Completely agree! I think the ‘meta-algorithm’ you refer to might be close to what Roger Penrose was getting at in his Emperor’s New Mind. But overall in agreement with your post. — Wayfarer

I think that here really lies some awesome axiom that is simply missing from our philosophical and mathematical vocabulary. Once we know that axiom, everything makes far more sense.

Indeed it's the 'meta-algorithm' problem. The 'meta-algorithm' is the way to avoid the problem, to get that needed external view to have an objective model. The problem is that you cannot just write the 'meta-algorithm'. In mathematics this means that there's obviously a correct model, but no way to make that model or to compute it. Here the problem is that we actually don't have a theorem for just what computation is (which likely is linked to the whole problem itself).

The basic issue is that this is seen as a problem, as a paradox that ought to be overcome by some way. The instant response is usually: "Let's think about this in another way."

I think the basic red line (in this hypothetical axiom) is the following: by negative self-reference, you get something that cannot be computed / modeled objectively. With positive self-reference, you basically get a self-fulfilling prophecy of an outcome that indeed can be computed and objectively modeled.

And naturally this comes close to many mathematical limitations, like Gödel's incompleteness theorem. Which at the most trivial can be summed up like Hans Straub puts it:

What – in layman’s terms – is the trick in Gödel’s incompleteness theorem?

The trick is the same as in the barbar paradox and all other real paradoxes. The trick is to make a sentence, a logical statement and …

1. to refer it to itself (self reference)
2. and then to deny it. (negation)

That’s the whole trick. With this combination, any classic formal system can be invalidated.

The point is to understand how subjectivity relates to this. The computer simply follows algorithms, it's not a subject itself: it doesn't make any choices itself, it only follows the rules it has been given, even if these rules extensively are about making choices.

So here's one interesting question: could one say that the ability to make a negative self reference means having subjectivity?

In Christianity Jesus talks about opening your heart to him to find God, not to "use your brain and think it through".

True, but "heart" had a much different meaning in both the Hebrew and Greek context (see below). The heart is often referred to as the "eye of the nous," the inner-most part of the mind that receives the highest forms of intelligible illumination in the Patristics (gnosis). It is not primarily a symbol for "emotion" or "sentiment," but often instead of the deepest possible sort of knowledge. Early Christianity is very much a religion of Logos in a way perhaps at odds with some contemporary sentimentalism.

I mention this not only because it's an interesting facet of changing language, but because it actually seems to have a lot to do with the rest of your post and this general topic. Knowledge used to be conceived of in very personal terms. It is also not for nothing that the path of knowledge in Plato, Saint Augustine, Boethius, etc. is called "the Erotic Ascent; Plato for his part speaks of the philosopher's desire for knowledge of the Good in terms of an ardor to "couple with the Good." The removal of these personal and erotic elements helps to explain the development of current notions of "objectivity," including the amazing shift whereby questions of goodness vanish from the "objective" frame.

The emergence of positivism is situated within a larger shift in anthropology, and particularly the anthropology of reason, so these changes all sort of tie together, there being a lot of interesting threads to explore.

I find it interesting that you mention computers' inability to motivate themselves. Reason has often been reduced to computation in modern thought (computational theories of mind might play a role here, although the shift predates them by centuries). On this view, the computer is sort of an idealization of rationality. But if it cannot act, does that mean all action comes down to a sort of non-rational sentiment? Something else?

Things are obviously quite different when "reason" or "the rational soul," has its own strong desires, which also tended to personalize knowledge.

Here is an interesting related quote:

But, having so defined [reason, as merely the power by which one goes from premises to conclusions], he gives as his first example, from Hooker, 'Reason is the director of man's will, discovering in action what is good'. There would seem to be a startling discrepancy between the example and the definition. No doubt, if A is good for its own sake, we may discover by reasoning that, since B is the means to A, therefore B would be a good thing to do. But by what sort of deduction, and from what sort of premises, could we reach the proposition 'A is good for its own sake' ?

This must be accepted from some other source before the reasoning can begin; a source which has been variously identified-with 'conscience' (conceived as the Voice of God), with some moral 'sense' or 'taste', with an emotion ('a good heart'), with the standards of one's social group, with the super-ego.Yet nearly all moralists before the eighteenth century regarded Reason as the organ of morality. The moral conflict was depicted as one between Passion and Reason, not between Passion and 'conscience', or ' duty', or ' goodness'. Prospero, in forgiving his enemies, declares that he is siding, not with his charity or mercy, but with'his nobler reason' (Tempest, v, i, 26). The explanation is that nearly all of them believed the fundamental moral maxims were intellectually grasped. If they had been using the strict medieval distinction, they would have made morality an affair not of ratio but of intellectus.

...The belief that to recognise a duty was to perceive a truth-not because you had a good heart but because you were an intellectual being-had roots in antiquity. Plato preserved the Socratic idea that morality was an affair of knowledge; bad men were bad because they did not know what was good. Aristotle, while attacking this view and giving an important place to upbringing and habituation, still made 'right reason' ( 6p6os Myos) essential to good conduct. The Stoics believed in a Natural Law which all rational men, in virtue of their rationality, saw to be binding on them. St Paul has a curious function in this story. His statement in Romans (ii. 14 sq.) that there is a law ' written in the hearts' even of Gentiles who do not know 'the law', is in full conformity with the Stoic conception, and would for centuries be so understood.

Nor, during those centuries, would the word hearts have had merely emotional associations. The Hebrew word which St Paul represents by Kap5ia would be more nearly translated ' Mind' ; and in Latin, one who is cordatus is not a man of feeling but a man of sense. But later, when fewer people thought in Latin, and the new ethics of feeling were corning into fashion, this Pauline use of hearts may well have seemed to support the novelty.

The Discarded Image - C.S. Lewis

Virgil's Aeneas is meant to be a man of "heart," but when he kills Turnus at the end in a fit of thymotic rage he is failing to live up to this archetype (just to include my own example :cool: ). What's interesting is that this does overlap the modern view to some degree (the exclusion of rage from reason), but not completely (i.e. doing the 'good thing' and living up to one's values being necessarily 'reasonable' is not such a strong connection today.)

True, but "heart" had a much different meaning in both the Hebrew and Greek context (see below). The heart is often referred to as the "eye of the nous," the inner-most part of the mind that receives the highest forms of intelligible illumination in the Patristics (gnosis). It is not primarily a symbol for "emotion" or "sentiment," but often instead of the deepest possible sort of knowledge. Early Christianity is very much a religion of Logos in a way perhaps at odds with some contemporary sentimentalism. — Count Timothy von Icarus

I didn't know this. Thank you!

I find it interesting that you mention computers' inability to motivate themselves. Reason has often been reduced to computation in modern thought (computational theories of mind might play a role here, although the shift predates them by centuries). On this view, the computer is sort of an idealization of rationality. But if it cannot act, does that mean all action comes down to a sort of non-rational sentiment? Something else? — Count Timothy von Icarus

The idea is that computers (or Turing Machines) follow algorithms. An algorithm is a procedure used for solving a problem or performing a computation and act as an exact list of instructions that conduct specified actions step by step.

No, I'm not trying to reduce reason to computation here. I'm just trying to make a simple model on where the issue is. And it's a very specific issue. First of all, a Turing Machine can do a lot. But this doesn't meant that all (or some) action "comes down to a sort of non-rational sentiment". That's why I'm referring to mathematics, which is quite logical. The fact is that there do exist mathematical statements that are true but not computable. They aren't illogical, false, they are only uncomputable.

That is, if you can show how psychological or economic models (for example) fail to offer consistently, predictable results, then that counts for me as a substantive blow against positivism as opposed to just an analytic attack on the self consistency of the theory. — Hanover

The thing is that the positivist conclusion comes form reflection on human experience, knowledge and judgement, so it is , like phenomenology, not strictly empirical.

So, claiming it is a performative contradiction is lacking a bit of nuance. By the same strict argument Popper's idea of falsifiability eliminates itself, since it is not itself strictly falsifiable.

Reflecting on our experience, though, we can see that there is much in human life in the way of simple claims about what is the case that are indeed verifiable by observation. It is more relevant to theories than it is to basic observations, to say that they cannot be definitively verified. It is also arguable as to whether theories can be definitively falsified.

The heart is often referred to as the "eye of the nous," the inner-most part of the mind that receives the highest forms of intelligible illumination in the Patristics (gnosis). It is not primarily a symbol for "emotion" or "sentiment," but often instead of the deepest possible sort of knowledge. — Count Timothy von Icarus

There's a similar term in Buddhism, namely 'citta' which means both 'mind' and 'heart', depending on the context - the organ of knowledge or insight. In Mahāyāna Buddhism 'bodhicitta' is the aspiration for the enlightenment of all beings.

So here's one interesting question: could one say that the ability to make a negative self reference means having subjectivity? — ssu

There's an aphorism from the Upaniṣads that I'm fond of quoting, to the effect that 'the eye can see another, but not itself, the hand can grasp another, but not itself'. It relates to the problem of reflexivity, that what is ordinarily considered knowledge is always considered in the subject-object framework, but as to the nature of the knowing subject, that is always outside the frame, so to speak.

By the same strict argument Popper's idea of falsifiability eliminates itself, since it is not itself strictly falsifiable. — Janus

But it wasn't intended as an empirical theory. It was intended as principle which was to be used to identify what was or was not in principle an empirical theory.

But it wasn't intended as an empirical theory. It was intended as principle which was to be used to identify what was or was not in principle an empirical theory. — Wayfarer

And the same can be said of the verification principle. Anyway you failed to notice my point that reflection on and analysis of human experience and our ways of knowing and judging are quasi-empirical investigations, as with phenomenology.

You also failed to notice the point that it is not all about theory it is also about observation. Observation reports are both verifiable and falsifiable. The thesis "there are no black swans" is not verifiable, obviously, but it is falsifiable. On the other hand the thesis "there are black swans" is verifiable but not falsifiable.