughts of them we are speaking and they are not grounds, but again, causes. Bolzano also notes a curious case, where the ground of a proposition being true or false are said to be its constituent representations. He thinks that in this case, the ground lies actually in the truths involving the constituents of the proposition.

Comparing further derivability and consequence relation, Bolzano points out that a proposition can be derivable from itself, but nothing is a ground of itself. Then again, derivability can hold between collections of propositions, and Bolzano thinks that the same is true of the consequence relation. We have already noted that while a ground can be a single truth (thus, A is a ground for “A is true”), it is often a collection of propositions and the individual propositions in that collection are just partial grounds. Similarly, individual propositions based on some ground are just partial consequences, and the collection of all these partial consequences is the complete consequence of the ground.

The notion of total consequence reveals yet another difference from the notion of derivability. While we can derive several propositions from one proposition, the total consequence – consequence in the proper sense of the word, Bolzano thinks – is always unique, as defined by all the partial consequences. It seems that a consequence can then have many grounds, but these are all just partial grounds, Bolzano argues, but the total ground is always unique.

Derivability is a transitive relation (that is, if A is derivable from B and B from C, A is derivable). Due to the just mentioned uniqueness, Bolzano points out, the consequence relation cannot be transitive. Similarly, while A can be derivable from B and B from A, the same sort of reciprocity does not hold for grounds and consequences: we do speak of e.g. reciprocal causality, Bolzano admits, but then it is actually a case of the interacting things having forces that cause some changes in the other thing – not both things literally causing one another. Then again, just like what is a derived conclusion can in another context be a premiss, so a consequence of something can be a ground of something else.

Derivability always survives summing up collections of propositions (e.g. if A and B are derivable from C and D and E and F are derivable from G and H, then A, B, E and F are derivable from C, D, G and H). With consequence relation this is not so easy, Bolzano states, since one collection might contain consequences of the other collection, which would cause difficulties, if the collections contained same truths (e.g. if A and B are consequence of C and D and C and D are consequence of E and F, the collection of A, B, C and D is not the consequence of C, D, E and F). Even if we avoided the cases where the collections contained same truths, the sum might still not work, Bolzano thinks, because the consequence relation requires a more intrinsic connection between the truths (e.g. the collection of “God is almighty” and “isosceles triangle has two equal angles” is not a ground of the collection of “the actual world is the best possible” and “the equilateral triangle has all angles equal”).

Collections of premisses and collections of conclusions appear to have no hierarchical order, and same seems to be true of the collection of partial grounds and the collection of partial consequences, Bolzano thinks: although there may be a preferred order how to present grounds in a scientific treatise, this is just a subjective preference. A more difficult question, Bolzano thinks, is whether just like with premisses, there could be partial grounds, one of which is a consequence of the other. Surprisingly, he suggests that consequence relation does resemble derivability in this respect: “every truth is something immaterial” is ground for the truth “the proposition that every truth is immaterial is itself a truth” and both of them are partial grounds for the truth “the proposition that every truth is immaterial is itself immaterial”.

Every proposition is both a premiss and a conclusion, but is every truth a ground and a consequence? According to Bolzano, every truth is a ground for further truths (at least for the truth that the truth is true). Then again, he thinks it probable that some truths are not consequences of anything (his example is the truth that something exists). Bolzano calls such truths fundamental. He suggests that there must be several fundamental truths, because it seems impossible that all others could be consequences of just one truth.

Bolzano considers what will happen if we ask for all partial grounds of a truth and then for partial grounds of these new truths and so on, creating a tree-like structure. If we reach fundamental truths, he notes, this process ends. Still, Bolzano suggests, there may be truths, where this search for further and further partial grounds continues indefinitely: his example is that of variable states of created substances, which seem to depend on an infinite series of causes.

Bolzano also coins the term auxiliary truth to refer to any truth in the just described tree-like structure, created from a given truth. Unlike the notion of ground, the notion of auxiliary truth is transitive, but like with ground, no truth can be auxiliary truth of itself. Then again, Bolzano notes, the same truth can be auxiliary for another truth in many different places of the same structure: just look at mathematical proofs, where we have to use some truth many times.

Bolzano notes that truths involving only pure concepts are grounded in other truths involving only pure concepts, although they might be known through experiences. Furthermore, pure conceptual truth that is a ground of another pure conceptual truth can never be more complex than the consequence (Bolzano thinks that this is not true of intuitive truths, since they are often grounded in general truths that are more complex). Since Bolzano has assumed that there is only a finite number of simple concepts, he can also assume that there is only a limited number of fundamental conceptual truths. Thus, at least with conceptual truths, the consequence relation is ordered so that the greatest number of consequences are based on the smallest number of fundamental truths.

Bolzano closes the discussion by noting that sometimes grounds are derivable from consequences and sometimes not: as an example of former we have “every A is B” and “every A is C”, which together form the ground of “every A is B and C” and are derivable from it, while as an example of latter we have “what has a, has b” and “what has b, has c”, which form the ground of “what has a, has c”, but are not derivable from it. Just like with causes, Bolzano defines condition in a wider sense as an auxiliary truth of some truth that is derivable from this truth.

Immanuel Hermann Fichte: Outline of a system of philosophy. Second division: Ontology – Internal and external

A completely new chapter in Fichte's ontology has begun. For the first time, the viewpoint of finite entities has been fully discarded. More likely, Fichte adds, it has dialectically destroyed itself, since the finite has shown itself as merely sustained by infinity. The positive infinite or absolute has cancelled the finite in its separation, but also raised it into a true reality. This is, Fichte thinks, the correct foundation for the ontology, and it properly begins only here, when the standpoint of ontology has become one of synthesis or one of absolute. If the task of philosophy is to consider things in their relation to truth, Fichte insists, this means knowing them from this standpoint, and specifically in ontology, according to absolute form. The first part of the ontology, he explains, is then only an ontological justification of this true speculative high point, just like the first part of the whole system was an epistemological proof of it.

Now that the absolute is determined as essence, Fichte continues, it is inevitably involved with relation, which is supposed to be the characteristic of all concepts of this second part. Thus, he insists, the essence must be defined only in opposition to what is not essential, while the inessential can be understood only in relation to the essence. Fichte admits that we did find examples of such reciprocal determining already in the previous book, and indeed, one might even think that this new opposition means a relapse into similar antithesis. The difference is, he explains, that at the level of essence the opposition does not appear from outside, but is posited with the original concept. Thus, in order that an essence can be an essence, it has to have in itself implicitly the other that it then actualises into an opposition with itself and divides thus itself into a fundamental duality that still is unity.

The first and most formal determination of this concept, according to Fichte, is that the essence is the true being that remains always the same, while against it lies something infinitely self-destroying and changeable that is not being, but only seems to be or even is an illusion (Schein). Such a seeming being is not just nothing, he explains, just like essence is not merely being. Instead, essence is against other and even itself becomes something else, but also asserts itself and persists in unity with this difference and change. Similarly, the merely unessential or merely seeming to be shows in itself only what seems to be the essence. Here the infinite and finite become again separated, because the essence excludes what just seems to be from itself. Still, Fichte emphasises, what is purely nothing cannot seem to be anything. The seeming is then caught in the contradiction, he notes, that it seems even an appearance (Erscheinung) of essence, but then it would not be mere seeming.

Despite this self-refutation, Fichte says, the notion of seeming provides the starting point for all speculation: the absolute alone is truly the essential, while the finite sense world is in comparison only seeming. Thus, the absolute remains eternally the same or invariable throughout the variation of the finite world, and just like what seems to be still shows the essence, variation can also exist only through the invariable. The finite world is thus not ejected out of the absolute, as if the world would exist outside the absolute in any sense, but its independent existence is in general denied.

The essence appeared as the opposite of inessential that therefore was designated as what just seems to be. This seeming then annihilated itself and was proven to be just the appearance of essence. Thus, Fichte states, the inevitably shifting distinction or the infinite seeming is derived from the essence, and only because of this derivation is the essence not empty or just quantitative abstraction, but the qualitative fullness of positive infinity. The inessential or the seeming is fully eradicated, or it has changed itself into the fullness or the infinity of essence. In other words, Fichte explains, all that seems uncovers the essence, which presents its fundamental basis or ground (Grund) in what seems to be. Thus, the essence is to be next determined as a ground of its infinitely seeming distinctions.

Seeming distinctions are thus grounded in the infinity of essence itself, Fichte summarises. Just like the essence cannot be without grounding distinctions, all distinctions also appear only as unveiling or appearance of the hidden ground, thus, he concludes, the essence is complete only in both the ground and in its infinite unveiling, since only with this relation it is not anymore empty or abstract. Fichte points out that the word ground has here, and indeed, in the common use of language, two meanings. Firstly, ground refers to the foundation (Grundlage) that lies hidden under what appears. In this sense ground is contradictory, because it expresses itself in appearance, but also doesn’t. This contradiction leads, Fichte thinks, to the second meaning of the word, according to which ground is the sufficient reason or the explanatory principle (ratio) of an appearance. With such a ground, the appearance should immediately appear from it as its consequence, and only in combination with its consequence the ground is fully thought of.

From the essence immediately appears something else without any particular assistance, through the mere characteristics of the essence. What follows from the essence, Fichte suggests, could be called the absolute characteristic of the essence itself. By having this something or consequence follow from it, the essence becomes ground, and indeed, wouldn’t otherwise be a ground. Thus, Fichte concludes, ground and consequence are simply inseparable, and they reproduce the relation of finite and infinite in a more fundamental level. The difference is that the finite and the infinite are still more in the shape of opposition, while the unity of the ground and the consequence is already more intimate. The consequence appears from the invariable nature of ground, like it would flow out of or emanate from the unmoving rest of its being.

Fichte finds here a new definition for the concepts of finite and infinite. The finite should be determined as not a ground of itself, but a consequence of something else, while the infinite or the essence is, on the contrary, in general a ground, thus also a ground of itself. Fichte calls the infinite even the Ur-ground or absolute ground, which grounds itself and everything else: the absolute is through itself, while the finite is through the absolute. Then again, when we look at an individual or determined finite, he points out, it has to have a ground outside itself, and in this context the ground can be found only in other determined individuals. This returns us to the already familiar relation of other against other, but in a new form, where the different individuals are grounds and consequences of one another.

Thus, a determined individual is taken as a ground of another individual with a different quality. Indeed, Fichte says, ground must always be in some sense different from consequence, or if they would be thought as having identical determinations, they wouldn’t be thought as ground and consequence. He points out that such a relation must be based on an implicit and unjustified axiom that something can be generated as a consequence from a ground, although it is not present in this as such. This means that not just the being of the individual consequence, but also its characteristics should appear from its ground and that this wouldn’t be a ground, if both couldn’t be explained from it. Fichte takes this as the common philosophical understanding of this relation, expressed in the so-called proposition of sufficient reason, where an individual is not to be arbitrarily taken as a ground of another, but only if the being and the determination of this other can be sufficiently or completely explained from it.

Fichte thinks that the proposition of sufficient reason can be refuted through a familiar endless regression into the empty or negative infinite. In other words, in order to explain a determined individual b through another individual a, the a as a determined individual has to be again explained through a third x, which is again only an individual further to be explained, and so backwards in infinite. Each individual, Fichte concludes, would require for its grounding an infinite regress, or the sufficient reason is never achieved, because it would require endless individual grounds. The mistake, he thinks, is to attempt explaining an individual from an individual, since nothing individual can be a sufficient ground or reason for another, just as little as an individual can be a mere consequence of another individual.

The sufficient ground of an individual can lie only in an infinity, which was just presented in a mere quantitatively endless series of individual grounds. Yet, Fichte insists, this infinity should be understood positively and in its fulfilment. He suggests that this touches the earlier question, how from a ground can appear something other as its consequence, which is not contained in the ground. A ground should bring forth from itself what it itself is not, and similarly a consequence is neither the corresponding ground nor its part. Indeed, precisely this difference makes one the consequence and the other its ground, or if something had generated just itself, it itself would not be a ground nor would what appears from it be its consequence. Yet, Fichte insists, this bringing forward something that is not contained in the ground is a contradiction that should find its dialectical solution.

According to Fichte, the contradiction lies again in taking individuals as grounds and their negations as corresponding consequences. Finite individuals have already appeared as void and cancelled in the positive infinity, and indeed, it should be the characteristic of the current standpoint to not admit finite as final truth, thus, it would be foolish to remain with individual grounds. In other words, Fichte explains, there are no individual grounds or individual consequences, but every consequence is an infinite complex of grounding, just like conversely it itself is not just a consequence, but in another context again a ground. When all these one-sided notions are cancelled, we find the true, positive infinity, which is now understood as the sufficient and complete ground in all seemingly individual relations of grounds and consequences. This sufficient ground is once again the absolute essence.

Absolute is not just an Ur-essence, which could still be understood as remaining beyond and outside the inessential, Fichte insists, but an Ur-ground that uses the opposition of determinations to reproduce its internal infinity. If the finite was earlier opposed to essence as what only seems to be, here it is the inseparable consequence of essence or its immediate externalisation (Äusserung). This makes, Fichte says, Ur-essence into Ur-ground, which is thus not abstract and empty, but contains the infinite fullness of such externalisations. In Ur-ground the seeming becomes expressly the appearance of essence, since the absolute brings out its hidden essence into an infinitely unfolded externalisation. Fichte calls this a genuinely speculative worldview, although it still uses very abstract categories, which must be enlivened with symbolic expressions. It is a step forward, he thinks, because the finite world is not separate from the Ur-ground that reveals its essence in the immediacy of finite things, but unsatisfying, because the supposed revelation of hidden seems still just a nonsensical expression.

Ground and consequence can be comprehended only through one another. This means, Fichte explains, that when our understanding of one side changes, the other side must also be expressed differently. The immediate way to understand their opposition, he continues, is to see the ground as the inner core of the externalised consequence. Ground as internal is the hidden and invisible foundation that does allow a manifold of appearances to flow out from itself, but always retains a remainder that is not uncovered. Thus, Fichte argues, the externalisation of the essence can never adequately match its interior. The current standpoint asserts a separation between both halves, where the essence expresses itself in its externalisation only imperfectly, leaving behind an unexpressed interior, but the exterior is still not completely detached from the essence as a seeming illusion without any reality. The relation between internal and external is so one of ambiguity, where the internal appears in external and does not or the both are opposed and also not. Despite this ambiguity, Fichte insists, this relation is a necessary conceptual moment in the development of ontology, and indeed, used in other sciences (for instance, psychology of his time spoke of the interior of human mind being expressed imperfectly in their external behaviour).

When the internal essence and its externalisation are kept strictly opposed, Fichte suggests, their relation is shown to be contradictory. Essence as a ground determines itself in general into external and therefore its interiority is inseparable from its external side. In fact, Fichte says, the essence is the common element, while internal and external are only inseparable moments of the same essence as ground. Thus, he argues that the internal side cannot be called more essential than the external side, since the ground is equally present in both. We have thus managed to mediate the opposition of internal and external, but they still remain also distinguished.

The invisible internal is understood as determining itself into visible external. Fichte thinks that this relation corresponds to the common opposition of supersensuous and sensuous or ideal and real. In other words, everything external, immediate or given in the visible world should have an invisible internal ground lying beyond this immediacy. Essence is thus at this stage purely ideal, Fichte underlines, but as a ground it infinitely determines and realises itself in immediate actuality, and indeed, it is the original source of everything actual. Yet, he points out, the distinction between the ideal interior and the real exterior is becoming more and more non-existent, therefore, the ideal should itself be real and not unreachable beyond. The ideal should also be the only principle of actuality, Fichte adds, and especially sensuous individuals are not their own principles.

The relation of internal, hidden and invisible ground and external consequence has highlighted the side of separation, although ground does become visible in its externalisation. Still, Fichte assures us, internal and external are not anymore completely separated, but more like two sides of the same coin and they just have to be mediated. Indeed, he explains, internal and external are not separated, but only distinguished from one another. Thus, Fichte concludes, the absolute inseparability of both sides should be expressed more clearly: the internal ground is to be seen as the qualitative and ideal content that is shaped by the external consequence or form and thus made visible.