Logic as Theory of Science

One might, as a first approximation, regard a scientific theory as a multiplicity of acts of knowing, of verifyings and falsifyings, validatings and calculatings, on the part of successive generations of cognitive subjects. Of course not every collection of acts of knowing constitutes a science. Such acts must manifest, for example, a certain intrinsic organisation, they must be set apart in determinate ways from cognitive acts of other sorts and also from their objects, and they must be capable of being communicated from one group of scientists to another. Husserl’s logic is, then, a theory which seeks to determine the conditions which must be satisfied by a collection of acts if it is to count as a science. It is in this sense that logic is a `theory of science’ and of all that is necessarily connected therewith.

Theory realises itself in certain mental acts, but it is clear that the more or less randomly delineated collections of knowings and judgings concretely performed by cognitive subjects on given occasions will have properties that are of little relevance to logic. Husserl however saw that we can put ourselves in a position where we are able to understand the intrinsic organisation of collections of scientific acts if we consider such collections from a certain idealising standpoint.

In fact, there are three distinct sorts of idealisation which are involved in the properly logical reflection on scientific acts:

I. The members of a collection of acts must be idealised, first of all, in that they are considered not as individual events or processes of judging, inferring, verifying, but as universals, as species or kinds of such events, capable of being instantiated in principle at any time or place: `the theoretical content of a science is nothing other than the meaning-content of its theoretical statements independent of all contingency of judgers and occasions of judgment’ (II A92/332).(2)

II. These species or kinds must themselves be idealised by being considered not as classes or extensions, but rather as ‘ideal singulars’. We are interested in species of acts not as collections of individual instances, but as proxies or representatives of such instances in the sphere of idealities, related together in representative structures of certain sorts.

III. The total collection of ideal singulars corresponding to each given empirical realm of individual instances must then in turn be idealised by being seen as enjoying a certain sort of ideal completeness: thus a scientific theory in the strict sense that is relevant to logic must enjoy the property of deductive closure.(3)

We shall have to deal, then, with certain ideal structures of species of simple and complex cognitive acts of various sorts. The most important nodes in such ideal structures are occupied by species of acts of judgment, and these can be divided in turn into two sorts, corresponding to the two different roles which individual judging acts may play on the level of underlying instances. On the one hand are the primitive judgment-species whose truth is self-evident (or is taken as such), for example red is a colour. On the other hand are the judgment-species which ‘are grasped by us as true only when they are methodically validated’ (I A16/63). It is at this point that we reach the heart of logic as Husserl conceives it. Some judgments are and must be derived by laws from others. We are thereby enabled to move beyond what is trivially or immediately evident to that which is enlightening, which brings clarification. (I A234/229) It is this fact which ‘not only makes the sciences possible and necessary, but with these also a theory of science, a logic.’ (I A16/63).

It is a matter of some note that such a science of science exists at all, that it is possible to deal within a single theory with that which all sciences have in common in their modes of validation, irrespective of the specific material of their constituent acts and objects. For it is not evident that there should be, as Husserl puts it, necessary and universal laws relating to truth as such, to deduction as such, and to theory as such, laws founded “purely on the concept of truth, of proposition, of object, of property, of relation, etc., i.e., in the concepts which as a matter of essence make up the concept of theoretical unity.’ (I A111/136)
On immersing ourselves in the practice of theory, however, we very soon discover that the modes of interconnection which bind together the judging acts which ideally constitute a scientific theory do indeed belong to a fixed and intelligible repertoire, being distinguished by the fact that:
 

1. they have ‘the character of fixed structures in relation to their content. In order to reach a given piece of knowledge (e.g. Pythagoras’ theorem), we cannot choose our starting points at random among the knowledge immediately given to us, nor can we thereafter add or subtract any thought-items at will’ (I A17/64),

2. they are not arbitrary: ‘A blind caprice has not bundled together any old heap of truths P1, P2,…S, and then so instituted the human mind that it must inevitably (or in “normal” circumstances) connect the knowledge of S to the knowledge of P1, P2,… In no single case is this so. Connections of validation are not governed by caprice or contingency, but by reason and order, and that means: regulative laws’ (I A18/64),

3. they are formal, i.e. they are not bound up with particular territories of knowledge: all types of logical sequences ‘may be so generalised, so purely conceived, as to be free of all essential relation to some concretely limited field of knowledge.’ (I A19/65)

This means that, the form of a given validation having once been established, it is possible for us to justify all other validations of this same form – all validations that conform to a given law – in one go, just as in mathematics it is possible for us simultaneously to determine the properties of a whole family of structures conforming to any given set of axioms.

Barry Smith, Logic and Formal Ontology

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s