Online research in philosophy

What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We will point to interesting examples of (ideal) physical machines that fall outside the class of Gandy machines and compute functions that are not Turing-machine computable.

Since the introduction of the imitation game by Turing in 1950 there has been much debate as to its validity in ascertaining machine intelligence. We wish herein to consider a different issue altogether: granted that a computing machine passes the Turing Test, thereby earning the label of ``Turing Chatterbox'', would it then be of any use (to us humans)? From the examination of scenarios, we conclude that when machines begin to participate in social transactions, unresolved issues of trust and responsibility may well overshadow any raw reasoning ability they possess.

Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein- the-system" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true. Goedel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.

A "machine" is any causal physical system, hence we are machines, hence machines can be conscious. The question is: which kinds of machines can be conscious? Chances are that robots that can pass the Turing Test -- completely indistinguishable from us in their behavioral capacities -- can be conscious (i.e. feel), but we can never be sure (because of the "other-minds" problem). And we can never know HOW they have minds, because of the "mind/body" problem. We can only know how they pass the Turing Test, but not how, why or whether that makes them feel.