A Logical Journey: From G?del to Philosophy (MIT Press)

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Subscriber sign in. Forgot password? Don't have an account? Sign in via your Institution. Sign in with your library card. Search within In This Article 1. The Turing Test 1. The Imitation Game 1. Objections to the Test 1. Fiendish Experts 2. The Chinese Room Argument 2. The Argument 2. The Part-Of Principle 2. The Chinese Gym 2. The influence of both of these can be described as largely but far from entirely negative.

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Although many of the comments about Kant in his writings are critical, one can hardly doubt that Kant made an impression that stayed with him. However, comment on ancient philosophy is infrequent in his later writing. But of the remarks from their conversations that Wang includes in his book, only three mention Plato, and they are very general. It may be that it is primarily the Leibnizian aspects of his own view that prompted him to describe his theory as idealistic. Since Kant is the philosopher of the relevant tradition about whom I know most, the largest part of this paper will be devoted to him.

I will then make some briefer remarks about Leibniz.

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The reflection on the subject treated in idealistic philosophy that is, your second topic of thought , the distinction of levels of reflection, etc. However, I cannot go along with the denial of the objective meaning of thought that is connected with it, [although] it is really entirely independent of it. I do not believe that any Kantian or positivistic argument or the antinomies of set theory or quantum mechanics has proved that the concept of objective being no matter whether for things or abstract entities is senseless or contradictory.

They seem rather to form a second plane of reality, which confronts us just as objectively and independently of our thinking as nature. CW IV , , trans.

I shall return to this passage in its own context. For the present I will note that it claims that certain insights of idealistic philosophy are compatible with a generally realistic point of view. This may be the most essential kinship that he discerned with Leibniz. With respect to mathematics, he shared the conviction associated with Hilbert that for every well formulated mathematical problem there is in principle a solution, although his own incompleteness theorem implies that this might require introducing new axioms beyond those used in current mathematics.

The same conviction undoubtedly disposed him against any form of physicalism or materialism in metaphysics, as well as against empiricism in epistemology. It may also have motivated his probably early reaction against the views prevailing in the Vienna Circle. But in his more developed philosophical thought only certain elements of this metaphysics appear, in particular his realism about mathematical knowledge and, buttressing this, about concepts.

In spite of his belief in systematicity in philosophy, we do not have evidence that he developed his metaphysical view at all fully. In conversations with Wang he describes his view as monadology, but he does not go into the problem of how, if underlying reality consists of monads, the physical world appears to us as it does.

Some theses of the above-mentioned statement are anti-naturalistic in the extreme, for example no. They are not developed in the conversations with Wang, still less in even draft papers. Concerning no. But there is no indication that he was ever prepared to defend views of this kind publicly. He did work out a version of the ontological proof of the existence of God, which became known in his lifetime because he allowed Dana Scott to discuss it in a seminar in The now famous disjunction from the Gibbs Lecture of is stated there:.

Either the human mind surpasses all machines to be more precise: it can decide more number theoretical questions than any machine or else there exist number theoretical questions undecidable for the human mind. Now let us turn to Kant.


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CW II Another passage is worth mentioning because it is much earlier and remains unpublished. In particular he writes:. Moreover, according to the Kritik of pure reason the mathematical concepts too are subjective since they are obtained by applying the purely subjective categories of thinking to the objects of intuition. It is interesting to note that apparently Hegel held that the categories themselves are subjective, so that there is a factor additional to the forms of intuition driving Kant toward a subjective form of idealism.

The background of these comments is a discussion that is more fully presented in the earlier now published version of the paper, version B2. He gives two short passages particular emphasis. He is perhaps clearest in the following statement:. Moreover, one may allege the passages 2 , 4 , 6 , which… seem to imply that the relations in question are in some sense the object of our representations [and] hence cannot consist solely in the act or disposition of representing. CW III The reader will probably notice that the passages that express a subjectivist reading of Kant are later than the Kant paper of —49, although the apparently abandoned footnote in the Gibbs lecture is only a little later.

That he might have changed his mind would be suggested by one striking remark reported by Wang:. For Kant, the mind is the transcendental ego which is subjective and separate from the outside world.

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But the unconscious accompanies sense perceptions: the ideas we form of sensations refer to the object itself. He tends to read the concept of things in themselves as just of things as they really are, and the result is that he comes close to a philosophically problematic interpretation, what I have elsewhere called the Distortion Picture, 23 according to which our representations of outer objects have as their objects things in themselves.

But we represent them as being in space and time, whereas things in themselves are not spatio-temporal. Therefore our representations represent them falsely. He begins the Einstein paper by noting the relativity of simultaneity that is already fundamental in special relativity, with the consequence that only a partial ordering of events as before and after can escape this relativity. But then he says. Following up the consequences of this strange state of affairs, one is led to conclusions about the nature of time which are very far reaching indeed.

In short, it seems that one obtains an unequivocal proof for the view of those philosophers who, like Parmenides, Kant, and the modern idealists, deny the objectivity of change and consider change as an illusion or an appearance due to our special mode of perception. This would agree with the view of Parmenides and such idealists as McTaggart, but of course not with the view of Kant.

Evidently special relativity poses a serious obstacle to the objectivity of time in the A-series sense. Change becomes possible only through the lapse of time.

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But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such nows in an objectively determined way. He considers that such a view gives the idealist what he wants regarding change. Mellor [] who maintain that the reality of time amounts to that of the B series.

In the Einstein paper he shifts ground immediately and gives an argument in which he makes use of his own results on rotating solutions of the field equations of general relativity. That argument also appears in the later versions of the Kant paper. Evidently this plays the role of an objection to the claims made on the basis of special relativity. This makes it impossible to define even an arbitrary global temporal ordering, because it could not be a linear ordering or even a partial ordering such as special relativity allows.

Whether this is true of the actual cosmos is, of course, an empirical question. He makes clear that he does not regard this as sufficient for the metaphysical conclusion of the reality of time:. For, if someone asserts that this absolute time is lapsing, he accepts as a consequence that whether or not an objective lapse of time exists i.

This is not a straightforward contradiction; nevertheless, a philosophical view leading to such a conclusion can hardly be considered as satisfactory. CW II — In the case of geometry, e. According to Kant, the limitation of our theoretical cognition of objects to conditions of space and time implies that the representation of them as spatio-temporal meets the highest standard of objectivity that we can apply.

He might well have found what I call the Distortion Picture of the relation of appearances and things in themselves less problematic philosophically, and perhaps even as an interpretation of Kant, than other readers of Kant would. One could object: Yes, only the present really exists now , but without that qualification the claim seems to assimilate a tensed and a tenseless way of speaking. A relative lapse of time, however, if any meaning at all can be given to this phrase, would certainly be something entirely different from the lapse of time in the ordinary sense, which means a change in the existing.

The concept of existence, however, cannot be relativized without destroying its meaning completely. CW II n. It seems to me simply wrong to say that existence cannot be relative to anything. The sentence is assumed to be in the present tense used with its common temporal meaning, not with the timeless meaning it assumes in mathematical statements and in many non-mathematical statements.

Imagine an observer A, who is located at a place in space-time that is spacelike separated from events on Earth at least from September on, but close enough so that much of the earlier history of the World Trade Center is in his past light cone. So we will assume that he knows of the World Trade Center and can say, speaking tenselessly, that the World Trade Center exists. Clearly, if the actual structure of space-time contains closed timelike curves, then no global time ordering can be defined.

What is contentious is how he argues on the assumption that the actual universe is not like his own models and, in particular, admits the sort of global time admitted by the models available before his own work. But this consistency proves nothing: all it shows is that general relativity does not rule them out, not that nothing does. But what Mellor says indicates that he would think little better of the argument if further physical laws were invoked.

He himself appeals to his own theory of causation to conclude that timelike loops are impossible. He does not note that in the discussion of these matters by physicists causal conditions have been considered that have the same effect. However, they do not seem to be regarded as such by everyone. Since there is a lot of strangeness about causal relations in contemporary physics, it would be hasty to accept the proposed criteria as the metaphysical truth.

But in a world without closed timelike curves, it is hard not to accept the protest of Earman that the existence of cosmic time is no less real for being contingent. However, since his argument is connected with Leibnizian echoes that he finds in the Kant paper, I will postpone considering it until the next section. But it can be questioned whether this is really the most fundamental issue.

If time is unavoidably local and in important respects perspectival, how gravely should we regard this? Basic notions of physics, such as motion, velocity, and acceleration, involve time. It is true that relativity theory changed more local notions involving time in important ways, first by the conclusion that the proper time between two events in space-time depends on the path between them. According to John Stachel, this fact diminishes the physical significance of a global time even if it can be defined. For example he remarks. He also presents a slightly longer version of his criticism of the A series.

No doubt the significance of time in human life depends on the fact that we do not find closed timelike loops in our actual experience, so that, for example, life proceeds from birth to death, and probably even human history proceeds from the beginning of homo sapiens to the eventual extinction of the species.

The actual existence of such loops would , as Stachel notes, have a bearing on local concept of time. He remarks that it would be an extreme example of path-dependence. It would show that along some paths, time can have a very peculiar structure. But it would not abolish time. It was a lucky break for this picture that the development of mathematical natural science and even its being brought to maturity by Newton did not undermine it. One might well regard this projection as resting on an illusion, something like the transcendental illusion that Kant claimed to arise in cosmological reasoning.

I now turn to Leibniz. As noted above, he described his metaphysical view as monadology. But he does not tell us much about what he understood the universal characteristic to be. In other places he maintains, apparently on the basis of undecidability results, that the project of a universal characteristic cannot be carried through. But he clearly thought that uncovering the right primitive concepts and coming to perceive them clearly would yield axioms of metaphysics rather than definitions, even infinitary ones. At this point I should return to the Kant paper.

He ends by saying:. It should not be surprising that he would not accept the reality of time as depending on genuinely contingent factors.