I am much more interested in unknowables simply because they are typically a simple insight away. The promise of unknowable unknowables is immense or at least unknowable and can only be found in a sea of data. elusive of course.
My discovery of the third and forth ordered Pythagorians was such and has been unknown for over two thousand years. It may have been known in Antediluvian times and the symbol of the I ching tells us that the Space Time Pendulum was and that certainly demands my higher ordered Pythagoreans
That really took two mathematical insights. this induced a physics insight and a deep understanding of TIME. All the physics was knowable unknowable.
Just as clearly tyhe discovery of the spoor of the Giant Sloth was really a unknown unknowable found in the data pool provided by the known unknowable of the Sasquatch ( 20,000 reports and climbing )
fortunately our thinking is now data dependent.
The ancient Sceptics used doubt as a way of investigating the world. Later thinkers undermined even that possibility
Bowl (c1898-1910) by George E Ohr. Courtesy the Met Museum, New York
Mahdi Ranaee is assistant professor of philosophy at the University of Siegen, Germany. He is the co-editor, with James O’Shea and Luz Christopher Seiberth, of Fraught with Ought: Selected Writings of Wilfrid Sellars (forthcoming, from Oxford University Press) and co-editor, with Luz Christopher Seiberth, of Reading Kant with Sellars: Reconceiving Kantian Themes (forthcoming, from Routledge). He is currently working on two book manuscripts, ‘Skepticism: Cartesian and Kantian’ and ‘Wittgenstein’s Rule-Following Skepticism’.
Edited by Sam Dresser
Ask any philosopher what scepticism is, and you will receive as many different answers as people you’ve asked. Some of them take it to be showing that we cannot have any knowledge – of, say, the external world – and some of them take it to be even more radical in showing that we cannot have any reasonable beliefs. In the interests of getting a handle on the varieties of scepticism, one can locate four different milestones of sceptical thought in the history of Western philosophy. These four milestones start with the least threatening of them, Pyrrhonian skepticism, and continue by Cartesian and Kantian scepticisms to the Wittgensteinian moment in which even our intention to act is put in question.
To our modern minds, scepticism is normally associated with frustration and sceptical conclusions are usually taken to be disturbing because they seem to stand in the way of certainty about the world and our place in it. But famously, or rather infamously, those people in ancient Greece who called themselves Sceptics – meaning ‘investigators’ – were pretty happy about it. They thought of their scepticism as a way of life – as a way of reaching ataraxia or tranquillity. In their view, having beliefs is the ultimate cause of anxiety, and therefore the best way to avoid anxiety, to achieve peace of mind, is to get rid of beliefs altogether. The Sceptics in this sense are often called Pyrrhonists after Pyrrho, the ancient Greek master Sceptic who lived in the 4th and 3rd centuries BCE.
Most of what we know of ancient Sceptics comes from the books written by Sextus Empiricus, who lived in the 2nd or 3rd century CE. We know almost nothing about this mysterious figure except that he practised medicine and belonged to the Empirical School of Medicine – hence his being known as ‘Empiricus’. The best known of his works is a book called Outlines of Pyrrhonism – sometimes also known as Outlines of Scepticism – which is the best and fullest account of Pyrrhonian Scepticism we have. But what is a Pyrrhonian Sceptic?
At the beginning of his book, Sextus differentiates three schools of thought: ‘When people are investigating any subject, the likely result is either a discovery, or a denial of discovery and a confession of inapprehensibility, or else a continuation of the investigation.’ The first group of thinkers, whom he calls the Dogmatists, believe that they have discovered the truth, and that they know things about the world and the human beings who live in it. The two most famous thinkers from this school are Plato and Aristotle, but scholars often maintain that it is the Stoic school of thought that is the major target of Sextus when he talks about Dogmatists. The second group are those who are called the Academics; they are opposed to the first group and believe that, so to speak, we know that we know nothing. The third group, with whom Sextus identifies himself, are the Sceptics. These people, contrary to the Academics, do not deny anything, they just withhold their assent from beliefs: they continue their investigations and maintain that this continued investigation leads them to tranquillity. Scepticism, for them, is a kind of skill, or, as Sextus described it:
an ability to set out oppositions among things which appear and are thought of in any way at all, an ability to which, because of the equipollence in the opposed objects and accounts, we come first to suspension of judgment and afterwards to tranquillity.
They offer different ‘modes’ – sometimes also called ‘arguments’ or ‘schemata’ – by means of which one can achieve such oppositions. The number of these modes varies among Sceptics, and Sextus himself offers four groups, comprising 10, five, two, and eight modes, respectively. One example, the second mode from the list of 10 modes, is that of ‘deriving [the opposition] from the differences among humans.’
Sextus starts by granting to the Dogmatists that humans are composed of two things: body and soul. He then goes on to argue that, in both body and soul, humans differ from each other – they have different bodies and different souls – and from that he infers that we should suspend our judgments about body and soul. He first considers the differences in body:
In our individual peculiarities we differ in such a way that some people digest beef more easily than rock-fish, and get diarrhoea from weak Lesbian wine. There was (so they say) an old woman in Attica who consumed four ounces of hemlock without harm. Lysis actually took half an ounce of opium without distress.
He goes on to offer more examples, but this much is enough to get a sense of what he means. But what about the differences among humans in their soul? By this he means the differences of opinion among humans, and he takes the endless disputes among Dogmatists about the nature of the world as an indication of such difference of souls.
Sextus takes this difference in accepting and rejecting, or liking or disliking, as evidence that we are not affected in a similar way by the same things. He continues:
if the same things affect humans differently depending on the differences among them, then it is likely that suspension of judgment will be introduced in this way too, since we are no doubt able to say how each existing thing appears, with reference to each difference, but are not able to assert what it is in its nature.
Since different things affect us differently, there is no way to know what the existing things are like independent of any human perception. There is no individual or group of people who can be considered as the ultimate judge in this matter. Even when the difference is between a common man and, say, Plato, we cannot prefer Plato over the common man:
When the self-satisfied Dogmatists say that they themselves should be preferred to other humans in judging things, we know that their claim is absurd. For they are themselves a part of the dispute.
Since there is no way to decide between the different perceptions or appearances, the best thing to do is to entirely suspend our judgment. But we might be tempted to say that the appearance of the majority is to be preferred: if the majority finds honey sweet, or finds hemlock poisonous, shouldn’t we just trust them? Sextus answers negatively. He argues that we cannot prefer the majority, because the perception of the majority of Greeks is often different from the perception of the majority of, say, the Persians. We must avoid making any judgments and withhold our assent. We must be sceptics.
The second milestone in the history of scepticism is the Cartesian moment. Cartesian scepticism is an if- or whether-question regarding the actuality of something. What I mean is that this kind of scepticism, for example, asks whether there is an external world, or is it just my illusion that there is such. As James Conant puts it: ‘Cartesian scepticism takes the possibility of experience for granted; its question has to do with actuality … are things really as they seem?’ The paradigm case of such Cartesian scepticism is to be found in René Descartes’s work Meditations on First Philosophy (1641).
Here, he argues in three steps, which are standardly known as three levels of doubt. The first level of doubt is when I believe something on the basis of perceiving it via my senses, but then I realise that ‘occasionally I have found that they have deceived me, and it is unwise to trust completely those who have deceived us even once.’ One example Descartes gives, which goes back at least to Sextus in his Outlines of Pyrrhonism, is that I see a tower from a distance and believe that it is round, while in fact it is square. Since the senses occasionally deceive us in this way, Descartes concludes that we should not trust them. But he is very quick in saying that it is only in non-normal situations that I make such mistakes. When the situation is normal – when I see the tower from a close enough distance – the senses are to be trusted.
The second level is his ‘dream example’. He first offers an example that he considers to be the best candidate of truth, something that is true if anything is to be true: ‘that I am here, sitting by the fire, wearing a winter dressing-gown, holding this piece of paper in my hands.’ But then he writes:
Often in my dreams I am convinced of just such familiar events – that I am sitting by the fire in my dressing-gown – when in fact I am lying undressed in bed! Yet right now my eyes are certainly wide open … Indeed! As if I didn’t remember other occasions when I have been tricked by exactly similar thoughts while asleep! As I think about this more carefully, I realise that there is never any reliable way of distinguishing being awake from being asleep.
If I cannot differentiate between being asleep and being awake, Descartes argues, I cannot believe with certainty that I am not asleep now. Therefore, even my best candidate for a true belief is doubtful.
That’s not all. Descartes has a more powerful weapon, which constitutes the third level of doubt: what if there is a malicious demon who is extremely powerful and who is set on deceiving me about everything I believe? In that case, I cannot be sure that what I see is really there; maybe the all-powerful demon is deceiving me to believe so. Descartes concludes:
So I shall suppose that some malicious, powerful, cunning demon has done all he can to deceive me … I shall think that the sky, the air, the earth, colours, shapes, sounds and all the external things are merely dreams that the demon has contrived as traps for my judgment.
What to make of these three levels of doubt? The First Meditation offers two different sceptical arguments with different aims and scopes. The first one, what I call the ‘Veil of Ideas’ scepticism, is designed to show that our beliefs about external objects are doubtful. This is the purpose of the first two levels of doubt. The first level is designed to show that there is a priority of inner over outer in our mind. That is, what we are directly aware of in our experiences are our own ideas, and we know about external objects only by inferring their existence or properties from these ideas. For example, when I see my cup of coffee on my desk, what I am directly aware of is my idea of my cup and my desk, and then I infer their existence – I do not perceive those objects and properties directly. How does this help us to reach a sceptical conclusion? It shows that when I consider myself as sitting by the fire wearing my dressing gown, what I perceive directly is not the fire or the dressing gown themselves, but only my idea of them. The problem is that these ideas can have many different causes. It might be the object itself that causes the idea in my mind – which leads to the happy case in which I have a true belief. But it can also be my dream that causes that idea – which leads to the unhappy case in which there is no fire, only the dream of a fire. That is the sceptical conclusion.
The Pyrrhonian Sceptic does not even imagine that there might not be an external world
There is a second sceptical argument in the First Meditation, which is often misleadingly called the ‘evil demon’ argument, but I prefer to call it the ‘Author of My Origin’ argument. Whereas the first argument is designed to show that our beliefs in empirical propositions – that I am sitting here by the fireplace, say – might be wrong, this second argument is designed to show that my beliefs about the so-called eternal truths – things such as a necessary mathematical proposition, for example, 2 + 2 = 4 – are also doubtful.
It starts with the metaphysically loaded assumption that God, or rather a malicious demon, could create the world in such a way that the eternal truths are false, or at least that I cannot say that God could not have created them in another way. What this reading does not consider, however, is another premise in Descartes’s argument. He starts this argument with the assumption that there is an omnipotent God who could ‘deceive’ him. But he does not end the argument there. He continues with another premise: that there might be no God, according to which
I am a product of fate or chance or a long chain of causes and effects. But the less powerful [these assumptions] make my original cause, the more likely it is that I am so imperfect as to be deceived all the time.
His argument is a disjunctive argument in the sense that either I have a powerful creator – or not. If the former situation obtains, then my creator – the author of my origin – has the power to deceive me even about eternal truths (note that he doesn’t talk of the eternal truths being false, but of my being wrong about them). And if the latter obtains – if there is no powerful creator of me – then it is more probable that I am wrong about the eternal truths. Hence, his sceptical conclusion that I might be deceived about the eternal truths – not that they might be false.
The Cartesian moment is more radical than the Pyrrhonian moment. The Pyrrhonian Sceptic does not even imagine that there might not be an external world, and Sextus, in describing his scepticism, normally takes for granted that it does exist. This is the point Myles Burnyeat makes in an oft-quoted passage. Ancient Sceptics,
however radical their scrutiny of ordinary belief, leave untouched – indeed they rely upon – the notion that we are deceived or ignorant about something. There is a reality of some sort confronting us; we are in touch with something, even if this something, reality, is not at all what we think it to be.
The ancient Sceptics take it for granted that there is something to be wrong about. But the Cartesian moment doubts exactly the existence of this something. If, for the Pyrrhonian Sceptic, I can be wrong in taking the water to be cold, for the Cartesian I can even be wrong about the existence of water, let alone its coldness.
Whereas Cartesian scepticism asks whether or not something is ‘actual’, Kantian scepticism, the third milestone in our story, asks ‘how it is possible’ that something is the case. To put it in a more philosophical tone, Kantian scepticism is a how-possible question regarding something which is not in doubt in the first place. As Conant puts it:
Kantian scepticism brings within the scope of its worry that which the Cartesian sceptic takes for granted: that experience possesses the requisite unity so much as to be able to be about something … [H]ow is experience (so much as) possible?
The Kantian moment goes further than the Cartesian one. If Descartes and other Cartesians doubt the existence of external objects such as the tree outside my window, they do not go so far as to question our experience’s bearing on those external objects – say, that my perception of the tree has any relation to the tree itself. This is exactly what Immanuel Kant and Kantians do.
What does it mean to question my experience’s bearing on external objects? To understand the force of this question, we should see that ‘experiences’ and ‘external objects’ are two different entities. Our experiences, and other similar sorts of things such as perceptions and beliefs, are things we can use in arguments – as the American philosopher Wilfrid Sellars once put it, they belong to ‘the space of reasons’. But external objects are physical entities that are outside ‘the space of reasons’ and cannot be used in arguments. Suppose you ask me why I believe that the desk in my study is brown. My response to you – my argument – is that it’s because I see that it is brown. I use my ‘perception’ as a premise in an argument. But I cannot say ‘because the table’. The table itself cannot be a premise of my argument, only my experience of it can be. Philosophers often describe this by saying that experiences, perceptions or beliefs are ‘normative’.
Now, if my experience of the world is normative and in the space of reasons, but physical objects are not, the question is: how is it possible that these two extremely different things – the two heterogeneous entities – can have a relation to each other? This is the basic question the Kantian sceptic asks. How is it possible that something that is in the space of reasons can bear on, or can be related to, something that is not? What is important here is that these kinds of questions do not involve any kind of doubt. The Kantian sceptic does not doubt that our experience bears on the external world. The question is not whether there is such a relation between the conceptual and the non-conceptual, but how it is possible that there is such a relation. These are questions that the Cartesian simply does not ask. Cartesians agree with the Kantians that there is no question that our experience bears on external objects. The difference is that the Kantian asks for an explanation for such a relation, but the Cartesian does not even ask for an explanation for such a fact – because the question has never arisen.
However much I investigate, I cannot see, or otherwise have any experience of, ‘causality’ itself
Let’s see Kant’s own version of Kantian scepticism in his Critique of Pure Reason (1781/1787) as an example. In this monumental book, Kant distinguishes between two faculties of the human mind: sensibility and understanding. ‘Sensibility’ is the passive or receptive faculty by means of which objects are given to us. ‘Understanding’ is what by means of which we think those objects. The sensibility gives us these objects through what Kant calls ‘intuition’, which is a particular relation to the object. And the understanding thinks these objects through ‘categories’, which are general concepts such as causality and substance, applicable to more than one particular thing. Kant’s own version of Kantian scepticism is a how-possible question regarding the relation of these two entities: how is it possible that the categories bear on the objects given to us by means of intuition?
Kant tackles this question in a part of the book called ‘On the Deduction of the Pure Concepts of the Understanding’. He enumerates 12 categories, but just one example will do for now: the category of causality. Here, Kant has in mind David Hume’s scepticism regarding causality. He argued that in seeing what we normally call a causal relation – say, seeing that fire makes water boil – what we really see is only the ‘contiguity’ between two different objects or events. I only see that, first, the fire burns, and second, that the water boils. However much I investigate, I cannot see, or otherwise have any experience of, ‘causality’ itself.
The problem is Kantian in nature. It is a how-possible question regarding the connection of the concept of causality and the objects and events in the external world. That is, the problem, for Kant, is how such a relation is possible. It might seem here that Kant takes the possibility that there is no such relation to the categories and objects as a genuine possibility (and this led many readers of Kant to mistakenly believe that he is a Humean in this respect). But this is only a seeming possibility – something, as he puts it, that ‘the sceptic wishes most’. He actually wants to show that such a ‘seeming possibility’ does not obtain at all; that it is nothing more than a pseudo-possibility or an illusion of the possibility. Put another way, the Humean sceptic thinks that there is a gap between the categories and the objects of perception, and the anti-Humean sceptic would try to bridge the gap in a way. But Kant’s answer is that the gap is not a genuine gap to begin with; it is nothing but an illusion of a gap. Contemporary philosophers are of course hesitant to call this problem ‘scepticism’, but Kant himself calls it by this name and names the Cartesian problem ‘material’ or ‘problematic idealism’. (This reading is meant to be quite close – although not identical – to one developed by Conant, John Haugeland and John McDowell.)
Ludwig Wittgenstein, the fourth and last milestone in the history of scepticism, asks something that even Kant did not. In all of Kant’s discussions, it is our experience of the world that is in question. It is the world that affects us, and even though Kant takes mind to be active in this process, it still in some important sense represents ‘the world’. As philosophers tend to put the matter, the ‘direction of fit’ is from world to mind. But Wittgenstein, in the rule-following considerations in his posthumously published book Philosophical Investigations (1953), poses a deeper question about what we do in the world. He reverses the ‘direction of fit’ from world-to-mind to mind-to-world by asking another how-possible question: how is it possible to follow a rule? In this question, we have something that is in the space of reasons – our ‘actions’ or ‘intentions’ to act – and something that is not – the physical event happening in the world. For example, I have an intention of drinking my coffee (this is the part in the space of reasons) and this causes a physical movement in my hand (this is the part outside the space of reasons). Like Kant, Wittgenstein doesn’t doubt that there is some relation between these two. What is at issue is a how-possible question: we need an explanation for this relation between two such heterogenous entities.
Wittgenstein initially formulated the problem using the case of mathematical functions. We have a student who is learning to write down series of numbers, and we have taught him to write a series of numbers of the form ‘+2’ up to 1000, but then:
he writes 1000, 1004, 1008, 1012.
We say to him: ‘Look what you’ve done!’ – He doesn’t understand. We say: ‘You were meant to add two: look how you began the series!’ – He answers: ‘Yes, isn’t it right? I thought that was how I was meant to do it.’ – Or suppose he pointed to the series and said: ‘But I went on in the same way.’ – It would now be no use to say: ‘But can’t you see…?’ – and repeat the old examples and explanations.
In writing down these series of numbers, we implicitly follow a mathematical function. In the case of natural numbers, for example, the function is ‘+1’. But there are other functions that give us the same results until a certain point. For example, when the function is to follow ‘+1’ if x<1000, and to follow ‘+2’ if x>1000. Both of these functions, if applied to a number less than 1000, give us the same result. The difference is only when we go further than 1000. But there is no way for us to see, when we are writing down the series when it is less than 1000, which of the functions we mean to use. Wittgenstein’s argument is that for every action, there is more than one description of that action. But we, as the agent who does that action, cannot be sure which of these descriptions would truly apply to our action. So there is a confusion here.
Descartes questions what the ancients take for granted: that there is an external world
The American philosopher Saul Kripke formulated a detailed argument for how this problem might work – an argument that, as Kripke himself admits, is Wittgensteinian but not Wittgenstein’s, and has come to be known in the literature as ‘Kripkenstein’. Here Wittgenstein is describing what he calls a ‘misunderstanding’. This is most obvious in the following passage, which is one of the best summaries of the rule-following problem to be found in Wittgenstein’s corpus:
This was our paradox: no course of action could be determined by a rule, because every course of action can be brought into accord with the rule. The answer was: if every course of action can be brought into accord with the rule, then it can also be brought into conflict with it. And so there would be neither accord nor conflict here.
That there is a misunderstanding here is shown by the mere fact that in this chain of reasoning we place one interpretation behind another, as if each one contented us at least for a moment, until we thought of yet another lying behind it. For what we thereby show is that there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call ‘following a rule’ and ‘going against it’.
The way I described the problem above, which is consistent with Kripke’s reading, captures the first paragraph of this passage. It describes a paradox we seem to face. But this is not the way Wittgenstein sees the situation. For him, seeing a paradox there is just a misunderstanding. It has not gone unnoticed by other readers that this way of reading the problem misses the second paragraph of this passage. Just as for Kant the gap between the conceptual and the non-conceptual was a pseudo-gap, for Wittgenstein, we misunderstand the situation if we think that we need an interpretation for our following a rule – say, for using a function in writing down a series of numbers. In following a rule, we just follow a rule, period.
Each milestone in the history of sceptical thought presents a situation more disturbing than the last. Descartes questions what the ancients take for granted: that there is an external world. Then there is something, which Kant puts his finger on, that never occurred to Descartes: that the conceptual bears on the non-conceptual, that our experience bears on spatiotemporal objects. And Kant himself never considers this problem in its most formidable sense: that the relation of the conceptual and the non-conceptual might be problematic even in the case of actions we take ourselves doing, when the direction of fit is from mind to world. This is the last milestone, the Wittgensteinian moment.
All these four milestones are meant to be – philosophically put – formal. That is, although these milestones discuss, and are named after, particular philosophers who presented the paradigm case of such sceptical worry, it is not that philosopher only who can, or did, present it. The Wittgensteinian moment is Kantian in nature, Kant himself engages in several places with his own version of Cartesian scepticism, and Descartes himself takes some of his sceptical problematics to have their roots in ancient Scepticism. And there are many other philosophers who do engage with these different forms of scepticism. This also explains why we can call these milestones ‘scepticisms’, even though three of the four thinkers we mentioned – Descartes, Kant and Wittgenstein – are by no means sceptics. They just consider these forms of scepticism either to reject them (in the case of Descartes), or to show that they are presenting merely a seeming possibility (in the case of Kant), or that they present only a misunderstanding (in the case of Wittgenstein).
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