On knowledge, theory and the unknowable

Josh asked:

What, beyond knowledge itself, may be known or validated, under any hypothetical circumstances?

An inanimate object existing outside of all conception, objectivity claims, can and does exist. Yet through what means? Supposing that there isn’t an omnipresent, omniscient God, such an object is considered existent; if nobody is looking upon a certain dining table, we do not speak with each other openly that it does not exist. Of course it will be there when we turn around, we say, as experience has taught us, and furthermore, of course that must mean that it is there now. You should be able to think of many hypothetical situations in which this assumption is flawed, but rather than asking ‘Can it not be there now?’, perhaps we should ask ‘Can it be there now?’. For what authority determines the existence of an inanimate object outside of all conception?

I have not resolved this question, and as such I am of the opinion that we are led astray by the natural equation of conception with physical actuality. What is the difference between assuming there is a car behind you, because you just parked it and are walking away from it, and imagining a series of events, such as those in Star Wars, and actually believing in them? Or even believing in other minds, for that matter; an assumption due to the emotion of empathy, i.e. the process of analogy of apparent experience. We are also capable of feeling empathy for objects and simulations; how do we jump from observation of weeping matter to the assumption that there is a mind that embodies that matter and is currently under some torment? Even in practice, we may only understand others through analogy, which often leads to misunderstanding (which isn’t always obvious either!). Hence why we empathise much less with more alien life forms, such as insects and plants.

And so, as I have asked many, many times before: How do we justify the presumption of true knowledge of the literally unknowable?

Answer by Jürgen Lawrenz

This is really difficult, because the first answer that has to be given is this: that as human beings we are ensouled creatures and we have a mind. And both of these together engender prejudices and presumptions based on our need to have enough knowledge to survive as bodies.

But if we are to ensure that we do possess this knowledge, the first criterion is that individual knowledge is just a tiny stone in a big kaleidoscope. The central concept here is collective knowledge. What we know is the result of pooling knowledge, teaching it, checking it, verifying. So, most of our knowledge is consensual. You know that ‘X’ exists, because everybody does. What I don’t know, someone else will know. Therefore in principle, what one person knows, everybody can know, because we all have the same equipment for gathering and evaluating and learning knowledge.

But stringently regarded this applies only to factual knowledge. We can turn this knowledge into science, technology, laws and socially useful practices. On the strength of our capacity for extrapolating the order which is implied in this knowledge, there are features beyond our immediate capacity to detect them, which we are entitled to hold as either possible or true. This is the basis of our exploratory drive. We discover and invent things, because we can perform these projections of existence from known states of affairs upon unknown states of affairs.

This reflects to some extent the division Kant made between phenomena and noumena. As rational creatures we are enabled to gather all phenomena, including those which we know nothing about (but may at some time discover), and put them in one basket as ‘existents’. E.g. until 1877 we knew nothing about the planet Neptune, but certain planetary phenomena pointed to the existence of an unknown planet whose energy influenced the wobbles in the orbits of known planets and it was duly discovered. The problem now arise that this can give birth to an attitude that we need not stop anywhere with this presumption. Being able to convert some data into presumed phenomena (e.g. the energy waves from Neptune could for some time only be rendered as mathematical patterns), we now assume that we can make mathematical models and ‘discover’ things that do not convey actual energy patterns – such as the ‘big bang’. Here we run into a discrepancy between observation and imagination. We can do no more than presume that the phenomenal aspects of the universe continue infinitely, and we certainly cannot prove it. All we can prove is that, by a rational performance, such existents may be possible. They are, to this extent, noumena – ‘creatures of the mind’.

When we teach this, especially to people without the relevant training and experience, they have no choice other than to put their trust in the speculations of people who do this work. That presumption is, that the world is altogether as we can experience it, in other words, phenomenal and therefore material. But you and I know very well that some things which we know indubitably to exist, cannot be measured. You mentioned ’empathy’. There is no device by which we can measure it; and in fact no way by which we turn it into a mathematical model. These issues are apt to plunge us into big problems.

They suggest to us, that a belief (or faith) in non-physical existents is an ‘irrational’ attitude. On the one hand, we therefore continue with our effort to explain them indirectly, e.g. ‘the mind’ is nowadays often explained away as a sort of chemical interaction occurring in the brain. If only we had enough knowledge of the work of neurons, we could make a physical model of the mind. This may be a delusion; at least it is misplaced confidence.

From here we can go on to ask a really fundamental question: if there is no intelligence in the universe at all, but the universe exists as it does, who is there to vouchsafe its existence? Anyone who points at the discernible history of the universe is making the same point, though unawares: that consciousness lights up the universe and raises it into existence. So existence is not a word that has an objective meaning. It postulates that ‘I exist’ and ‘this fork exists’ and then, by peering through a telescope, I can say ‘Mars exists’. It is a logical conclusion from this that, if I (deputising for all living creatures in the world) cannot say ‘I exist’ — because there is no life — then existence is a nullity.

This is where God comes in; but I refrain from enlarging on it. We are not debating faith here, but knowledge.

In sum: knowledge is not an absolute. Even though there is a science/philosophy called epistemology, this is little more than pumping up the human intellect on the model of God. Nearly all absolute demands on us are made by people who (pretend to) forget that we are mere creatures. If Kant is right — and I think he is — then the sum total of our knowledge is what phenomena deliver to us. By the same token it is not irrational to believe there is more to the world than empty space irregularly interrupted by a few million galaxies and their dirt. Life itself has never been satisfactorily explained. On this and many other (quite important) issues, our knowledge would not bring a thimble to overflowing. It’s worth bearing this in mind. This is one tiny planet in an immensely vast cosmos. True knowledge is a rare and precious acquisition. It is a human foible to try and stretch it well beyond what can be reasonably accepted. Instead we should learn to value what we can know, and not dabble as much as have done, and still do, in uncertain domains for answers.

 

Struggling with Gödel’s incompleteness theorem

Phillip asked:

Is it an implication of Godel’s Incompleteness theorems that all statements/ claims are equally valid/true because all statements/claims are based on unprovable assumptions?

Answer by Craig Skinner

Ah, Godel – the man without whom mathematics would be complete!

No, there is no such implication as the one in your question.

His theorems are technical proofs about formal axiomatic systems, and have implications only for such systems – for maths & logic, for classical (algorithmic) computing, and for cognitive science insofar as cognition includes formal deduction.

Plane geometry was axiomatized by Euclid, non-Euclidean geometries (using variant parallel lines axioms) followed in the 18th/19th century, and arithmetic was axiomatized in the 19th century.

It was rather assumed that all true theorems and no false ones could ultimately be derived from the axioms, so that mathematics was complete and consistent. Hilbert and followers struggled to prove this. But hopes were permanently dashed by Godel, Turing and Church who all proved in their different ways that the goal is impossible.

Godel proved that any axiomatic system contains some true statements not provable in the system (incompleteness), and that no axiomatic system can ever be proved to be consistent. His genius was to use the notation of a system (arithmetic) not just to derive theorems within the system, but to construct a theorem ABOUT the system, which theorem was obviously true but couldn’t be proved in the system.

His theorems are hard going if you have Uni-level maths, near impossible otherwise. A standard ordinary-language illustration is as follows:

Consider the statement: This sentence is unprovable.

If it is true, what it says is correct, so it IS unprovable, and we have a true statement which cant be proved (system is incomplete).

If it is false, what it says is incorrect, so it ISN’T unprovable, it’s provable, and we have a false statement provable within the system (system is inconsistent).
It follows that in any consistent axiomatic system there exist true but unprovable statements.

As regards maths, we happily work with incompleteness, and although consistency cant be proved, we reasonably assume it since no inconsistency has ever shown up.

Godel’s arithmeticized statement, and plain-language equivalents, are self-referential. They are not just statements in a language, but about it. And this can seem paradoxical.

A simple example is that these (contradictory) sentences both come out true:

‘This sentence contanes exactly two erors’
‘This sentence contanes exactly three erors’

The first sentence has two spelling mistakes, so two errors.
The second sentence has the same two errors, plus a mistaken claim about there being three errors, which constitutes the third error.

To deal with this, rules have been drawn up governing first- and second-level expressions (languages and metalanguages) which I wont go into.

Human consciousness is self-referential – I talk about ‘my self’, ‘knowing my own mind’, and right now am aware of writing this sentence, and am aware that I am so aware, and of that awareness, and so on. So Godel is sometimes cited in explanations as to how life and consciousness can arise from dumb matter, notably Hofstadter’s brilliant book ‘Godel. Escher, Bach: an Eternal Golden Braid’ which makes extensive use of self-referential theorems, art and music

A classical computer (algorithmic software analogous to a formal axiomatic system) cant grasp the truth of a Godel-type sentence, it cant step outside the system. Humans can. Some people (notably Penrose) think this is an essential difference between humans and any possible computer. This view may provide some spiritual comfort for us, but I see no good reason to hold it, and advances in computing look set to produce systems that wonder whether humans can grasp the truth of Godel sentences.

Finally, many new big ideas in science or maths get misapplied. A Newtonian ‘science’ of human affection was attempted with people being ‘attracted’ to each other, ‘gravitating’ to the more attractive others, affection diminishing inversely as the square of the distance between lovers, and other nonsense. Darwin was swiftly misapplied to justify ruthless laissez-faire capitalism (‘Social Darwinism’). Then Einstein (‘everything’s relative’), Heisenberg (‘nothing’s certain’), quantum mechanics (‘there is no mind-independent reality’ or ‘expand your mind by resonance with quantum field vibrations for only 69.99’), Godel, catastrophe theory, chaos theory and more.

 

Answer by Helier Robinson

No. First of all, not all antecedents of arguments are unprovable assumptions. Descartes’s cogito is an example. Secondly, Godel’s theorems apply to formal systems such as Whitehead and Russell’s Principia, and not all philosophic arguments are such. More basically, Godel’s incompletness theorem says that a formal system large enough to include arithmetic necessarily cannot prove itself to be complete; and this does not mean that all statements are equally valid.

 

Answer by Shaun Williamson

No it isn’t and that is all can say because I don’t know where you got this idea from. Godel’s proof applies to our system of mathematics. It doesn’t apply to our system of logic. You should also keep in mind that we have proofs in mathematics and in logic. The idea of proof does not apply to everything.

Suppose you look out of the window and say ‘It is raining’. Someone else says ‘Prove it’. That can only be interpreted as a joke because we don’t have a system of proofs for remarks about the weather nor do we know what such a proof would look like.

 

Comparing the Buddha to Socrates, Plato and Descartes

ID asked:

Was Siddhartha Gautama (The Buddha) more like Socrates/ Plato, or more like Rene Descartes, or neither one of these regarding the metaphysics (the reality) and epistemology (how we come to know) of THE TRUTH?

Answer by Peter Jones

Of the three philosophers you mention it seems to me that Socrates would be the most similar to the Buddha in both his approach and his worldview. Socrates’ views, as expressed by him or on his behalf, those that are available to us, would not obviously contradict the Buddha’s as recorded in the sutras, and neither would his practice-based approach to philosophy as the study of oneself. Perhaps Descartes would be most unlike the Buddha, consistent with his central role in European philosophy, for no Buddhist would agree that ‘cogito ergo sum’ would make a sound axiom, nor even a true one without some careful provisos and a decidedly non-Cartesian definition of terms. Plato I find confusing on many topics, but he and Descartes are two of the most significant philosophers in the Western tradition while Socrates seems rather too ‘mystical’ to be fully included, and this strongly suggests that the question is not too difficult to answer. Socrates seems to represent a much older and very different tradition of thought and practice, that from which the Buddha sprang.

As for metaphysics, the Buddha has very little to say about it, although here and there the odd remark can be found. Nevertheless, the sutras clearly imply a metaphysical theory even if they do not express it directly, and the worldview implied is later formalised as a metaphysical theory by Nagarjuna as the doctrine of Two Truths or Worlds, and so perhaps in metaphysics there is a sense in which Descartes have something significant in common with Nagarjuna, even if not the Buddha, in that both sought to present a systematic metaphysical argument for their worldview.

It may be in relation to epistemology that their differences are most marked. The crucial question is: How do we know things? For Russell this is the most important question in philosophy. It is central in Buddhism, and it must be answered if we are ever to have secure knowledge. How did Descartes know ‘I think’, and thus think that he must certainly exist, and know this so well that he could confidently propose it as a secure axiom for a metaphysical theory? Can we really know something when we do not know how we know it? On this question the Buddha’s view seems profoundly dissimilar to that of Plato or Descartes, neither of whom offered an explanation for knowledge, while there may be no reason to suppose that his view was not quite similar to that of Socrates.

It seems clear at least that Socrates would have approved of the Oracle’s advice and that of the Buddha to ‘know thyself’ for anyone in search of ‘THE TRUTH’, as the question puts it, and would have concurred on the question of whether such knowledge is possible. Whereas Plato and Descartes appear to have preferred a different route, one by which our ability to know things remains to this day an enduring intellectual mystery, a problem mot just unsolved but apparently unsolvable. On the little evidence we have available to us it is possible to speculate that Socrates actually was a ‘buddha’, or it is difficult to dismiss this speculation, but this would not be a plausible idea for Plato or Descartes.

Utilitarianism versus deontology

Jerica asked:

Discuss the chief advantages and disadvantages of utilitarianism and deontological theory. Think specifically about how the theories would work in a concrete situation. Provide a concrete example to support your response.

Answer by Tony Fahey

Hi Jerica, notwithstanding the fact that this seems suspiciously like an assignment question, I believe the two theories do merit some discussion. However, while I will give some detail on the shortcomings of both theories, as we are discussing ethical theories, drawing on these examples, I suggest that you seek specific concrete examples yourself.

Utilitarianism is a moral theory that argues that an action is right if and only if it conforms to the principle of utility. Founded during the Victorian era, its founder, Jeremy Bentham, came to believe that there was a need for society to rely on reason rather than metaphysics. The central tenet of utilitarianism is what is called the ‘Greatest Happiness Principle’. Because the human beings are rational self-interested creatures, says Bentham, they seek to maximize their pleasure and minimize their pain. Thus, a morally acceptable action is one which results in the greatest possible happiness within a given set of circumstances.

Set against utilitarianism is deontology. Deontologists are concerned with the concept of duty. That is, they are concerned with fulfilling (what they believe is) their moral duty – whether or not it makes people happy. In short, deontologists hold that right actions are defined by duty. Once we know what it is that we are duty bound to do morally, then we can carry out this ‘natural’ right action regardless of the consequences. What matters, they argue, is that we do what is right what is right, and what is right is that which conforms to moral law.

One of the leading exponents of this theory is Immanuel Kant. For Kant, right actions are those which are done purely and simply from a sense of duty and not by following impulses, inclinations, or adherence to the ‘Greatest Happiness Principle’. Human beings, says Kant, are, by nature, rational beings and as such need have a rational basis to their lives: they need to know what make right actions right. Ethics, he maintains, is concerned with identifying moral imperatives, and providing rational explanations as to why we should obey them.

Central to Kant’s duty ethics is the view that right actions are those actions that are not instigated by impulses, inclinations or desires, but by practical reason. Right action is right only if it is undertaken for the sake of fulfilling one’s duty, and fulfilling one’s duty means acting in accordance with certain moral laws or ‘imperatives’. To help us identify those laws which are morally binding Kant has provided us with the ultimate calculus: the ‘categorical imperative’ which states ‘Act only in accordance with the maxim through which you can at the same time will that it become a universal law’. To the categorical imperative, Kant offers a codicil which relates specifically to human will, ‘So act that you use humanity, whether in your own person or in the person of another, always at the same time as an end, never merely as a means’.

Whilst deontology, or ‘duty ethics,’ can be said to hold considerable merit, in that it advocates that human beings should be treated as ends in themselves rather than means to ends, I would argue that, as an ethical theory, it fails in that it looks on people, not as sentient beings, but as duty automatons. Moreover, any ethical principle, such as the Greatest Happiness Principle, that advocates that the happiness of the majority takes precedence over the minority cannot be counted as a reliable ethical model.

Reading original philosophical texts

Phil asked:

How can I improve my ability to read and understand original philosophical texts?

Answer by Craig Skinner

Some thoughts after recent distance learning for a degree in philosophy.

Versions

Strictly, if you wish to read original texts and don’t want to miss out some of the greats, you have to read ancient Greek, Latin, French and German. And that’s only Western philosophy. Probably, like me, you will read English translations. What’s more they’ll be modern translations. This has the effect of making, say, Descartes, seem more modern than Locke or Hume (we read these latter in quaint, original, 17th and 18th Century English requiring translator’s footnotes alerting us to changed word meanings). A recent book about Locke’s theory of personal identity even includes the author’s modern-English version alongside Locke’s original. But, no problems from 19th century onward as most analytic philosophy is from UK, USA and latterly Australasia.

Background

Authors typically hold many of the common views of their day, or have strong opinions about them, but don’t spell out what these are (educated readers at the time would know). Religious or scientific views for instance. Thus, in arguing about personal identity, Locke aims to show that the person rewarded/punished at the Last Judgment can be the same person that did the deeds, and thereby be justly treated, even if he has a different body (material substance) and a different soul (nonmaterial, thinking substance) from when he did the deeds. The soul argument is unfamiliar these days, and we may dismiss Locke as confused here, and conclude (wrongly) that he is simply arguing for the memory-connectedness idea of persistent personal identity.

As regards science, early modern greats were influenced by Newton. Kant goes so far as to say that Newton’s views on space and time are necessarily true and constitute one of the categories in which we must perceive the world. Of course the rug was pulled from under him when it turned out that Newton’s theory, far from being necessarily true, wasn’t even true (and neither was space Euclidean as Kant also thought necessarily true). Hume hopes to produce a science of man modelled on Newton’s science of matter and motion, and compares his own scepticism to Newton’s approach to the true nature of gravity (‘I feign no hypothesis’). Leibniz thinks the idea of gravity, acting on another body not by contact but mysteriously acting across vast distances of empty space, is a return to superstition. Berkeley is horrified by the soulless, purposeless, mechanical world picture and tries to show that matter does not exist, indeed the the idea is incoherent.

Reading

It’s not like reading a car magazine where you get the gist in 5 minutes and all you need to know in 30. It’s hard work, takes hours of reading and rereading to get full value.

Have a go at the text yourself before reading what others think.

First, read the text through only to answer two questions – what is the position being advocated or defended ? Why does the author think it important ?. Often they dont tell you clearly, and you must work it out! Write down the answers.

Next, reread to find out what argument(s) the author relies on. List these (not the details, just the number of arguments and a word or two to characterize each).

Next, close reading of text to elicit the steps in the argument(s) and the conclusions. List these as series of steps, best as premises and conclusions if you can.

Now look at the arguments. Are they valid (conclusions follow from premises). Are they sound (valid plus true premises). Do they support the position being advocated (check, you wrote this down earlier), or perhaps only some lesser conclusion, or maybe just fail.

Now reread, asking: does the author consider (and refute) arguments for a position contrary to his? Does he consider (and rebut) objections to his own arguments.

Form your own provisional view.

Now read what others think (see aids below). Did you miss things? The answer will be yes. Don’t worry. Scholars sometimes spend a career wrestling with a famous text, and after years of study, may change their mind about what it all means or what the author intended. A recent book on Locke’s theory of personal identity opens with the author saying he has been misrepresenting Locke to his his students for 15 years. Also scholars disagree about what an author means or thinks. Two recent books by noted academic philosophers give different accounts of what Hume’s views on causation really were, both accounts based on the same Hume texts.

Finally, form your own view, be prepared to defend it, but stay open to new ideas, arguments or evidence.

Aids

Best is dialogue with somebody further along the philosophical road than yourself. Easy if you are a student at University or on a Pathways module. Not so easy for the distance student or the informal learner. I recall discussions up the pub with my two (engineer) mates who argued against my contention that numbers don’t exist, or gamely responded when I asked what made it the case (if it was) that we three old boys presently drinking our pints were the same old boys that had entered the pub 20 minutes previously. In addition I signed up for Pathways tuition and found it excellent value.

Every great text has spawned a shoal of Introductions, Guides, Companions, Essentials Of, etc. and I cant deal with all that here. But you will need a selection of these for serious study.

There are two series of books explicitly designed to foster reading/ understanding texts. First, the short ‘How to Read X’ books published by Granta, described (on the blurb) as ‘a personal masterclass in reading’. They deal mostly with authors not topics, and include a few philosophers, none living, eg ‘How to Read Plato’.’ Secondly, the longer ‘Reading X’ by Blackwell Wiley, described as ‘a series that aims… to teach you a technique for reading and analysing philosophical texts’. They give general introductions to the topic, excerpts from classic texts, both ancient and modern, get you to engage with them at key points and write down your thoughts and answers to questions, and conclude with ‘interactive commentary’. I used two of the How to Read X’ series (Plato, Hume) and two of the ‘Reading X’ series (Epistemology, Ethics). They are good books. But, looking back on it, I doubt that they added much to improving my ability to read/understand texts over and above what I’ve already suggested to you.

Online Stanford Encyclopaedia of Philosophy has good, critical, up-to-date, referenced articles on most everything. I used it a lot.

Finally, an example:

Getting started with Descartes

Text: ‘Meditations on First Philosophy’ by Descartes (English translation by Haldane and Ross, 1934)

Position advocated: a new grounding is needed for science. He doesn’t say why, but must think science, unlike say chess, needs a philosophical foundation, and that the time-honoured Aristotelian basis is unsound.

This grounding will be knowledge reached by reason alone (not observation) from what remains certain after using the Method of Doubt (to accept as true only what is presented so clearly and distinctly to the mind as to be certain)

Argument: he can doubt the existence of the external world, including his own body, but in order to doubt he must exist, so that he accepts as true ‘I think therefore I am’ (‘cogito ergo sum’, ‘je pense donc je suis’). He then argues his way back via knowledge of the existence of God to knowledge of the existence of the external world and his own body.

Steps in argument:

1. I can’t doubt my existence as a thinking thing, so I know this.

2. I know it solely by clear and distinct perception.

3. So, what I perceive very clearly and distinctly is true.

4. I have a clear and distinct idea of God

5. The idea of God includes necessary existence, so God exists

6. God, being all good, is no deceiver.

7. So I can rely on my God-given reason and senses, properly used.

8. Using them I have clear and distinct ideas of extension, size, shape, situation, movement, duration and particulars of an external world.

9. So, the external world, including my body, exists.

10. I (my soul) and my body (a kind of machine) are distinct substances but intermingled.

We now have framework for detailed appraisal – method of doubt, dreaming/evil demon arguments, res cogitans under 1/2/3, arguments for God’s existence/nature under 4/5/6/7, res extensa under 8/9, dualism under 10.

We can go on to consider sub-arguments (e.g. two for God’s existence: three for ‘real’ distinction of mind and body – here ‘real’ is a scholastic term meaning the distinction is between two substances).

Objections/ Replies: helpfully, Descartes sought objections and published them with his replies as a separate chapter.

Descartes’s text is orderly and systematic rather like a scientific paper or maths theorem (he was a noted scientist and great mathematician). With many other texts, we are not so lucky.

Aristotle’s conception of eudaimonia

Ian asked:

Eudaimonia is the feeling of perfect satisfaction with ones life?

Answer by Caterina Pangallo

I think ‘perfect satisfaction’ is a little over the top.

The word can almost be literally rendered in English as ‘good spirits’. This implies all the good things that make a person be of good spirits. Like prospering in your career, having good friends, eating well etc.

Generally we translate the word as ‘happiness’. For Aristotle this includes achieving a state of being good and generous with others. He thinks that being generous, altruistic and charitable belong also to eudaimonia.

In his Nicomachean Ethics, Aristotle says that eudaimonia means ‘doing and living well and being content’. For Aristotle this implies that eudaimonia involves activity and a striving for excellence. It is human nature to strive for self-development. Therefore the best form of eudaimonia is gained by the proper development of one’s best powers and the most humane attitude. This identifies us as ‘rational animals’. It follows that eudaimonia for a human being is the attainment of excellence (arete) through the use and application of reason.

So all these issues hang together. Further, he claims this excellence cannot be isolated and so it requires social competence as well as high professional standards. From this it follows that eudaimonia, living well, consists primarily in activity. Which is to say, to be fully engaged in the activity of his/her work and in a social network of friendships in order to achieve success.

In Aristotle’s ethical theory, eudaimonia is a virtue. This is because it is a balance between two possible defects. One can be ‘too happy’, too carefree without striving for excellence. Some people on the other hand never stop complaining, even when they are successful.

Actually I believe that Aristotle discovered something really fundamental about human beings.

As a philosopher he asked himself, ‘what do humans really want out of life?’ Answer: ‘Happiness’. To achieve this you need not be the wealthiest person of your tribe. You need to strive, recognise your potential, aim for self-fulfilment and cultivate love and friendship. This is the way to eudaimonia. Just as we say, ‘money can’t buy love,’ so Aristotle would say, ‘You can’t buy eudaimonia’. It’s something you have to do.