Bernard Bolzano: Study of science – Analysing propositions

Bolzano rounds up his discussion of propositions with the favourite pastime of the later logicist school: that of revealing the hidden logical structure of ordinary linguistic expressions. Remember that Bolzano's ultimate goal is to show that all propositions bend to the universal form of “A has b”. Thus, he uses the rather convoluted terminology that a representation has objectivity, when he wants to say simply that a representation refers to an object. In line with this, Bolzano suggests that “nothing is B” or means actually that the representation of something, which has the characteristic b, has no objectivity, rendering it unnecessary to take the word “nothing” as the subject of this proposition. Similarly, he thinks that “an A is B” means actually that the representation of an A, which has b, has objectivity.

Bolzano moves on to impersonal sentences, using in German the “Es gibt” -structure, translatable often with the words “there is”, which is again another way to say that a representation refers to an object. This is true, he insists, even of weather reports, which form one subspecies of “Es gibt” -sentences (for instance, “it snows” should mean that a representation of snowfall happening now refers to an object). Other expressions with the “Es gibt” -structure have different readings for Bolzano: “they say…” means that there are people who say something, while “it is true that…” means that a certain proposition is true.

Bolzano points out that “some A are B” in its usual sense means that characteristic b belongs to several, but not all and not even to remarkably many A. On the other hand, he states, “many A are B” means that the characteristic b belongs not to all, but to a great number of A. Indeed, Bolzano continues, the word “many” is relative and could mean many things: an absolutely great number of things, like 3 billion, a great number in relation to something else, like the number of stars we can see with bare eyes, in comparison with the number of all of them, and a great relation of numbers in comparison with something else, for instance, when many of our family are sick, although it covers only a tenth, in proportion to other families this is much.

Bolzano goes through some relatively simple cases. “n As are Bs” means either that there are at least n As that are Bs or that exactly n As are Bs, both easily turnable to his favoured form. Comparative proposition “A has characteristic b more than C has” speaks actually of the degree or magnitude of the respective characteristic of the objects, while exclusive proposition “only A alone is B” means that the characteristic b belongs exclusively to A and implicitly to some A (whether it belongs to all of them depends on the context). On the other hand, Bolzano notes, “A is only B alone” does not mean that it would have no other characteristics, since everything has infinitely many characteristics, but that it has of some relevant characteristics only that of b (for instance, “Caius is only good to invent rhymes” suggests that he has no other characteristics of a good poet).

What Bolzano calls a restrictive proposition – “A, as C, is B” – can have many different meanings. Firstly, “Earth, as consisting of many substances, is destructible” suggests that consisting of many substances is a ground for Earth being destructible. Then again, “Caius, as a musician, is wonderful” does not mean that Caius himself would be wonderful, but his musicianship is. Finally “Titus, as a judge, should accept no gifts” does not mean that Titus should accept no gifts, because he is judge, nor that his judgeship should accept no gifts, but points to a special relation between the three concepts – Bolzano does not explicate this relation more precisely, but it is something to the effect that it is a characteristic of his position of a judge that while doing his duty in that position, he should not accept any gifts, which would be considered bribes. Bolzano also notes that a proposition “A as A is B” is equally ambiguous, but usually means that the characteristic b, ascribed to A, is derivable already from concept A.

We have already seen Bolzano deal with the phrase “A is, because B is” which means that the B is a ground or at least a partial ground of A. He adds that often this form is used merely to indicate that A is derivable from B. Bolzano points out that if-then -structure is also often used to describe the relation of derivability, but it is in some cases applied elsewhere. For example, “if digits in a number are arbitrarily switched and the result is subtracted from the original, then the result is always divisible with 9” indicates no derivability, he thinks, because there are no obvious variable representations, and instead it describes certain relations between numbers (that the number differing from a given number only thus that its digits are in a different order, is to this one in such a relation that their difference is always divisible by 9). Similarly “if Caius is silent in this situation, he is unthankful” does not indicate derivability, but describes a general proposition that anyone who is silent in the situation of Caius is unthankful, while “if Caius is dead, then Sempronius is a beggar” deals with relations between Caius and Sempronius, which make the latter necessarily a beggar with the death of the former.

“A determines B” (for instance, “two sides of a triangle and the enclosed angle determine the whole triangle”) means, Bolzano thinks, that certain propositions expressing characteristics of B are derivable from certain propositions expressing characteristics of A in regard to representations that concern characteristics of A. “A determines B wholly or completely” means then that all propositions concerning characteristics of B are derivable from certain propositions concerning characteristics of A (for example, centre and radius determine circle completely, because all characteristics of the circle can be derived from their characteristics).

“Either-or” -structure, Bolzano says, means in its strongest sense that only one of the options presented is true, but it can also mean that at least one and possibly several of the alternatives are true. Similarly, he adds, it can refer to options present in the sentence or use some variables. Furthermore, Bolzano points out, “all A are either B or C” does not mean that either all A are B or that all A are C, but that each individual A is always either B or C.

Bolzano goes into great detail with the so-called modal terms or necessity, impossibility, possibility and contingency. In their strongest sense, he thinks, these concepts refer to actual existence of objects – “must” means “must exist” and “can” means “can exist”. More precisely, Bolzano explains, if something (say, God) is necessary = there is a conceptual truth of the form “A exists”, where A comprehends the object in question. Something is then impossible if its existence is a conceptual falsity. Possible thing is then defined as not impossible and contingent thing as existing, but not necessarily. Bolzano's definitions imply that any object that can be represented with a pure concept referring only to it is either necessary or impossible, thus, contingent is something that we can represent only through mixed representations or intuitions.

This strong sense of the modalities can be relativised, so that e.g. something is necessary relative to another thing (Bolzano speaks also of external necessity) if neither is by itself necessary, but the existence of one is derivable from the existence of the other (like punishment is necessary relative to a sin). Furthermore, Bolzano adds, in an improper sense these concepts can be extended to truths in themselves. Thus, b belongs necessarily to A, if “A has b” is a conceptual truth; b is impossible for A = “A has no b” is a conceptual truth.

Bolzano points out a final way to use especially the concept of possibility. In this sense, something is possible or something could be, if we do not know it to be impossible, that is, if we know of no conceptual truth that would express the opposite. Obviously this does not mean that it might not really be impossible.

If a proposition speaks of an actual object and the characteristics ascribed to it in the proposition do not always belong to it, Bolzano thinks, the proposition must determine a time, when the characteristics belong to the object. Thus, we have verb tenses for present, past and future times, and sometimes the determination of time is even the object dealt in a proposition (Bolzano’s example is “cherries bloom earlier than grapes”, which should mean that the relation of the season of cherries blooming to the season of the grapes blooming is the relation of an earlier to a later season).

Bolzano is especially interested in propositions about the beginning, the enduring and the end of a state. A state endures through some period of time, he says, when the proposition that the state is actual at the moment x remains true, whatever moment included in the period of time is put in the place of x. A state enduring now means then that it endures through a period of time including the present. Bolzano finally defines a beginning or an end of a state at a certain moment in such a way that the proposition that the state is actual at the moment x is true, as long as x is replaced with a moment that is a bit later than the moment of beginning or a bit earlier than the moment of ending, but false, if the x is replaced with a moment earlier than the moment of beginning or later than the moment of ending.

Bolzano also emphasises the importance or propositions speaking of becoming. Such becoming, he says, involves actual existence in a future time, but mere existence in future time is not always becoming. The difference lies not just in how far in the future the event is, Bolzano thinks, because we do speak of events centuries in the future as already becoming. Instead, he suggests, becoming requires change, and the future event becoming must be caused by this change. Then again, Bolzano continues, change requires something that is changed: an internal characteristic of the changing thing does not remain the same even for the smallest time, when the change is going on. Given this definition of change, becoming of M can then be defined as an on-going change causing M to exist in the future. If we say that M becomes from A, this means that the object A is undergoing the change, which causes the future existence of M. Finally, Bolzano concludes, if M becomes through or because of P, the object P is a total or partial cause for the change that causes the future existence of M.

Bolzano concludes the section on propositions by suggesting a few examples, where one and the same sentence actually combines several propositions. Thus, differentiating proposition “not X, but Y does have b” is a combination of proposition “X does not have b” and “Y has b”, compared to one another, while extensive expression “all A, including those that are X, have b” says that all A have b but that the listeners probably won't believe this and think that X are an exception.

Bernard Bolzano: Study of science – Propositions about propositions

Bolzano has already mentioned the possibility of propositions about propositions, but he then left a fuller account of that notion to a time after the discussion of relations between propositions, since many propositions about propositions deal with just such relations. As he is now finally in a position to deal with the topic, Bolzano is especially interested in showing how to present such propositions in his official form of all propositions: “subject has a predicate”. Thus, for instance, the notion of compatibility of propositions would be fully expressed as “representation of a collection of certain representations, which put in place of i, j… in the propositions A, B, C… makes them all true, refers to some object” (the notion of incompatibility is, of course, expressed by a negation of this proposition). As he is well aware, we express such complex propositions in a much simpler manner and especially the notion of variable representations in the propositions is usually left implicit (for instance, we just say that the propositions can be true at the same time).

Bolzano goes quickly through all the various forms of compatibility and incompatibility, but we really need to look at just the notin of derivability, as it is the only one where he feels the need to give the full official form. It is really no wonder he refrains from doing it in other cases, since even this one is a mouthful: “representation of certain parts in A, B, C… M, N, O…, which are such parts that every arbitrary collection of representations, which put in their place makes the A, B, C… true, makes also the M, N, O… true, refers to objects”.

From the species of compatibility and incompatibility of propositions, Bolzano moves on to discuss the relation of complementarity, which is obviously important to disjunctions. We may quickly go through Bolzano's official structure for the basic notions in this regard, that is, the material complementarity – “representation of a true proposition among M, N, O… refers to some object” – and formal complementarity – “representation of a true proposition among a collection of propositions, whatever else is put in place of representations i, j…, following rule R, refers to some object” (it is not clear what this rule R refers to). Bolzano is as quick in presenting his official structure of propositions on probability – “relation of the set of all such representations that make the propositions A, B, C… true to the set of those that in addition to A, B, C… make also M true is m” – although he does add that we commonly say something to be probable, when this m is more than ½.

Bolzano's official structures for material and formal consequence are by now probably not surprising, former being “relation of truths M, N, O… to truths A, B, C… has the characteristic of a relation of consequence to its ground”, and the latter “the relation of propositions M, N, O… to the propositions A, B, C… has the characteristic that each collection of representations that put in the place of i, j… makes the A, B, C… true, makes also the M, N, O… into such truths that are the consequence of the former”. What is more interesting is his remark that we often speak of grounds and consequences, when we should actually speak of partial grounds and consequences. Furthermore, Bolzano defines cause as an existing object, the existence of which is a partial ground of some truth, and effect as an existing object, the existence of which is one consequence of an existence of a cause. He also points out that the existence of a cause implies the existence of an effect, but not necessarily the other way around, since an effect could have many possible causes. Thus, he defines condition as a full or partial cause, the existence of which is derivable from the existence of the effect.

Bernard Bolzano: Study of science – Relations between propositions

Moving on to relations of propositions, Bolzano begins by noting, just like with representations, that there are no two completely equal propositions in themselves. Again like with representations, he continues, propositions in themselves can still be similar in the sense they have so many commonalities that they can be easily confused with one another. Bolzano points out that propositions with similar representations are not necessarily similar and that similar propositions need not have very similar representations. For instance, “some As are B” is similar to “representation of an A that is also B has objectivity”, although the representations in them are not, and “Sun lights the Earth” and “Earth lights the Sun” have similar representations, but are not similar propositions.

Just like with representations, Bolzano states, we can compare the content of propositions, that is, their constituents. He points out that all propositions share at least the copula “have”. Thus, to make the definition sensible, Bolzano takes affinity of propositions to mean that they share at least one constituent beyond “have”. Clearly, he points out, such affinity can have degrees, and propositions with affine representations are affine, and affine propositions have some affine or same representations.

Bolzano goes on to define some types of affine propositions. Some of them, he says, can have the same subject or predicate or a contradictory subject or predicate. Bolzano particularly defines converted propositions as such that are otherwise completely same, but two representations have switched their places. Such switches can occur in different places of the propositions, but Bolzano defines as perfectly converted the propositions “what has a has b” and “what has b has a”; technically “a has b” and “b has a” are even more converted, he admits but it is so rare to find two characteristics that characterise one another. Bolzano defines as conceptually converted two propositions “representation of A that has the characteristic b has objectivity” and “representation of B that has the characteristic a has objectivity” – in other words, this is the familiar relation of “some As are Bs” and “some Bs are As”. He also mentions the traditional notion contraposition as the relation between contraposed “what has a has b” and contrapositing “what has not-b has not-a”.

Bolzano notes that the extensions of the propositions bring forth new relations. Still, he passes these quite quickly, since the extensions of the propositions were defined by the extension of the subjects of the propositions so that the relations really introduce nothing radically new. Bolzano also adds that similar relations could be defined in terms of extensions of predicates.

What Bolzano considers the most important relations of propositions come up with the use of variables, introduced with the notion of validity of propositions. What the notion of variables allows Bolzano to do is to introduce in modern logic very familiar analogies between propositional logic and algebra of sets (in Bolzano’s logic, relations of extensions of representations). For instance, he defines compatible propositions as such that, when taking the same representations in them as variable, some choice of these variables makes all the propositions true – similarly, incompatible propositions are then such that taking the same representations as variable, no choice of these variables makes all propositions true. Clearly the notions of compatibility and incompatibility of propositions are analogical to the compatibility and incompatibility of representations, and indeed, one could be defined in terms of the other – propositions are compatible, if the collections of representations making them true are compatible, and representations are compatible, if propositions saying that an object represented by one of these representations are compatible.

Yet, there is a catch in Bolzano’s definitions: the relations of compatibility and incompatibility depend on the choice of variables, so that propositions that are compatible with one choice could be incompatible with another choice. In practice, this dependence on the chosen variables does not usually affect that much of Bolzano’s discussion, just as long as the chosen variables are always the same.

Bolzano goes on to describe simple features of these new concepts, such as that if a proposition is compatible with another and this with a third, the first and the third might not be compatible (compatibility is not a transitive relation, we would say nowadays). What makes his discussion a bit more complex is that instead of propositions he is usually discussing collections of propositions, and as he notes a few times, what holds for individual propositions might not hold for collections of propositions (this is more evident with notions a bit more complex than just compatibility and incompatibility).

Bolzano shows special interest in propositions of the form “X has a” or “A has x”, where either the subject X or the predicate x is the only variable. Thus, he notes, propositions with predicates as variables – say, “A has x” and “B has y” – are compatible, just as long as their subjects refer to some objects: we just have to pick suitable predicates that fit with the kinds of objects. Similarly, propositions with the subjects as variables – “X has a” and “Y has b” – are compatible, just as long as their predicates are characteristics of something: we just have to pick suitable subjects that have these characteristics. Then again, Bolzano points out, the case is somewhat more complex, if the propositions had the same subject that was then taken as variable – for instance, with “X has a” and “X has b” – since such propositions are compatible if and only if the predicate representations are compatible or are characteristics of some shared objects.

So, what are the other similar notions discussed by Bolzano. Well, he defines derivability of a collection of propositions, in analogy with comprehension of representations, as a relation where the derivable collection of conclusions is always true, when the collection of compatible propositions or premisses from which it is derived is also. Here we find an example of the complexity involved with Bolzano speaking of collections of propositions, instead of just individual propositions. Thus, an individual proposition can never be derivable from both an individual proposition and its negation, Bolzano points out, unless it is formally true, that is, always true with this particular choice of variables. Then again, if a proposition is derivable from a collection of several propositions, it could be derivable, even if some or even all propositions would be replaced by their negations: for instance, conclusion “B and C are not equivalent” is derivable from premisses “every A is B” and “it is false that every A is C”, but also from their negations.

Bolzano also defines the stronger relation of exact or adequate derivability, where none of the premisses or their constituents could be dropped without removing the relation of derivability. In this case, he points out, neither the conclusion nor any of the premisses can be formally true and no premiss is derivable from other premisses. While derivability is a transitive relation, exact derivability is not, although it has particular instances of transitivity. Thus, Bolzano can define composed derivability as a relation where the premisses of an exactly derivable conclusion are again exactly derivable from further premisses and the final conclusion is then also exactly derivable from these more ultimate premisses. Then again, he thinks, there are also cases of simple or non-composed derivability such as a proposition “all A are C” being derivable from “all A are B” and “all B are C”.

Further relations of this kind are equivalence (collections of propositions being derivable from one another), subordination (one-sided derivability), independence (collections of propositions being compatible, but not derivable from each other), exclusion (when all propositions of a collection are true, propositions of another collection are false), mutual exclusion (two collections excluding one another), contradiction (if all propositions in one mutually exclusive collection are false, all propositions in the other are true) and contrariety (mutually exclusive collections are not contradictories). None of these have anything surprising in them, so we can skip Bolzano’s discussion of them.

Bolzano moves on to discuss relations concerning not just what happens if propositions or their collections are true, but determining what propositions in a collection are true. Here, it can be a case of speaking about the truth and falsity of the propositions as such or as case of speaking about the truth and falsity of the propositions with some representations taken as variable – in the former case, the concepts are defined, Bolzano says, materially, and in the latter, formally, although most of the concepts make best sense in their formal meaning. The simplest example is when all propositions of a collection are true or all are false, but more interesting examples are discovered, when some, but not all propositions in a collection are true – Bolzano calls this a case of complementary propositions. Complementation, he points out, can be one-membered complementation or disjunction, so that only one proposition in a collection is true, and disjunction can be exact, when no proposition could be removed from the collection, without cancelling the feature that it has always at least one true proposition. Complementation might also be multimembered, if it has more than one true proposition, and in this case, it might even always have some exact number of true propositions. Finally, even if a collection of complementary propositions does not have any exact number of true propositions, its propositions might still be compatible, that is, all its propositions could be true in some cases. At the end of all this, Bolzano notes that all thus defined notions could also be conditional, that is, we could restrict our attention to such representations that make certain presuppositions also true.

Bolzano extends this notion of presuppositions to his previously defined idea of validity of propositions, calling it comparative validity and identifying it with the notion of probability. In principle, he suggests that we find out representations making the presuppositions true and then from these the particular representations making a proposition we are interested in true – the probability of this proposition is the number of the latter collection of representations divided with the number of the former collection. In practice, Bolzano admits, we have to make some limiting assumptions about the number of the cases, because the number of possible representations that could be used is infinite, due to all equivalent representations: basically, he restricts his whole discussion to rather simple cases of pulling balls out of a box. As always, Bolzano is interested to extend his discussion from individual proposition to collections of propositions, which he manages to do by proving that with suitable choice of variables and presuppositions, the probability of a collection of propositions is the product of the probabilities of the individual propositions

Bolzano discusses the relation of a proposition that is ground to a proposition that is its consequence. He notes that this relation does bear some affinity with the earlier notion of derivability, but is stronger: for instance, the proposition of weather getting warmer is derivable from the proposition of thermometer rising and vice versa, but only the former is the ground for the latter, not the other way around. Bolzano points out that the consequence relation can also be connected with the notion of probability. Thus, the presupposition of summer coming increases internally the probability of a proposition that thermometer rises, because the coming of summer is, together with other propositions, a ground for thermometer rising, while a weather report increases its probability only externally, because this report is no part of a ground of thermometer rising.

The final relation Bolzano considers is that of an answer to a question – or actually we have here many relations to consider. We may speak of an answer fitting a question, which is simply the truth desired in the question, if it is not absurd and has one. Furthermore, Bolzano notes, we can also define an answer given to a question as any proposition that someone suggests as the required truth. Such an answer can be correct or fit the question or incorrect, he adds, and while a correct answer must be a true proposition, incorrect can be true or false. A determined question, Bolzano points out, can have only one answer, or at least just many equivalent answers, while there are innumerably many incorrect answers, even for absurd questions. He also defines solution as an answer to a problem in the restricted sense: such a solution, at least if it is a correct one, will consist of rules, that is, of propositions expressing how a certain undertaking for a determined goal is to be effected.

Immanuel Hermann Fichte: Outline of a system of philosophy. Second division: Ontology – Causality and dependence

Fichte now approaches causal categories that he points out as familiar to common thinking. Yet, he at once adds, the ontological meaning of these categories is far more removed from their common meaning than it was the case with otherwise similarly causal concepts of ground and consequence. Indeed, Fichte points out, the dialectical refutation of the notions of ground and consequence was in a sense proof of inherent flaws in the everyday causal concepts. Thus, he argues, when it was shown that everything actual is a realisation of its self-creative ground, this showed that causes and effects are not separated, as it is commonly thought. Instead, the effect should not be external to the cause, but only its actuality, and the acting cause thus brings about only itself or its own actuality, and both are just aspects of one substantial unity.

All acts of substance or monad toward another substance or monad, Fichte argues, are thus immediately only self-actualisation of this substance and only mediately affect the other substance: when the first substance varies its state, this variance evokes a varying relation to the other substance and also a variance of the state of this other substance. He connects this outward effect of the self-actualisation with the necessary quantitative, and more particularly, spatio-temporal form of substances – each substance or monad must be in the same system of relations with an infinity of others. Monads are thus self-creative, but also dependent from all others. Understood in the most immediate manner possible, Fichte states, this means that they act externally or mechanically on one another as causes and effects.

Monads as in itself locked substantial unities arrive through their self-assertion immediately to having causal relations to one another. The reciprocal influence between them, Fichte explains, is external, because their independent essences are not reshaped by these causal relations. Being a cause is then accidental to the substances, he adds, and in their acting they just assert the integrity of their original essence. Thus, in the first type of causality external independent entities act on one another, but the effect is immediately extinguished and the old state returns, because the causal relation remains contingent and accidental to acting entities.

Fichte notes at once that this notion of causality requires some correction. As we have seen, he reminds the reader, self-assertion is connected to a relation with an infinity of others, thus, self-asserting monads must also at least exclude or provide resistance to one another. Hence, Fichte concludes, their mere existence implies also immediately that they act and are acted upon. We have thus found a seeming contradiction: earlier cause and effect were described as something accidental or inessential to the things, but now they appear as inseparable to the notion of self-asserting existence.

Fichte notes that the balance to this contradiction is already achieved in the concept of abstract self-assertion that essentially implies causal relations toward others, which still touch only part of the existence of things, but remain contingent to their internal essence. Thus, he explains, things act and are acted upon, because they in general are, not because they are these specific entities, but because they are independent of one another and thus exclude others. Hence, Fichte concludes, all things universally affect one another.

The opposition of isolated cause and effect is null, Fichte states and adds that this just repeats the same development that refuted the idea of individual grounds and consequences. In other words, he explains, an individual effect would have its cause in something else, which would then have its cause in yet further things, presupposing a realised external infinity. Instead of such a series of infinite causes, Fichte suggests, each individual should receive an effect from an infinity of other entities and cause such an effect in all of them. The concept of individual causes and effects is then dissolved in this system of reciprocal acting and reacting, where these opposite directions are intertwined in every moment, while the internal infinity of this system produces unity and rest from these varying causal relations.

Concrete things act on other things through their mere formal existence. In other words, Fichte explains, a thing modifies the being of another thing through its own determination or transmits something to the other thing without destroying its independence and in general leaving it essentially what it is. The interacting things remain then external to one another, he states, but they balance themselves by modifying their nature, without still losing their essential characteristics.

Now, when a thing influences another, Fichte continues, this influence opposes the unique nature of the other. The other thing does not just passively accept this influence, he explains, but reacts against it and thus acts on the first thing. Fichte notes that we could picture this intertwining of reaction and interaction with a physical example of two objects putting pressure on one another. Since the two things have now affected one another and transmitted some determinations, the result should be a resting balance, where the action and the reaction are extinguished, or at most, a new action and a new reaction are reproduced cyclically. In any case, Fichte insists, causality at this stage produces nothing really new.

The relative difference of interacting things is extinguished through their balancing communication. Thus, Fichte notes, a uniformity appears, binding things into a larger unity, although the individual entities do remain essentially untouched by it and thus different from one another. The result of the interactions of things is then this universal link that comprehends everything, but also leaves space for things to be different from one another, he explains and adds that this result is both the end and the beginning of this causal process. In fact, Fichte suggests, it is not the things themselves that make it possible for them to act on one another, but this is done by a universal or fundamental cause or principle that acts through and realises itself in individual things.

Fichte’s conclusion is that at this stage of causality it is actually not the individual things that act, but an absolute or universal principle acts through the individuals and their actions and reactions. He calls this principle that is realised through the specification of things a resting cause that reveals itself in a system of uniform actions and reactions. The principle thus rules a manifold of things, only to present its universality at each of these individual things. Then again, Fichte notes, this universal joining of things does not just allow specification of things, but indeed, even presupposes and requires such. This raising of the status of specificness implies a transition in a higher causal relation, where precisely the distinction of things or their specific opposition enters into the relation of acting and reacting. Still, Fichte assures us, the just described interaction of universal causes does not completely vanish, since any two abstract existences act at least in this universal fashion to one another.

Fichte begins a new phase by stating that things do not interact just externally or their specified essence affects the causal processes. Thus, he explains with a reference to an earlier stage of ontology, things are related not like abstract distinctions nor only like opposites, but like specific differences: what one is, lacks precisely the other, and each finds in its other or in the cancellation of their difference its complement, so that only both together or the whole forms their true essence. Fichte describes this new position as things becoming forces. In other words, things specified in such a manner do not have, but are forces: determined manners of acting with a specific, self-asserting existence, which does not affect vaguely anything whatsoever, but only a sharply limited circle of other determinations. Fichte lists a number of phenomena involving such forces: attraction and repulsion of matter, chemical affinity and chemical combinations and dissolutions, sexual attraction, love and hatred and intertwining of various characters in a human society. According to him, the common feature of all these forms of interaction is that it is not anymore a case of external action and reaction, but internal, where both opposites produce a common third that cancels their independence and tension toward one another.

Force is the specific essence of a thing in a relation to its specific complement, Fichte sums up and adds that the force as such is nothing outside its effect, but also nothing outside the specific essence of things. In other words, he explains, just by the sheer existence of a suitably specified thing, the force is activated and starts to interact with it, while without this appropriate counterpart the essence of the thing remains the same, but it cannot become active or force. Fichte notes that when such a specification is not related to a counterpart, it has been called a latent force, which seems a contradictory concept, since force is both assumed to exist and still its actuality or effectiveness is denied. Yet, he admits, the notion of latent force at least implicitly designates the true character of force that it is nothing in itself: it is just an immanent determination of each specific essence that it in general has its counterpart and can interact with it.

There is no simple force, Fichte thinks, since a thing is not specified just in a single relation, but toward many other things. Thus, he insists, substance or monad must be a system or a closed totality of forces. The notion of force replaces then such earlier notions like characteristic, property, part and perception, all of which described the relations of a thing to other things. More precisely, Fichte explains, we can differentiate between the fundamental Ur-force of a thing and its manifestation in a manifold of activities that forms the system of forces.

Fichte suggests that the notion of causality is also intensified in the notion of force, in the sense that the relation of actions and reactions has become more intimate. In other words, the force does not just act and then react, but its actions are always also reactions and vice versa, because the relation of the interacting substances is not just external to them. The notion of distinguished causes and effects is thus destroyed, Fichte insists, and in the interaction of forces there is no separation of an active and a passive party, but instead, this interaction forms a completely new entity.

Moving on from the topic of how the notion of force is related to previous categories, Fichte begins anew by describing the start of the interaction of forces: a force finds its specific counterpart and offers itself as a counterpart to this other, and both are then at least relatively independent of one another. This relative independence or the distinction of the forces, he says, is the first moment in the process, but then this relative independence is cancelled by the very relation of the forces to one another: each requires the other, and only both together form their whole truth. The process of the forces is characterised by this drive to self-cancellation, while the whole produced is not just an abstract unity, but a completely new entity cancelling the independence of the forces.

Fichte goes through the process again from a different angle. The specific nature of an independent thing finding its counterpart makes it into a force acting on the specific other. This mutual interaction, Fichte suggests, is then striving to overcome their own isolatedness and a search for their truth in this intertwining with the other. This striving or internal attraction transitions in the process of actual intertwining, where the forces realise their balance and reach their truth. As a third point in the process, following this mutual neutralisation of forces, appears a new actual substance or product that both has extinguished the difference of the forces and still contains them balanced in itself.

According to Fichte, the product mediating the differences is again just a new individual specification and thus must have a further counterpart of its own. The process that was extinguished in one sense, is in another sense only rekindled. In other words, Fichte clarifies, each neutralising individual product generates only new differences that again balance themselves in a product and so forth in the external infinity. He declares this infinite and never terminating play of combining forces and dissolving combinations as the second moment of the category after the first moment of a single process of interacting forces. Then again, Fichte notes, the independence of individuals is nowhere the final truth and therefore this external infinity of interactions of forces is also not the true expression of this relation. Instead, he insists, all these individual processes must display a universal and absolutely fundamental law as their internal infinity.

Fichte sees still a contradiction: the forces should be relatively independent in the sense that they subsist beside one another and step from this isolation only when they find their counterpart, but on the other hand, they should also exist only in relation to others. In other words, he explains the second part of the contradiction, the forces are not just neutralised and combined into new products in their interaction, but weren’t even independent in the first place. Fichte thinks that this contradiction is solved by noting that the conflicting concepts are more determinately limited by each other, that is, although each specific force is independent, it is still at the same time prepared for its counterpart in the sense that it has precisely what the other lacks. Thus, the state of isolation of forces is unsatisfactory and in need of completion, and the counterparts prepared to one another are so mediated by something beyond them.

Relatively independent forces are from a different viewpoint not originally independent, but exist only through a higher principle realising itself in them. Fichte reminds us that a similar result was found at the previous stage of causality, where the infinitely isolated actions and reactions were also mediated by a common ground. The difference was that in the first stage the specific internal essence of things was untouched by the principle of causality, while here it is precisely the specific content of the thing or force that appears from the all mediating law that penetrates the very essence of forces. In other words, Fichte suggests, each force is what it is only through the law that posits it in a specific relation with its counterpart, and this law or principle precisely balances them, so that each is capable of providing what the other is in need of. Furthermore, he adds, this law is not just abstract universality that would make everything just the same as everything else, but results in a system or universe of specific forces complementing one another through this all prevailing fundamental principle.

What is established here, Fichte suggests, is the importance of the third moment of this category or the all mediating principle, in which the specific forces return, when they cancel their isolation. He notes that we could thus define the absolute as the specifying law that connects the prepared forces and activities into an intertwined world with eternally varying interactions still repeating only this one fundamental principle. Fichte immediately adds that this is not the highest notion of absolute and that we cannot stop with the concept of law that only abstractly unifies things in a pantheistic manner. Thus, this absolutely specifying law and the world order presenting the law are again mere moments or preconditions of a higher principle and a higher order. Similarly, Fichte explains, the interaction of forces is also not the highest and final form of causality, but serves only as a foundation, in which a higher causal relation realises itself. Indeed, he suggests, all causal relations of lower kinds are merely tools or means for realising a purpose or a final cause.

Fichte goes over this transition from a different viewpoint. Individual forces are one-sided and thus search for a complementing counterpart. Finding it and so their truth, they neutralise one another and produce a new individual, which again as an individual requires a new complement. This whole sphere of causality, Fichte insists, is afflicted with a contradiction that, on the one hand, forces seek something beyond them, but on the other hand, they fail to generate this beyond by themselves, being capable of producing only individuals. The internal truth or solution of this contradiction, he thinks, can be found only in a higher form of causality, while the interaction of forces serves as a mere middle step between the most abstract and the highest forms of causality.

In the new form of causality, Fichte states, the relation of the cause and the effect is turned around, that is, what is generated is now the cause for that from which it appears, while the generating element is dependent on and determined by what follows from it. Ground and consequence or cause and effect do not so much swap their roles, so that the cause would become effect and the consequence ground, he explains, but these concepts are given a new meaning. Thus, the cause is still a cause, but in another sense a mere consequence, while the consequence becomes a true cause or ground for that, from which it appears, just because it can only appear from such a cause. The product of neutralised forces is the most original, because of which the forces are presupposed, or it is the cause for these, but this cause of forces is conversely only to be brought about by them or is their consequence, in other words, the forces have the product as their goal or end (telos), to which they are prepared and in which they are destroyed. Thus, the earlier opposition of cause and effect transitions, Fichte notes, in a new relation between purpose and means. Purpose, he explains, is the cause assumed as consequence or it is active without being already actual and causes its own cause. Similarly, Fichte adds, means is the consequence as a cause that generates its own proper cause.

Fichte continues from this general characterisation of the new conceptual field to the relation it has to earlier forms of causality. At first, he begins, it seems that the product of the interaction of forces is simply nothing final, but only for the sake of something else, of which we do not yet know what it might be. What we do know, Fichte suggests, is only that it is simply beyond the earlier circle of concepts, which is then the means for the beyond as purpose. The earlier causality of infinitely each other balancing and differentiating opposites is then complete in itself, but at the same it acts toward a distant and never completely reachable goal. This means, Fichte insists, that this earlier series of causes and effects has been turned around and the cause is now what follows and what is caused is the preceding. In other words, the cause as purpose acts already in the means throughout, but without being itself already expressly there, since it can become actual only through the means, the cause of which it is. What isn’t yet, Fichte summarises, acts back to what is and thereby becomes, which he admits to be a contradiction.

Because the concept of final cause or purpose is the truthful expression of the category of causality, Fichte states, purposes must have appeared already in the earlier, mechanical and chemical forms of causality. In other words, he clarifies, the world of mechanical and chemical processes should realise a system of purposes, and while an effect might seem just external, it still realises a purpose. Thus, Fichte concludes, final causes are not a form of causal relation in opposition with the other forms, but they are more likely present in all causality as the absolute goal of all causal processes. Of course, he admits, this absolute goal or purpose has earlier remained unknown, but now the dialectical process of the causal concepts has shown that the notion of goal is demanded by their very nature. Fichte refers back to Kant as the originator of the idea that purposes are not merely humanly subjective, but that to all things is implanted a purpose as a shaping principle, not in the sense of human or even divine intervention into the mechanical course of the world, but as an absolute purposefulness penetrating everything actual. Fichte considers himself as giving a proper ontological account of this idea, but he has to at first try to solve the previously mentioned contradiction in it, and this solution cannot be, he says, a subjective notion of a universal law nor a vague instinct guiding all things.

Before going to this contradiction, Fichte starts to investigate individual moments of the concept of purpose. At first, he says, purpose and means appear as externally related opposites: the purpose is a concrete, in itself completed thing, opposed to its means, but beyond this relation these two things are not dependent on each other. Thus, one thing is one-sidedly considered as means and another thing as its purpose, and both are in this manner externally related to one another. This relation could be interpreted as a mere judgement of an external observer or as a concrete instance of a person taking one thing and using it as means. Both of these interpretations, Fichte insists, belong not to ontology, but more to the field of practical philosophy, where human spirit mimics the creator by imprinting their varying purposes on the things. This mimicry is, he states, finite and contingent, and indeed, refutes itself immediately, since each of these judgements could be replaced by a different assignment of purposes.

According to Fichte, the first, provisional opposition of purpose and means is insufficient because the externality of the relation of purpose and means displaces us back to the causality of forces or even to the mechanistic causality of externally independent substances, while the proper concept of final cause has been lost. He suggests moving on to the original contradiction of purpose acting without yet being. This contradiction breaks into an opposition of two conflicting propositions, Fichte says, namely, on the one hand, that the purpose must be already contained in its means as acting through it, but on the other hand, that the purpose cannot be contained in its means, because it in general is not yet, but should only become through this. Both propositions are equally valid, he insists, and neither can be rejected.

The contradiction cancels firstly the separation or contingent externality of purpose and means toward one another, Fichte says, or the true purpose cannot be sought outside the means and the true means cannot be found outside a purpose. Instead, he emphasises, both are in one another, that is, the purpose has simply its means, in and through which it realises itself, while the means fulfils and satisfies immediately its purpose. Thus, the purpose realises itself constantly, because it is immediately present in its means, and so the externally mechanical process of causality is, Fichte emphasises, what Kant and Hegel have called internal purposefulness. Thus, it is essential that a purpose does not remain outside its means and also not outside the mechanical causalities, as if it would lie above them, in a distant world, or would be added to them as a completing supplement. Fichte notes that the standpoint of mechanical causality is, on the one hand, reproduced, since the purpose realises itself immediately through the subordinate causal relations in every point, but on the other hand, these causal relations have been lowered only to the status of means.

Fichte thinks only the first of the contradictory propositions has been engaged with, while the other side has been disregarded. In other words, no matter that the purpose is also a self-completing means, still, according to the second proposition, it must behave either as purpose or as means to something else. Thus, Fichte suggests, just like in all the previous stages, the isolation of the individuals has to be cancelled and their infinite relation has to be reproduced. This means, he says, that each individual has its purpose in itself and at the same time in something else, and conversely, that each individual is means to all others. Thus, the earlier seemingly isolated things have now been integrated into a system of an infinity of to each other related purposes and means. Fichte connects this idea with the earlier concept of a monad, which should be precisely such an identity of purpose and means, because it is a unity resulting from and renewing itself from distinctions, but each of these distinctions is also a self-purpose.

The problem is, in Fichte’s opinion, that if everything is both a purpose and a means, nothing in fact remains anymore true means or true purpose. Indeed, he suggests, we have just returned to the notion of causality between all things. This consideration, Fichte thinks, renews the conflict of the two propositions. Firstly, the final cause must suppose an absolute purpose that can in no sense become means. Yet, secondly, this absolute purpose is to be thought only in a system of infinite relations of means and purposes, which the absolute purpose uses as its means. The conflict is, Fichte explains, that the absolute purpose must be completely separate from the system of means and purposes used as its means, but the absolute purpose must also be embodied in this system.

Fichte suggests solving this conflict in such a manner that, on the one hand, the purpose is present in the totality of its means by them being also self-purposes, but that none of these are pure purposes, still striving to a truly absolute purpose. In other words, the purposes would form a hierarchy, so that what would in one sense be a self-purpose, would in another sense be just means for a higher purpose, all the way to the highest purpose that is not means to anything. Thus, each relative purpose fulfils the idea of purposes being also means, but this series of purposes does not reach into infinity, since there is an absolute final purpose that still is eternally embodied in the system of subordinate purposes.

The final turn highlights the other side of contradiction in the most heightened sense possible, Fichte suggests, since the higher final cause is actual in lower final cause, but also not actual, because it first requires this as its means of realisation. He begins solving this contradiction by pointing out that actuality is here understood in two senses. Firstly, it means the anticipation of non-actual purpose in its means, and secondly, the reality of the purpose generated through the means. The second concept is clear by itself, Fichte deems, but the first concept is the proper seat of contradiction. The anticipation of the still not actual purpose, he thinks, can only mean its pre-existence or ideal presence in its means, so that the means is prepared for the sake of purpose in such a manner that only the purpose can appear from the means. In order that means can be prepared in such a manner, Fichte argues, there must be something preparing it and this something cannot be the non-actual purpose, but can only be the creative absolute that orders means and purposes. We have thus arrived, he points out, to the third and final moment in the category of final cause, namely, by moving from isolated purposes and means to a system of an infinity of means and purposes and finally to the creative absolute unity. The notion of absolute, Fichte concludes, has thus gained an important new feature as the ultimate positing of purposes that lead the whole created world through subordinate causal relations to a goal beyond them.

The true concept of purpose cannot be thought without assuming the existence of the absolute positing all purposes, Fichte summarises, or the world of purposes is only possible, insofar as it is penetrated by an absolute consciousness. In other words, as certainly as there are purposes or goals that have not yet been actualised, as certainly there should be an actual absolute that orders everything to anticipate these purposes. Fichte explains that we have not yet fully proven an existence of such a purposeful absolute, but it has not yet been made properly comprehensible in an ontological manner.