Hypostatic Abstraction. Thought of the Day 138.0

Hypostatic abstraction is linguistically defined as the process of making a noun out of an adjective; logically as making a subject out of a predicate. The idea here is that in order to investigate a predicate – which other predicates it is connected to, which conditions it is subjected to, in short to test its possible consequences using Peirce’s famous pragmatic maxim – it is necessary to posit it as a subject for investigation.

Hypostatic abstraction is supposed to play a crucial role in the reasoning process for several reasons. The first is that by making a thing out of a thought, it facilitates the possibility for thought to reflect critically upon the distinctions with which it operates, to control them, reshape them, combine them. Thought becomes emancipated from the prison of the given, in which abstract properties exist only as Husserlian moments, and even if prescission may isolate those moments and induction may propose regularities between them, the road for thought to the possible establishment of abstract objects and the relations between them seems barred. The object created by a hypostatic abstraction is a thing, but it is of course no actually existing thing, rather it is a scholastic ens rationis, it is a figment of thought. It is a second intention thought about a thought – but this does not, in Peirce’s realism, imply that it is necessarily fictitious. In many cases it may indeed be, but in other cases we may hit upon an abstraction having real existence:

Putting aside precisive abstraction altogether, it is necessary to consider a little what is meant by saying that the product of subjectal abstraction is a creation of thought. (…) That the abstract subject is an ens rationis, or creation of thought does not mean that it is a fiction. The popular ridicule of it is one of the manifestations of that stoical (and Epicurean, but more marked in stoicism) doctrine that existence is the only mode of being which came in shortly before Descartes, in concsequence of the disgust and resentment which progressive minds felt for the Dunces, or Scotists. If one thinks of it, a possibility is a far more important fact than any actuality can be. (…) An abstraction is a creation of thought; but the real fact which is important in this connection is not that actual thinking has caused the predicate to be converted into a subject, but that this is possible. The abstraction, in any important sense, is not an actual thought but a general type to which thought may conform.

The seemingly scepticist pragmatic maxim never ceases to surprise: if we take all possible effects we can conceive an object to have, then our conception of those effects is identical with our conception of that object, the maxim claims – but if we can conceive of abstract properties of the objects to have effects, then they are part of our conception of it, and hence they must possess reality as well. An abstraction is a possible way for an object to behave – and if certain objects do in fact conform to this behavior, then that abstraction is real; it is a ‘real possibility’ or a general object. If not, it may still retain its character of possibility. Peirce’s definitions of hypostatic abstractions now and then confuse this point. When he claims that

An abstraction is a substance whose being consists in the truth of some proposition concerning a more primary substance,

then the abstraction’s existence depends on the truth of some claim concerning a less abstract substance. But if the less abstract substance in question does not exist, and the claim in question consequently will be meaningless or false, then the abstraction will – following that definition – cease to exist. The problem is only that Peirce does not sufficiently clearly distinguish between the really existing substances which abstractive expressions may refer to, on the one hand, and those expressions themselves, on the other. It is the same confusion which may make one shuttle between hypostatic abstraction as a deduction and as an abduction. The first case corresponds to there actually existing a thing with the quality abstracted, and where we consequently may expect the existence of a rational explanation for the quality, and, correlatively, the existence of an abstract substance corresponding to the supposed ens rationis – the second case corresponds to the case – or the phase – where no such rational explanation and corresponding abstract substance has yet been verified. It is of course always possible to make an abstraction symbol, given any predicate – whether that abstraction corresponds to any real possibility is an issue for further investigation to estimate. And Peirce’s scientific realism makes him demand that the connections to actual reality of any abstraction should always be estimated (The Essential Peirce):

every kind of proposition is either meaningless or has a Real Secondness as its object. This is a fact that every reader of philosophy should carefully bear in mind, translating every abstractly expressed proposition into its precise meaning in reference to an individual experience.

This warning is directed, of course, towards empirical abstractions which require the support of particular instances to be pragmatically relevant but could hardly hold for mathematical abstraction. But in any case hypostatic abstraction is necessary for the investigation, be it in pure or empirical scenarios.

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Distributed Representation Revisited

If the conventional symbolic model mandates a creation of theory that is sought to address the issues pertaining to the problem, this mandatory theory construction is bypassed in case of distributed representational systems, since the latter is characterized by a large number of interactions occurring in a nonlinear fashion. No such attempts at theoretical construction are to be made in distributed representational systems for fear of high end abstraction, thereby sucking off the nutrient that is the hallmark of the model. Distributed representation is likely to encounter onerous issues if the size of the network inflates, but the issue is addressed through what is commonly known as redundancy technique, whereby, a simultaneous encoding of information generated by numerous interactions take place, thus ameliorating the adequacy of presenting the information to the network. In the words of Paul Cilliers, this is an important point, for,

the network used for the model of a complex system will have to have the same level of complexity as the system itself….However, if the system is truly complex, a network of equal complexity may be the simplest adequate model of such a system, which means that it would be just as difficult to analyze as the system itself.

Following, he also presents a caveat,

This has serious methodological implications for the scientists working with complex systems. A model which reduces the complexity may be easier to implement, and may even provide a number of economical descriptions of the system, but the price paid for this should be considered carefully.

One of the outstanding qualities of distributed representational systems is their adaptability. Adaptability, in the sense of reusing the network to be applicable to other problems to offer solutions. Exactly, what this connotes is, the learning process the network has undergone for a problem ‘A’, could be shared for problem ‘B’, since many of the input neurons are bounded by information learned through ‘A’ that could be applicable to ‘B’. In other words, the weights are the dictators for solving or resolving issues, no matter, when and for which problem the learning took place. There is a slight hitch here, and that being this quality of generalizing solutions could suffer, if the level of abstraction starts to shoot up. This itself could be arrested, if in the initial stages, the right kind of framework is decided upon, thus obscuring the hitch to almost non-affective and non-existence impacting factor. The very notion of weights is considered here by Sterelny as a problematic, and he takes it to attack distributed representation in general and connectionsim as a whole in particular. In an analogically witty paragraph, Sterelny says,

There is no distinction drawable, even in principle, between functional and non- functional connections. A positive linkage between two nodes in a distributed network might mean a constitutive link (eg. Catlike, in a network for tiger); a nomic one (carnivore, in the same network), or a merely associative one (in my case, a particular football team that play in black and orange.

It should be noted that this criticism on weights is derived, since for Sterelny, relationship between distributed representations and the micro-features that compose them is deeply problematic. If such is the criticism, then no doubt, Sterelny still seems to be ensconced within the conventional semantic/symbolic model. And since, all weights can take part in information processing, there is some sort of a democratic liberty that is accorded to the weights within a distributed representation, and hence any talk of constitutive, nomic, or even for that matter associative is mere humbug. Even if there is a disagreement prevailing that a large pattern of weights are not convincing enough for an explanation, as they tend to complicate matters, the distributed representational systems work consistently enough as compared to an alternative system that offers explanation through reasoning, and thereby, it is quite foolhardy to jettison the distributed representation by the sheer force of criticism. If the neural network can be adapted to produce the correct answer for a number of training cases that is large compared with the size of the network, it can be trusted to respond correctly to the previously unseen cases provided they are drawn from the same population using the same distribution as the training cases, thus undermining the commonly held idea that explanations are the necessary feature of the trustworthy systems (Baum and Haussler). Another objection that distributed representation faces is that, if representations are distributed, then the probability of two representations of the same thing as different from one another cannot be ruled out. So, one of them is the true representation, while the other is only an approximation of the representation.(1) This is a criticism of merit and is attributed to Fodor, in his influential book titled Psychosemantics.(2) For, if there is only one representation, Fodor would not shy from saying that this is the yucky solution, folks project believe in. But, since connectionism believes in the plausibility of indeterminate representations, the question of flexibility scores well and high over the conventional semantic/symbolic models, and is it not common sense to encounter flexibility in daily lives? The other response to this objection comes from post-structuralist theories (Baudrillard is quite important here. See the first footnote below). The objection of true representation, and which is a copy of the true representation meets its pharmacy in post-structuralism, where meaning is constituted by synchronic as well as diachronic contextualities, and thereby supplementing the distributed representation with a no-need-for concept and context, as they are inherent in the idea of such a representation itself. Sterelny, still seems to ride on his obstinacy, and in a vitriolic tone poses his demand to know as to why distributed representation should be regarded as states of the system at all. Moreover, he says,

It is not clear that a distributed representation is a representation for the connectionist system at all…given that the influence of node on node is local, given that there is no processor that looks at groups of nodes as a whole, it seems that seeing a distributed representation in a network is just an outsider’s perspective on the system.

This is moving around in circles, if nothing more. Or maybe, he was anticipating what G. F. Marcus would write and echo to some extent in his book The Algebraic Mind. In the words of Marcus,

…I agree with Stemberger(3) that connectionism can make a valuable contribution to cognitive science. The only place, we differ is that, first, he thinks that the contribution will be made by providing a way of eliminating symbols, whereas I think that connectionism will make its greatest contribution by accepting the importance of symbols, seeking ways of supplementing symbolic theories and seeking ways of explaining how symbols could be implemented in the brain. Second, Stemberger feels that symbols may play no role in cognition; I think that they do.

Whatever Sterelny claims, after most of the claims and counter-claims that have been taken into account, the only conclusion for the time being is that distributive representation has been undermined, his adamant position to be notwithstanding.

(1) This notion finds its parallel in Baudrillard’s Simulation. And subsequently, the notion would be invoked in studying the parallel nature. Of special interest is the order of simulacra in the period of post-modernity, where the simulacrum precedes the original, and the distinction between reality and representation vanishes. There is only the simulacrum and the originality becomes a totally meaningless concept.

(2) This book is known for putting folk psychology firmly on the theoretical ground by rejecting any external, holist and existential threat to its position.

(3) Joseph Paul Stemberger is a professor in the Department of Linguistics at The University of British Columbia in Vancouver, British Columbia, Canada, with primary interests in phonology, morphology, and their interactions. My theoretical orientations are towards Optimality Theory, employing our own version of the theory, and towards connectionist models.