Maimon Reading Group: Chapter 4

[by Nick Midgley, London]

Chapter 4 : Subject and Predicate, the Determinable and the Determination


This chapter launches straight into an analysis of how in a synthesis one term is defined as subject and the other as predicate, it establishes a criterion for these attributions. The first paragraph analyses syntheses that Maimon describes as ‘one-sided’ and which give rise to ‘absolute’ concepts, whereas the second paragraph begins with an analysis of syntheses that are ‘reciprocal’ and give rise to ‘relational’ concepts. Later in the chapter both these syntheses, as syntheses of the understanding containing necessity, are contrasted with the merely contingent syntheses of the imagination. The distinction between these three kinds of synthesis had already been introduced in chapter 2 (s.35-6), and Maimon will discuss it further in chapter 8. Chapter 4 as a whole concentrates on one-sided syntheses, and it is only these syntheses that are characterized as the determination of a determinable, the topic of the chapter.

Maimon describes how subject and predicate are assigned in a one-sided synthesis thus:

if one of the constituent parts of a synthesis can be thought without reference to the other, i.e. either in itself or in another synthesis, but the other cannot be thought without reference to the first, then the first is termed the subject of the synthesis and the latter the predicate

He cites as an example a triangle thought in the syntheses right-angled or oblique-angled, triangle is subject because it can be thought in itself independently of these determinations, whereas the determinations themselves cannot be thought without triangle. On the other hand in a reciprocal synthesis…

neither of the two constituent parts can be thought without reference to the other…each is at the same time subject and predicate in relation to the other.

Here the example is the synthesis of cause and effect, which together comprise the concept of cause and neither of which can be thought without the other (this is explained better in chapter 2, s.37).

I will address the topic of  the chapter under three headings: first the formal analysis of the relation of determination, second the relevance of this relation to transcendental philosophy – viz, how can it be a criterion of objectivity (the first is reasonably straightforward but the second is much more important and harder to grasp), third a comparison of Maimon’s account of determination with Kant’s account in CPR, finishing up with a look at the account of determination Maimon presents in the “Short Overview of the Whole Work”. There are lots of difficult issues here so I apologise in advance for any density and lack of clarity.

  1. Formal analysis of the relation of determination

(a) Historical note:

Determination is a notion used by Leibniz and Wolff, in particular it occurs in Wolff’s definition of the actual   as ‘omni modo determinato’  (determined in every way), a definition that Maimon rejects (Chap 5 s.101-2); it is also used in CPR (I will examine this use below). Atlas claims that Maimonides is the immediate source of Maimon’s use of the notion, but commentators seem to be in agreement that Maimon’s account of it is original to him. He returned to it in later books where he refers to a Law or Principle of Determinability (Satz der Bestimmbarkeit) [in eg. the Categories of Aristotle and the Logic], which he counterposes to the law of contradiction, the former being the principle of synthetic a priori judgements just as the latter is the principle of analytic judgements, and regarded it as one of his most important philosophical discoveries. Within the Anglo-American philosophical tradition, there is a very intriguing deployment of the notion in W E Johnson’s Logic (Cambridge University Press, 1921) which bears a strong resemblance to Maimon’s but is apparently independent of it, see the article ‘Determinates versus Determinables’ and  in Stanford Encyclopedia of Philosophy: which unfortunately does not give any historical background to Johnson’s use of the notion.

(b) Maimon:

Maimon defines the relation of determination of subject by predicate in these terms: the same predicate can only belong to one subject and a subject can only have one predicate. A subject can only have one predicate because the predicates stand in a relation of exclusive disjunction to one another. Maimon says that he understands that the reader may find it difficult to accept that a predicate can only belong to one subject: we are, for example, accustomed to predicating ‘black’ of many different subjects  and to say that it can determine only one subject is surely false. To refute this objection Maimon distinguishes the synthesis of the understanding that is determination from mere syntheses of the imagination. Thus ‘black triangle’, ‘black circle’ are mere syntheses of the imagination, not of the understanding, by this he seems to mean that no connection is understood between being black and being a triangle, they just happen to be combined in intuition, so triangle is not determined (qua triangle) by black, whereas it is determined by ‘right-angled’. A determinable can be subject to successive determinations, for example the determinable space might be determined as a triangular space which in turn is determined as right-angled, whichin turn  is determined as having sides of ratio 3:4:5 and so on. In “My Ontology” (s.244-5) Maimon deals with the problematic case of a synthesis like ‘equilateral triangle’ where it seems that either of the terms of the synthesis could be subject or predicate. That is to say, one could determine space as an equilateral space (which could then be determined as triangle, square, pentagon etc.) or as a triangular space (which could then be determined as equilateral, isosceles, right-angled, etc.). He argues that either of the terms can be taken as the determinable, depending on whether in the subsequent use of the concept one is concerned with laws for equilaterals in general or laws for triangles in general. Fundamental to the relation of determination is that it has a one-sided or non-reciprocal necessity, which is to say that the subject can be thought wi thout the predicate but the predicate cannot be thought without the subject.

2.  The objectivity of syntheses of determination

Now let’s try to address the more difficult question of the importance of this synthesis of determination to transcendental philosophy. Already in chapter 1 (s.20), Maimon introduced the synthesis of determination thus:

The understanding counts as an object only a synthesis that has an objective ground (of the determinable and the determination) and that must thus have consequences, and no others.

Is there a mapping of the three syntheses ( = concepts) of this chapter onto the three kinds of judgement of CPR?

This question is clearly complicated by the difference between concept and judgement, Maimon discusses this difference in the sixth paragraph (s.93) and argues that although subject and predicate apparently swap places in concepts and judgements, a deeper analysis reveals that concepts and judgements are identical. In CPR the transcendental deduction concerns concepts whereas the schematism concerns judgements. The deduction establishes the categories (pure concepts) as conditions for objects, the schematism shows how objects can be subsumed under these concepts in a judgement. But the relation of deduction and schematism, concept and judgement is a subject of much debate and disagreement in Kantian scholarship and is too big a topic to be other than gestured to here. So in what follows, forgive me for jumping between talking about concepts and talking about judgements, a more adequate account would address this issue more fully.

If we compare Maimon with Kant on this question of the relation of determination to objectivity we can say that they face a similar problem. Kant’s account of the difference between analytic, synthetic a priori and synthetic a posteriori is clear and convincing: analytic judgements are clarificatory, setting out what is already contained in the concept (and for this reason are also necessary) whereas synthetic judgements are amplificatory, adding a new concept to the original concept. Synthetic a priori judgements (SAPJs) are necessary and universal whereas synthetic a posteriori judgements are neither. All the problems arise in explaining (1) How SAPJ’s are possible, i.e. the question arises: if they are truly amplificatory doesn’t this point to a lack of connection between subject and predicate, how then can they have a necessary connection (2) How do they connect to the world. Recent Kant scholarship (Allison in particular) has argued that the formal distinction of analytic from synthetic a priori with which Kant introduces these notions has misled commentators – they are not different kinds of proposition, rather a synthetic a priori judgement is actually a synthesis of concept and intuition, so on this reading SAPJs are the connecting of concept to world and question 2 becomes the essence of question 1. Equally with Maimon we get a formal account of what differentiates a synthesis of determination (SD)  from a reciprocal relation which is clear and convincing enough of itself, but what matters is what it is about the SD that gives it objective rather than merely formal truth.

How does Maimon’s notion of determination relate to Kant’s definition of analytic and synthetic judgements? Determination is neither clarificatory nor amplificatory, to determine is to make the universal particular, it does not explicitly set out what was implicit in the concept (the universal), nor does it add something from outside, rather it determines the universal in a particular way. Thus Maimon has found a connection that is not analytic but does have a (one-sided) necessity to it, and one can imagine that this in itself would have made him think that he had the makings of a new account of the nature of SAPJs as SDs. This then would go some way towards answering question 1 above, the problem of the possibility of a necessary synthesis. This leaves question 2, the problem of how these syntheses connect to the world. This is the ‘quid juris?’, and in chapter 2 Maimon had put forward a solution in terms of ideas of the understanding, so the question arises of how the notion of determination fits together with the ideas of the understanding  to solve the ‘quid juris?’‘. Thus I  think Gueroult goes too far in saying in his monograph on Maimon: ‘Maimon’s solution to the problem quid juris? is the principle of determinability’ (Gueroult, Martial, La philosophie transcendentale de Salomon Maimon, Felix Alcan, 1929, Paris, p.44) because of the importance of the ideas, however Maimon certainly thinks that the importance of SDs lies in the connection between SDs and objectivity and the question ‘quid juris?‘.

Maimon claims that the one-sided relation of SDs makes them objective in a way that reciprocal relations are not. In his footnote to s.88, he states that for a finite understanding only a SD takes place as object, whereas a reciprocal synthesis (let’s call it an SR, synthesis of reciprocity) is merely a form that does not determine any object. Also pertinent is the distinction between merely symbolic cognition / syntheses and real cognition / syntheses (s.88, s.91-2 – the distinction is developed at length in “On Symbolic Cognition and Philosophical Language”, s.263ff). So we could ask: why is a right-angled triangle a real concept whereas the concept of cause (cause – effect) is not? Is it because a determinable is inherently real? Maimon seems to be saying this, in using the criterion of a concept having or  not having consequences (s.88). A real concept is absolute and has consequences whether or not it is determined in any particular way. Whereas in an SR neither concept is meaningful outside its relation to the other since this relation defines it. In the footnote Maimon compares this with a mathematical relation between x and y where each is a function of the other. However for an infinite understanding all cognition is in terms of SRs. Why? It seems to be that the totality of relations has reality or confers reality on thought (this relates to ideas of the understanding, at infinity object and concept are the same), whereas for the finite understanding ‘the subject is what is given in itself and the predicate is what is thought in relation to it as object’ (footnote 1 to s.86). So this would make the given the determinable and mean that what marks our finitude is that we always have to start from something given which we then determine. This would align M aimon’s thought on determination with the traditional identification of the determinable with matter and the determination with form, which is discussed by Kant (see below). Thus is chapter 2 Maimon wrote:

For a cognition to be true, it must both be given and thought at the same time: given with respect to its matter (that must be given in an intuition;  thought with respect to its form that cannot be given in itself… ( because a relation can only be thought not intuited).(s.61)

Let’s now look at what Kant says about  determination to see if that will help in understanding how Maimon relates it to objectivity and the ‘quid juris?‘.

3. Comparison of determination in CPR and in Maimon’s Essay

The notion of determination comes up in two places in CPR, in the Schematism where schemata are defined as time-determinations and in the Amphiboly of the Concepts of Reflection where, with reference to time-determination, Kant states that whilst traditionally (and in particular in Leibnizian philosophy) matter is the determinable and form its determination, in transcendental philosophy the terms are reversed and it is the form that comes first as the determinable that is determined by matter. Space and time as determinables precede all appearances and make them possible. This gives rise to two questions: (1)  is Maimon guilty (in Kant’s eyes) of returning to the pre-critical notion of determination; (2) since Kant’s time-determinations are what mediate between the categories and intuition, i.e. they are part of Kant’s solution to the ‘quid juris?” does Maimon think that his notion of determination works in a similar way? Maimon’s clearest account of his theory of determination in relation to Kant’s comes in the ‘On the Categories’ section of the “Short Overview of the Whole Work” (s.212 ff). Here he says that the reciprocal relations that characterise the forms of thought consititute objects of thought but not of cognition, this gives rise to the question ‘quid juris?’ of how we are to ascribe them objective reality. For this, he says, they must first be supplied with determinate objects because they cannot produce them. This happens by means of the concepts of reflection, identity and difference, they take us from the mere logical object to determinate objects, and then the categories refer to objects indirectly by means of this first determination: the first relation ‘is so to speak the matter of the second relation which is its form’. So here Maimon posits identity and difference performing the mediating role between concept and intuition that the schemata (time-determinations) play in CPR, they produce the objects to which the categories can then be applied (And remember that Maimon rethinks the concepts of space and time as concepts of difference). Detemination is the production of determinate objects for the categories. However Maimon goes on in the same paragraph (s.214) to say that the concepts of reflection by themselves are insufficient because they do not distinguish what comes before from what comes after, hence one also needs time-determinations in order for, say, the category of cause/effect to be applied to the objects. I haven”t got to the bottom of whether this notion of a priori time is compatible with denying that it is an intuition. The final thing that needs to be said is that instead of aligning the role Maimon gives to identity and difference with the role that Kant gives to time-determinations, one could instead align it with the syntheses that give rise to an object that make up the transcendental deduction, for Kant does indeed himself make use of comparison, identity, difference in describing the production of objects there. Either way, there is a clear connection between determination and differentiation, a triangle in general is, so to speak , differentiated into a right-angled or equilateral triangle, sensations and positions are differentiated from one another by infinitesimal differences. The categories like cause/effect supervene upon these prior determinations but are not themselves determinations (they cannot directly determine intuitions).  Thus if determination solves the quid juris? of applying categories to experience it is by mediating between indeterminate given and concept. However in chapter 4 Maimon says that the relation of predicate determining subject when applied to experience gives us the concept of a substance and its accidents (s.95), thus correlating determination with a particular category – this complicates things yet further!

One thought on “Maimon Reading Group: Chapter 4

  1. “However for an infinite understanding all cognition is in terms of SRs. Why? It seems to be that the totality of relations has reality or confers reality on thought (this relates to ideas of the understanding, at infinity object and concept are the same), whereas for the finite understanding ‘the subject is what is given in itself and the predicate is what is thought in relation to it as object’ (footnote 1 to s.86).”

    Perhaps this is a question that deals with a larger issue of Maimon’s argument from the “infinite intellect” and it will be addressed later at some time (although some of these things have already come up in the discussion of infinitesimals), but I am not sure how the switch from finite intellect (“us”) to infinite intellect (“God”?) works and what exactly it does (and whether it is in fact infinite enough)? I think someone (Nick, perhaps) already mentioned certain objections to infinities in math and Maimon’s defense of them – I wonder if in connection to possible critiques of infinities in mathematics one can think of certain related objections to the use of infinities (“infinite mind”) in philosophy? Take the above example: how does going from finite to infinite help us figure out the relationship between, say, subjects and predicates? It seems that what Maimon really means by “infinite mind” is not infinite but only “slightly but importantly larger and more informed mind” than a human mind. While we don’t see that statement X is analytical and take it as amplificatory (synthetic), a slightly more informed mind does have the knowledge and therefore knows that X is analytic – do we have to go to infinity to guarantee that this is the case with every single statement N? Or do we need to push the boundaries of human mind just a bit further in our attempt to explain how what appears synthetic is in fact analytic (because we don’t have the insight)? Maybe put differently it’s something like this: is Maimon’s infinity (“infinite mind”) really that infinite and not just a kind of “bad infinity” of continuous expansion (n+1) of human finitude?

    On a related note, and I don’t want to burden anyone with questions, I realize that this is a casual conversation about very interesting issues, but is Kant’s description of that which is necessarily outside of space and time (since they are only forms of intuition, not objective realities, as long as we are not engaged in intuiting, we are outside space and time) a description of infinity or just a kind of negative moment of absence of the commonsensical space and time “measurements”? What sort of state is this state of no space and time?

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