Indelibility of consciousness (continued)

Lowell asked:

What evidence exists for the idea that consciousness is indelible?

Answer by Jürgen Lawrenz

A forthright answer to this question is: None. It should perhaps be unpacked by the additional remark that we commonly assume that evidence is a persuasive criterion for our belief in the reality of whatever it suggests. But evidence can be false, fictitious, mistaken, manipulated, wrongly interpreted etc. Hence it is pointless asking for evidence in a situation where it is proof that we demand. “Is x possible?” cannot be ascertained by speculative means, for this is precisely what your question amounts to.

Bear in mind that facts related to consciousness are notorious for their denotational blur, and so thin on the ground that no-one could confidently stand up and claim that he/she is discoursing on a well-defined thing or process – it does not even exhibit an unambiguous phenomenology. Which is not surprising, after all, since every living thing has its own individualised consciousness, while at the same time it is one kind of universal phenomenon that clearly demarcates living things from all other phenomena. And then we confront intentionality: does it imply a genuine autonomy or can it be reduced to the mechanical give and take that Descartes postulated for biological machines? Not to mention memories: What are they? Pictures, movies? Where and how are memories stored? How are they accessed by consciousness? Once again candour should rule: we are not in possession of enough knowledge to settle such arguments, though we can be reasonable certain that human organisms don’t keep a photo album or a zip files on a hidden hard drive.

This leaves us with two very dubious ways out of the dilemma. We can appeal to the ancient philosophical dictum that a soul is not made of parts, therefore it cannot fall apart on the demise of its owner. But at bottom this is a “take it or leave it” argument. Alternatively we can play around with thought experiments which typically begin with the words “I can imagine…”, and proceed with propositions of such hair-raising improbability as no-one can actually “imagine” because the idea cannot be fleshed out in any semblance of reality – for example “anything that can happen will happen”, which takes up a mortgage for eternity in the name of logic, whereas the very notion of ‘eternity’ is already logically defective in that it pretends to knowledge that is impossible to have.

And so I will propose a sample right now, that “I can imagine” scientists of the future replicating my hippocampus and wiring it into a computer, so as to engender mental events in the machine that will duplicate my sense of selfhood, conscious intentionality, memory formation, dreams etc., and that this device can then be manufactured on an assembly line and installed in any number of artificial Doppelgangers here on Earth and eventually on far away planets of other galaxies, so that the word “I” can be pronounced by all of them in the full conviction that each is speaking for itself.

Can I really imagine this or is it just blabber? If asked, I could not enlighten a questioner about the merest details of this supposedly imaginative scenario, so yes, mere blabber.

Let us return to home ground and interrogate the sole reliable witness (aka evidence), which is of course the hippocampus. As it is an organ, it is mortal. Therefore it is utterly improbable to expect from it the creation of thoughts and ideas and conscious states that can outlive it. Conclusion: Indelibility is not on the agenda of any mortal creature.

Indelibility of consciousness

Lowell asked:

What evidence exists for the idea that consciousness is indelible?

Answer by Gershon Velvel

I take it, Lowell, that by ‘indelible’ you mean something like ‘indestructible’. Consciousness, once it exists (and we are not asking how it comes into existence) cannot be wiped out. Although its nature could change in all sorts of ways, some of which we might not be able to imagine.

The evidence is not empirical evidence. It comes from logic. This is a page for philosophy not theology or apologetics. Maybe there’s a God. Or maybe the Devil rules the universe. Or nothing, it makes no difference so far as the logic of the argument is concerned.

The argument proceeds via two ‘lemmas’, or subsidiary proofs.

Lemma 1. Whatever is contingently possible is necessary in infinite time.

It is possible that it will rain tomorrow, and also possible that it will not rain tomorrow. Is it also possible that it will never rain again, anywhere on Earth or indeed anywhere else in the Universe? Why not? Maybe the day after tomorrow the Universe will be wiped out of existence and therefore there will be no more rain, anywhere, ever.

But now we have to deal with the tricky question of infinity. Never say ‘never’. ‘Never’ refers to infinite future time, and I’m not sure that either you or I really grasp what that means. The Universe could have gone out of existence for a very, very long time (pick a number, any number) but it is always possible that another Universe will come into existence, and that there will be rain, on some planet in some solar system in some galaxy in that Universe.

You might think that this falls short of showing that rain must occur at some time in the far future. When in geometry one says that, ‘parallel lines meet at infinity’ that doesn’t mean that the lines actually meet. It’s more like a convention. But our claim does not rely on an analogy with geometry.

Nor is it like mathematics where (as Wittgenstein once remarked) as yet there is no proof or disproof that a sequence of four 7s occurs in the expansion of Pi. A disproof could yet appear, in which case we would know, as well as we know the truth of any arithmetical statement, that it does not. But this is something we might never be able to ascertain, either way. Given our present state of ignorance, no-one can say now that four 7s ‘must’ appear somewhere in the expansion of Pi.

Rain, by contrast, is a contingent phenomenon. It is not, like the expansion of Pi, the product of some necessary rule. In the absence of any mathematical or logical rule that would restrict what is or is not ‘really possible’, all contingent phenomena must be realized in infinite future time. If, in infinite future time, it can rain again then it must rain again.

Lemma 2. The identity of consciousness is not dependent, in whole or in part, on spatio-temporal continuity.

This is a claim that would be strongly contested by any philosopher of a materialist persuasion. The objection isn’t just the implication that consciousness is not constituted from matter. That would be to beg the question. Rather, the problem concerns the definition of identity, or what it is for some entity, identified at time t1 to be ‘one and the same’ as an entity identified at a later time t2.

Let’s say that while visiting your house I carelessly knock over a precious vase, bequeathed to you by your grandmother. ‘I know a shop where I can find exactly the same vase,’ I say. ‘It won’t be the same vase because it won’t be the one my grandmother bought back from her trip to Brighton in 1955.’ There’s no answer to that, except for me to get out the Araldite and laboriously stick the pieces back together.

After the universe has come to an end and another universe has come into existence, there is nothing, in logic, that could count as the vase in question ‘coming back’. Maybe there will be another Brighton just like Brighton on the South coast of England, etc. but the vase that comes from there won’t be one and the same vase. That possibility is ruled out by the definition of identity in terms of spatio-temporal continuity.

But now let’s suppose that the Bomb drops. The last thing you remember as you looked out of the window of your apartment, is a blinding white flash and the agonizing sensation of your flesh being burned off your bones. And now, here you are, awake and intact, in a place you’ve never seen before. You are alive. Maybe this is Heaven, or Hell, or just some planet in some Universe far, far in the future.

Materialists will come back at this saying there is no way on this picture to distinguish between ‘true’ and ‘false’ memories. Which is true. But it is also true that nothing can override your subjective certainty that you have, indeed, survived a direct hit by an atomic bomb. You know that you are you, just as surely as you know this every time you wake up in the morning. Run through the thought experiment a few times, if you are not sure, until you are convinced.

To prove: consciousness is indelible.

From Lemma 2, we know that consciousness — that is to say, you — can always come back at some time in the future. From Lemma 1, we know that if you can come back you will come back. Therefore, you can never we wiped out permanently. Your consciousness is indelible. Q.E.D.

Socrates, Plato and Aristotle on wealth in the polis and the soul

Bilyaminu asked:

What have Socrates, Plato and Aristotle contributed to the idea of a nation’s wealth creation?

Answer by Georgios Tsagdis

Socrates and Plato query wealth in its relation to personal and civic virtue. The former will be canonised as the forefather of Stoicism, a way of living thought in austere abnegation of comfort and luxury, while the latter will expend considerable effort critiquing in many of his dialogues theoretically, but also dramaturgically the function and effects of wealth in the soul as well as in the polis. (It is important to note that the ‘nation’, in all its complexity as a unifying ground among the Greeks, does not form the basis of political organisation and remains uncoupled from territorial sovereignty — therefore one cannot strictu sensu speak of ‘national wealth’ in ancient Greece.)

The principal text is of course the Republic, but if you wish to stay with the notion of the nation and follow the potentially devastating effects of wealth on it, the myth of the Atlantis in the dialogues Timaeus and Critias is most relevant.

Aristotle’s understanding of the significance of wealth for the individual and the polis draws on and nuances further that of Plato. Here the Nichomachean Ethics and the Politics are key. Importantly, wealth cannot be understood in Aristotle outside of the framework of mean (mesotes), which far from being a mere average, designates the perfection and flourishing of virtue.

Doubts about Gödel’s theorem

Wayne asked:

Typically all expositions of the 1st Gödel incompleteness theorem start with an instance of the diagonal lemma with the Gödel sentence on the left side of a biconditional and an abbreviated version of a horribly complex sentence one the right side.

The expositions continue with an argument by constructive dilemma. If the right hand side, which written out in basic syntax not abbreviated, is inconsistent with the Peano Axioms, you can never get the Gödel sentence from the instance of the diagonal lemma.

I am incapable of even imagining the full unabbreviated version of the right side of the instance of the diagonal lemma. So why should I assume it’s not inconsistent with PA? So why should I accept standard expositions of the 1st Gödel incompleteness theorem?

Answer by Geoffrey Klempner

First, I will state that I am not a mathematician and I could not reproduce an accurate version of the proof of Gödel’s First Incompleteness Theorem even if my life depended on it. However, your question isn’t really about that specific proof.

Decades ago for my BA Symbolic Logic paper, I studied an exposition of Gödel’s theorem by Nagel and Newman. I note that a newer version has appeared, edited by Douglas Hofstadter. That endorsement alone would be sufficient to convince me that the exposition is a good one.

I recall the basic point Nagel and Newman made, that the critical formula is not like the semantic paradoxes, such as ‘This sentence is false.’ What Gödel discovered was a way of defining statements about arithmetical propositions in terms of actual arithmetic functions. Using this method he was able to produce a formula that was true but unprovable within the system, as defined by the set of axioms for arithmetic devised by the mathematician Peano.

The actual proof is laborious, because of the necessity to ensure that every single mathematical formula or expression has a unique ‘Gödel number’. Plenty of room for error, don’t you think?

My answer to your question depends on whether you are a philosophy student or a maths student. If the latter, then there really is no excuse for you not to go back to Gödel’s original paper and work through it, line by line. You will burn a lot of midnight oil and learn quite a bit of maths too.

Diagonal proofs have a tendency to induce incredulity on a first encounter. So what if just one, one single formula falls outside the bag of theorems we can prove from Peano’s axioms? You get a similar reaction with Cantor’s proof of the existence of transfinite cardinals. The answer is, if we can devise one recalcitrant formula, we can make any number of them, because we now have a method for doing so.

Wittgenstein in his Remarks of the Foundations of Mathematics (1956) pondered the problems that arise with the unsurveyability of mathematical proofs. How can we be sure that we haven’t made a mistake somewhere? So what if some group of mathematicians agree that no errors are to be found? Couldn’t they all be wrong? There’s really no answer to that. Cantor faced a wall of hostile incredulity when he first published his theorem. Even professors of mathematics can turn out to be wrong.

I remember reading in the 80s the sensational announcement that with the aid of a computer a proof had been discovered of the Four Colour Theorem. The ‘proof’ runs to thousands of pages, and states that any possible map only requires four colours to define every boundary within the map. As Wikipedia states ‘It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. Since then the proof has gained wide acceptance, although some doubters remain.’

So, the problem you have raised is a real one. But on purely empirical grounds I doubt very much whether Gödel’s Theorem will turn out to have been unsound.

Socrates, Plato and Aristotle on the ‘wealth of nations’

Bilyaminu asked:

What have Socrates, Plato and Aristotle contributed to the idea of a nation’s wealth creation?

Answer by Graham Hackett

I am not sure that this question would have made much sense to the three philosophers mentioned, in the way in which you have expressed it. Adam Smith and any of the 18th century physiocrats would have understood exactly what was meant by the idea of a “nation” and “national wealth”. At the time Adam Smith was writing, the reality of, and conception of the national state was well understood, and therefore, the associated matter of national wealth would be thought of as a key policy pursuit for those in government. At the time Plato and Aristotle were writing, the city state was thought of as the natural unit of government, and the main concern of politicians was to compete with other states similar to theirs. Of course, resources were important if a city state was to be healthy, but it was a secondary requirement to stability.

No Athenian citizen participating in the voting and running of their state would regard economic activity as a fitting concern for a good citizen. Freedom from such activity would be regarded as necessary for a proper citizen. Trade was a concern for the lower classes, and foreign trade was left to metics (foreigners) who were without full citizen rights. Economics and national wealth were not thought of as central concerns for Athenian citizens.

Of course, you can always delve into a good history of economic thought. Eric Roll’s History of Economic Thought is a good (though dated) read. It was originally subtitled “From Moses to Marx”. You will always find, in such texts, an account of how Plato made a penetrating analysis of division of labour, and Aristotle provided a fairly clear — for its time — analysis of the nature and importance of a currency as a means of exchange. However, Plato’s analysis of the division of labour was undertaken for completely different reasons to those demonstrated by Adam Smith. For the latter, division of labour was a central development in economic life which fully explained how growth and national wealth could be pursued. For Plato, division of labour, though undoubtedly an efficient way to get things done, was primarily of value because it allowed people to pursue those activities for which they were naturally fitted, and which enabled them to be happy, balanced individuals. Division of labour was an excellent metaphor for how the soul was divided, and for how city activities could be best pursued. For Plato, there was a strong ethical content to division of labour.

However, although Plato Aristotle and Socrates did not regard economic issues as of central importance, they certainly did have important ideas about the contribution that a happy and balanced individual could make to a strong and balanced polity, and therefore create a solid foundation for a healthy economy. For Plato, a happy and balanced person would first have to reconcile the conflicts in their own souls. A polity would need to reconcile the conflicts between the three parts of the state. This would create balance and harmony, without which, Plato would regard economic activity as impossible. Aristotle was more pragmatic about political organisation, but his key insight was that any government contained elements of democratic, aristocratic and monarchic practices, where the problem was how to keep these elements in balance.

I hope you do not find my views on the contribution of these philosophers to economics disappointing. However, if you consider their views on harmony and balance irrelevant to economics, then just consider how often phrases like “economic confidence” are used in modern accounts of business activities. Think about those endless discussions about how preparation for Brexit in Britain has caused problems for this so-called “business confidence”.

Finally, when Keynes wrote his own penetrating analysis of economic wealth, and how it was created, although he gave central importance to such factors as the multiplying effect of investment, he fell back on the necessity of providing stability and business confidence.

Perhaps Socrates Plato and Aristotle had something after all.

Thought experiments

Andrew asked:

Are thought experiments a legitimate philosophical method?

Answer by Geoffrey Klempner

I wonder, Andrew, whether you are responding to the previous question from Val, and the answer given by Hubertus Fremerey?

The question was about the statement, “If X might exist but we have no reason to suppose that it actually does exist, then as metaphysicians we should not concern ourselves with X.” I can’t fault Fremerey’s answer but there is an issue which he did not touch, concerning hypothetical questions about contingent non-existents, popularly known as ‘thought experiments’ — or in Daniel Dennett’s words ‘intuition pumps’.

Here’s a thought experiment that has troubled me over the years. Suppose that there existed (as there does not, so far as you or I are aware) a fission ray gun. You point the gun at someone and when you press the trigger, the fission ray causes them to divide like an amoeba, resulting in two identical versions of the person you just shot.

Let’s make this personal. We’ll call the two resulting persons Andy1 and Andy2. Andy1 remembers posting your question on ‘Ask a Philosopher’ and so does Andy2. In every aspect, the mental and physical states of Andy1 and Andy2 are identical, save for the fact that they occupy different positions in physical space, and will from this point onward diverge in their mental and physical properties.

This is a question for you: if you saw the fission ray gun demonstrated and it apparently worked, how would you expect things to turn out when the gun was pointed at you?

‘If all the world was apple pie/ And all the sea was ink/ And all the trees were bread and cheese/ What should we have to drink?’ Why pose questions about things that could not possibly happen? Unless, of course, the simulation hypothesis is true, in which case there could be all manners of violations of the laws of nature, such as vampires, werewolves etc.

So, back to the question. I’ll put myself in your place. Someone would find himself on the left and someone would find himself on the right. We’re ruling out telepathy, so they can’t both be I, can they? Logic says there are three alternatives: both are ‘I’, neither is ‘I’, one is ‘I’ and the other is ‘not-I’. If you want to be exhaustive you can include a fourth alternative, ‘The question makes no sense.’ It’s tempting to go with that last possibility, but I don’t think we have the right to let ourselves off the hook so easily.

You have to do work, ‘real philosophical work’ if I can put it like that, to justify your choice out of the three remaining options. My view would be that the very idea that the ‘I’ is something that persists through time is an illusion. As I have stated before, the existence of I in the world is a deep mystery: ‘I might have not existed but someone exactly like me might have existed in my place.’ But I am talking about I-now, not an I that persists through time.

To ‘prove’ the point here are two more thought experiments. The universe was created five seconds ago, with most of ‘my’ answer already written. Can I still claim authorship? Or there’s a ring on the doorbell and the postman hands me a video showing how the ‘original’ GK was kidnapped during the night and how a perfect physical copy got out of my bed this morning and enjoyed my favourite breakfast meal of peanut butter on toast with coffee and orange juice.

The notion that ‘I-now’ and ‘the world’ are two separate existences is a theory. I have been prompted to make that theory by considering a thought experiment. My theory could be wrong, maybe the thought I have just expressed about my contingent non-existence, everything else remaining the same, makes no sense. Dennett is right to call this kind of thing a mere ‘intuition’. But, ultimately, our notion or sense of what ‘makes sense’ not has to be based on how things seem to us, on our intuitions, once all the logical moves have been gone through. There’s simply nothing else to go on.

Metaphysics and contingent existents

Val asked:

“If X might exist but we have no reason to suppose that it actually does exist, then as metaphysicians we should not concern ourselves with X.” — Is this true? Why or why not?

Answer by Hubertus Fremerey

As in so many similar cases, the problem here is not “is it true?” but “what does it mean?”

Insert for X not only the worn out item “God”, but as well “liberty”, “justice”, “human dignity”, “progress” etc.. In all those cases it is not even clear what we say when we say “X does exist”.

This is a general problem. of semantics and ontology. We are using “concepts” or “labels” as if they were “things”, but they aren’t. This is the core problem of nominalism that was already known to Aristotle when he asked whether Platos “ideas” were “real” or just “concepts”.

Even when applied to “objects” it is not clear what we mean. While “a human” seems very much more “real” than, say, “justice”, we would be confused by the statement “a human is a bunch of molecules”. While true in a sense, almost a banality, this is not the answer we had in mind when we put the question.

Instead of seing a human as “a bunch of molecules” we attach to it a whole “aura” of other concomitant concepts as are “the character”, “the biography”, “the culture”, “the opinions”, “the hopes and fears” etc.etc.. They all together “constitute” what a certain human is — which is even much more than what the biologist or the medic sees.

So once more: What does it even mean to say that “X might exist”?

Among the few cases where the question look simple and straight forward is in math: “Does a solution of this equation exist?” In the case of Fermat’s Problem the answer to m3 + n3 = X3 would be “X does not exist”. But X here is a logical variable, while reality does not consist of logical variables in this sense.

In common and philosophical language, even “a human” is a logical variable, but from a different sort of logics, a different sort of language. This point should not be missed. It is a common cause of meaningless debates.