The current entry is part of the Research Workshop titled “Computational Modelling“, which will be held on 11.03.2019 in Cracow, at John Paul II University. It concerns the text by Professor Hajo Greif on the possibility of computational realization of such human cognitive abilities like intuition and invention.
I would like to invite to the blog discussion not only the workshop participants, but all interested readers of the blog.
Of course, Hajo Greif will be present at the workshop and available for face-to-face discussion of his paper.
The whole text can be read HERE.
Below, however, I put a short abstract of the article and slightly longer final remarks.
This short philosophical discussion piece explores the relation between two common assumptions: first, that at least some cognitive abilities, such as inventiveness and intuition, are specifically human and, second, that there are principled limitations to what machine-based computation can accomplish in this respect. In contrast to apparent common wisdom, this relation may be one of informal association. The argument rests on the conceptual distinction between intensional and extensional equivalence in the philosophy of computing: Maintaining a principled difference between the processes involved in human cognition, including practices of computation, and machine computation will crucially depend on the requirement of intensional equivalence. However, this requirement was neither part of Turing’s expressly extensionally defined analogy between human and machine computation, nor is it pertinent to the domain of computational modelling. Accordingly, the boundaries of the domains of human cognition and machine computation might be independently defined, distinct in extension and variable in relation.
I have no proof or other formal conclusion to end on but merely one observation, a morale, another observation and yet another morale: First, the relation between the limits of computation and the limits of human inventiveness remains an open question, with each side of the equation having to be solved independently.
Second, it will be worthwhile to expressly acknowledge and address the relation between human and machine abilities as an open question, and as multifaceted rather than as a strict dichotomy. Any possible decision for one position or another will have rich and normatively relevant implications. On most of the more tenable accounts outlined above, the domains of human cognition and machine computation will be distinct in kind and extension, but this will be not a matter of a priori metaphysical considerations but of empirical investigation and actual, concrete human inventions.
Third, whatever the accomplishments of AI are and may come to be, intensional equivalence is not going to come to pass. In fact, several of the classical philosophical critiques of AI build on the requirement that the same cognitive functions would have to be accomplished in the same way in machines as in human beings for AI to be vindicated. Even if questions of AI are not involved, different kinds of computing machines – for example analog, digital and quantum computers – might provide identical solutions to the same functions, but the will do so in variant ways. Hence, intensional equivalence will remain out of reach here, too.
Fourth, intensionality is an interesting and relevant concept in mathematics and partly also in computing, to the extent that one is concerned with the question of what mathematical objects are to human beings (which was the explicit guiding question for Feferman 1985). However, intensional equivalence might prove to be too much of a requirement when it comes to comparing realisations of computational processes in human beings and various types of machines. Extensional equivalence will have to suffice. It might become a more nuanced concept once we define the analogies involved with sufficient precision and move beyond the confines of pure Turing-computability. After all, Turing’s computer analogy builds on extensional equivalence between human and machine operations. This kind of equivalence and its possible limitations are essential to the very idea of computer modelling. This leaves open the possibility of other relations of extensional equivalence to hold between different types or levels of systems, computational or other.
I cordially invite you to a discussion in which we can refer both to the details of Professor Greif’s argumentation and to some general issues that constitute the philosophical background of the article.
Here are three examples of these issues:
1) What is extensional and intensional equivalence in the theory of computation, with particular respect to comparisons between computing machines and the human mind?
2) Do we have good reasons to believe that the mind is not extensionally equivalent to a digital computer (with potentially unlimited resources)?
3) What is the relationship between human intuition and inventiveness?
Once again, I warmly encourage everyone to discuss — Paweł Stacewicz.