The Problem of Induction HM5501 Lecture 3

October 15, 2017

HumeThe justification of science appears at first glance to be the generalisation of experience. I heat metal x and see that it expands, I heat metal y and see that it expands, I heat metal z and see that it expands, and so on, such that it seems natural that I can claim that all metals expand when I heat them. When you hear then talk, then you would think that most scientists think this is what a scientific argument is, and most would also think this is what we might mean by scientific objectivity. There are, however, two questions we might ask of them. First of all, does the inductive method really produce knowledge in the way they think it does, and secondly even if it did is this how science itself operates in its own history? I actually think the second question is more important than the first. The first question is about scientific method, the second is more about what scientists actually do, and not what they say they do. It is a matter of pragmatics, rather than the logical definition of a method in the abstract.

Let us take the first question first, because it is the more traditional problem of induction, and has its canonical form in the argument of Hume. To understand his problem with induction we first of all need to understand, even if in the most basic way, his epistemology. For Hume, there are two kinds of propositions: relations of ideas, and matters of facts. In the first relation, the truth of our ideas is confined by our ideas alone. Thus if you understand the concept ‘bachelor’ you know the idea ‘unmarried man’ is contained within it. When it comes to matters of fact, however, we have to go beyond our concepts to experience. They tell us something new about the world and not just the ideas we already know. A matter of fact would be that Paris is the capital of France, or metals expand when heated. Of course when you know the idea then you know what is contained in it, but to obtain the idea you first of all have to get the knowledge. You only know that Paris is in France, if you have knowledge of basic geography. You only know that metals expand when heated, if you know metallurgy.

There can be false relations of ideas as there can be false matters of fact. Thus if you think that a whale is a fish, then you have made an error about a relation of ideas (you don’t know that a whale is a mammal), and if you think that Plato died in 399 BC, then you have made an error at the level of facts (Ladyman 2002, p.32). Relations of ideas can be proved true by deduction since the negation is a contraction. Basically relations of ideas are tautologies, you cannot assert that Peter is not a bachelor at the same time as asserting that he isn’t married as well, since being unmarried and being a bachelor are one the same thing. On the other hand, matters of fact cannot be proved by logic alone, but can only be derived from experience and their contradiction is not a fallacy. If I say that Everest is the tallest mountain on Earth, none of the terms have a logical relation to one another, so I could assume that there is taller mountain. I would have to experience the different tall mountains on Earth to know which one was tallest or not (Ladyman 2002, p.33). For this reason Hume was extremely sceptical about what one could claim to know deductively. All that one could claim are logical relations between concepts that we already known (whose origin anyway would be the senses). What we cannot claim is to produce new knowledge about the world simply through examining our concepts (as theology and metaphysics is wont to do in his opinion).[1]

These distinctions seem very straight forward and at first glance appear to back up the ‘inductivist’ view of science. The problem for Hume, however, is whether the idea that matters of fact could have the same necessary conclusions as relations of ideas, as the idea of expanding metals as a universal law implies. The key to this problem for Hume is whether I can assert that what happens in the past is a necessary certainty for what will happen in the future. I have experienced the fact that the sun rises every morning. Does this give me the right to say it will rise again tomorrow, when I haven’t actually experience this dawn yet? If it does rise then I will be certain, and in terms of the past, I know that it did rise, but now can I know that I will rise again tomorrow? It is perfectly possible, even if it were unexpected, that the sun might not rise.

Induction for Hume is based upon causal arguments. Our only knowledge of cause and effect is through experience itself because there is no logical reason why any causal relation should hold or not hold. I know matches cause fires, because I know that from experience, not because matches logically contain fire. Just as we can only infer future behaviour of the world from the actual experience of the world, then we can only understand the category of causality from experience. In other words without experience we would not have the concept of causality as a generality. If I always experience the dawn as the rising of the sun then I conjoin this events. If A always follows B, then I will say that A causes B. This because I believe that the future always follows the same path as the past. So that if A happens, then B will happen. Linked to conjunction is contiguity and precedence. Contiguity means that B follows A in time and space, and precedence is that the effect is always after the cause. (the flame is after the lighted match and not before). It is because of conjunction, contiguity, and precedence, that we feel that we have good reason to say that A causes B, or that the sun will rise tomorrow. Hume assertion, however, is that this can never be a necessary reason, as is suggested by generalisation of a universal law, however compelling I feel this causality to be.

Take the example of billiard balls, which seems the most basic relation of causality. The ball X hits the ball Y and causes it to move. But what do we mean by that? Do we mean that the ball X makes the ball Y move or that it produces its movement? We think there is a necessary connection between the two events. X moving and Y moving. What we experience is conjunction, contiguity and precedence, what we do not experience is some mysterious ‘necessary connection’. What we see is ball X and ball Y, what we do not see is some other third thing (like an invisible connection, indeed what we do not see is causality). What does it add to our explanation of the events, even if we were to add this mysterious cause. Wouldn’t the ball X and the ball Y just move in exactly the same way?

The point for Hume is just because two events have always in the past be conjoined, does not mean that we can be universally certain that they will always do so. The conclusion of inductive argument could be false but that would never make it invalid (indeed it might make it more interesting, if the sun did not rise the next day), but this is never the case with a deductive argument if the premises are true, then the conclusion is necessarily true. What underpins the inductive generalisation is the belief that nature is well ordered spatially and temporally, that what happens many times will happen again in the same way. But that is just an assumption. Why must the future always be the same as the past and it certainly is not a logical contradiction if it were not.

Now of course we make these kind of inferences all the time, and Hume accepts that. I probably would not be able to live if I really though the sun would not rise tomorrow every time I went to bed. But this uniformity is a result of our psychology (perhaps it is an evolutionary trait) rather than reason or logic. We find regularity in nature because our habitual associations of events, and not because these events are necessarily connected.[2]

There is no doubt that Hume’s problem is very profound and does make us look at induction more critically, but we might think that the idea that science itself is inductive in the simple way that ‘inductivism’ implies is too simplistic. So the problem is not with induction as such, but how we are using it. It is important to note that this is a very different critique from the methodological one. In the first case, we investigate the method of induction, and like Hume say that is flawed, or might even argue that Hume’s own account of induction is not a correct description of induction.[3] Whereas in the historical account of science, we are arguing whether the description of method is actually how scientists themselves work. One is a description of the content of scientific knowledge, the other is a description of the activity of scientists themselves. Do scientists really act the way that Hume’s example suggests they do? This is a completely different way of doing philosophy of science. For it does not first of all describe a method of doing science and then apply it to scientists, rather it examines what scientists do and from that derives the method. We shall see that this way of understanding science is going to be very important to Kuhn.

Why might we think that scientists do not use the inductive method in the way that induction has been described so far? Take the example of Newton’s Principia (Ladyman 2002, pp.55–6). Newton presents in this work the three laws of motion and the law of gravity. From these laws in explains natural phenomena like planetary motion. He says that he has inferred these laws through induction from observation. Now it is French philosopher of science Duhem that points out that there is a problem with Newton’s explanation. The data he is using is Kepler’s. His data proves that the planet will move in circles, whereas Newton’s in ellipses. This means that he could not have inferred gravity from Kepler’s data, rather he already the hypothesis of the law of gravity to interpret Kepler’s data. Even Kepler’s theory could not have be derived from observation, because he took his data from Brahe, but could only organise it by already assuming that planets moved in circles, a hypothesis he didn’t receive from data, but from the mystical Pythagorean tradition.

So there are two reasons why we might be sceptical of the simple inductive explanation of science. One is methodological through the problem of induction (though we might come up with a better inductive method to solve this), and the other is historical, that science does not work in the way that theory of induction describes. I think the latter is the more serious issue than the former. For in the end science is what scientists do, and not what philosophers might idealise that they do. If you like, the problem of induction is a problem for philosophers. It isn’t one for scientists. They work in a very different way indeed.

Works Cited

Ladyman, J., 2002. Understanding Philosophy of Science, London; New York: Routledge.

 


[1] A group of philosophers from the 20th century called logical positivists also liked this distinction, and differentiated mathematical and logical truths, on the one hand, and science on the other. Anything that didn’t fit this schema was said to be nonsense or meaningless. I am not sure that Hume would have gone that far.

[2] Kant’s argument against Hume is that causality is not merely a habit of the mind but a necessary part of our representation of the world. It would not make sense without it.

[3] This is what Ladyman does when he lists all the different ways in which we might counter Hume, the most telling being induction as the ‘best explanation’ (Ladyman 2002, pp.46–7).

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Kant’s Transcendental Idealism – Lecture 3

April 9, 2016

immanuel-kant-2To understand Kant you have to, of course, understand what he is rejecting. If you don’t the know context of a philosopher, which is always what problem they are facing, then you won’t really be able to understand the point of their work. You will, for example, think it is easy to dismiss a whole or part of their argument, because it disagrees with some contemporary position (as though they were guilty of some unforeseen stupidity on their part, as though they should have none better). Thus Plato is dismissed because he thinks forms can be separate from instantiations of them, or Aristotle because he believed that reality was made of 5 elements, or Descartes because he believed in God, and so on. Of course, once one has grasped the context of a philosopher that does not mean that one has to take on board all the they say, but it does mean that one won’t dismiss them in a superficial way.

One way of understanding Kant’s philosophy is seeing how it arises out of the perennial conflict between empiricism and rationalism in Western Philosophy (though we shall see that it is not as simple as simply unifying them as some might believe). We have already spent some time in discussion of rationalism because of our lecture on Descartes, so this time we will look at, in a little detail, empiricism, and more specifically Hume.

He famously woke Kant from his ‘dogmatic slumbers’, since before reading Hume, he was a rationalist of a kind.[1] What then is the basis of Hume’s philosophy? We do not require unjustified metaphysical speculation in order to have a rational scientific understanding of nature. To rid ourselves of this metaphysical speculation we have to become sceptical has to the objective basis of science, but this is necessary if we are not to base it on fictional and imaginary ideas. For Hume the source of all our ideas are the senses. This limitation is very important for Kant. Like Hume, he will argue that our knowledge of the world is limited to what is given in experience. Outside of that we can know nothing. In this sense, Kant is more Humean than he is Cartesian.

Sensations themselves are divided into two for Hume. On the one had there are impressions, and on the other ideas. Impression are direct sensations. I see the colour blue. Blue is the immediate sensation. Ideas are the relations between impression. I see many blue things, and I compare them through the concept ‘blue’. This does not mean ideas are separate from impression in terms of their existence. An idea exists only because there are impressions, and these impressions have their source in the sensation of the world. Ideas are, if you like, impressions that have become older. They are less vivid and present than immediate sensations, but they are made of nothing but sensations. A blind man, Hume argues, could not have an idea of a colour, because he has not seen it, nor a deaf man sound, because he has not heard it (Hume & Buckle 2007, p.16). Hume’s question is whether there is a necessary order in the relations of ideas, as there is in the order of impressions (in sensation, one impression comes after the other). In other words, what groups or orders my ideas together. If I think of x, must I also think of y?

The answer is that I associate one idea with another. There are three kinds of association for Hume, resemblance, proximity and causality. If I see a picture of a fox, then I am likely to think of a fox, if I imagine a room in the university, then I am likely to think of a room next to it, and finally, if I think of stone dropping from someone’s hand, then I likely to think of falling to the ground. Now it is the last association that is fundamental to how we think of the explanations of natural sciences. When we think of explanations in total, then are two kinds: relations of ideas and matters of fact. For the former, Hume is thinking of logic and mathematics. For these, we do not have to go beyond the ideas themselves (if you understand the meaning of one idea, then you will know why the other idea is necessarily associated with, so that ‘bachelor’ must mean ‘unmarried man [remembering that these ideas still have their origin in impressions]). But for matters of fact this is not the case, because they tell us something new about the world, rather than just analyse what we already know. Why do we believe that the sun will rise tomorrow, when we could equally believe the opposite. Hume is not arguing that we shouldn’t believe that the sun will rise (in fact he has good argument to think why we do), but there is no logical reason why we shouldn’t. The reason why we do is that we associate one idea with the other, the idea that the sun rose yesterday with the idea that the sun will rise tomorrow. We might think that we get to this second idea through an argument, where the statement ‘the sun rose yesterday’ is a premise. If it is an argument of this kind, then it could only be a relation of ideas or a matter of fact. It can’t be the first, since there is no contradiction in thinking the opposite, but it can’t be a matter of fact, because it is precisely that kind of argument I am trying to prove, so I appear to be going around in circles.

The answer must be that my conviction must have its origin elsewhere and that a belief is not the same a giving a reason or having a reason (indeed Hume will argue that our reasons have their source in our beliefs rather than the other way around). His answer is that the source of this belief is in our impressions rather than in our ideas first of all. It is because I have had the vivid experience of the sun rising again and again in the past. The belief that it will do so in the future is a habit and custom of the mind that I associated with the impression of I am having now. Thus when I see the see the dawn, whether directly or indirectly, I immediately associate it with the idea of the sun rising and I cannot help but do so because this custom or habit belongs to human nature intrinsically. A belief then is a particular vivid idea. Not as vivid as a direct sensation, but more vivid than a reason or a concept, and it is this that cause me always to associate x with y. Of course experience is open ended. It is perfectly possible that one day my belief will be unconfirmed rather than confirmed by experience.

Kant is more on Hume’s side, as we have said, rather than Descartes. In these sense, he is an empirical realist, that our understanding and experience of the world is given by experience, and we cannot deduce facts about the world by arguing from ideas. Where he differs from Hume is how far he is willing to take this. He argues that causality cannot be just an habit of mind, an association, but must be fundamental to our experience as such, so fundamental that we would even be having experiences of objects at all, rather than worrying whether the sun might rise tomorrow or not.

What is fundamental to Kant’s difference from both Descartes and Hume is how he conceives of the relation between the subject and object. For both of them, though they give completely diametrically opposed answers to the problem, it is a question of how the subject conforms to the object. For Descartes, my knowledge conforms to the object through ideas, whereas for Hume, it does so through sensations. For Kant, on the contrary, and it is this that is totally novel in his approach, the relation between the subject and object must be reversed. It is not how does the subject conform to the object, but how does the object conform to the subject. As Kant writes,

Hitherto it has been assumed that all our knowledge must conform to objects. But all our attempts to extend our knowledge of objects by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge […] We should then be proceeding on the lines of Copernicus’ primary hypothesis. (Kant 2007, p.Bxvi)

Both Hume and Descartes relate knowledge to knowing the thing as it is in itself. One asserts that we can now it through ideas, the other through sensations. But it precisely this ‘thing’ that we cannot know, Kant argues. We can know how the object appears to us. Appearance itself is split into two: the content of appearance and the form of appearance. The content of appearance is what is given in experience (what Hume calls sensations or impressions). The form is how these contents appear to us. Thus, we can distinguish between what the chair is, and how the chair appears to us.

It is Kant’s argument that the form of appearance is universal and necessary. Unlike the habits of Hume, then, they are true of all human cognition, and we cannot experience the world in any other way. In the transcendental aesthetic, Kant describes the pure forms of sensation, time and space; in the transcendental logic, the pure forms of the object (the categories of the understanding); and finally in the transcendental dialectic, how philosophy gets into difficulties when it treats these pure forms as though they were objects of experience that one could know directly.

Let us look at Kant’s argument for the pure form of space in the Critique of Pure Reason, because by examining this one argument we will see how Kant’s employs a transcendental method to solve the age old antagonism between empiricism and rationalism. Kant is arguing that space and time are a priori and synthetic. What he means by that is that space is prior to experience but also adds something to experience (it unifies it; this is the formal element). We can already see that Kant is doing something novel here, because usually we think that the a priori is analytic, and the synthetic is a posteriori, so it seems quite strange to argue that space and time are a priori and synthetic.

Let us first of all look at the belief that space is something real, just like the objects that we can see. Kant’s argument against this common sense view is quite simple: space, he argues is the outer form of things for us. In other words, things that are outside of us are always in space (the difference from time, is that this is the inner form of ideas – are memories are not literally in space). To say that space is derived from experience is therefore to beg the question, for the very thing that one is trying to prove, spatiality, is already appealed to in the proof. Secondly, space cannot be derived from experience because of its necessity. The necessity of space for every appearance is that it is possible to imagine space without any appearances, no tree, no house and so, but it is not possible to imagine the absence of space and appearances (of course it is possible to think the absence of space, but it is not possible to imagine that there is something and no space). The argument against the Newtonian view that space is something real (a self-subsisting entity, as Kant calls it) is that this would mean that space were a container, but this container itself would have to contained and so on ad infinitum.

This would seem to imply that space, therefore, can only be a concept of things rather than something real, but Kant has to show that space is the pure form of sensations, and not just a concept that we have of things. This is much harder to prove than that space is not real and Kant, for this reason, spends more time doing so. The philosopher he has mind, who thinks space is just a relational concept, is Leibniz. For Leibniz, space is not something, so to speak that exists outside of objects and thus independently of them, rather it is an idea that expresses the relation between objects. Space is, therefore, not something real, but merely an idea. How can we best understand this notion of relational ideal space? Think of two places and the distance between them. Let us think of the two cities of Plymouth and Exeter in the South-West of England. We might say that Exeter is near to London than Plymouth, but is this being nearer a property of Exeter, or does it not rather express the relation between Exeter and Plymouth. For there to be space at all, there needs to be at least two objects. With just one object, there would be no space. If space were not a relation between objects, then it would exist, if there were only one object.

Kant needs to show that space is not simply a thought that we associate with objects, but their necessary form of presentation. He does this by showing that how we use pure intuition of space, is not the same as how we use concepts.[2] The intuition of space is unitary, singular and unique. This means that diverse spaces are parts of one and the same Space. The relation between these spaces, and Space, is not the same as the relations between the concept Tree and instances of trees. All the diverse parts of space belong to one space, but trees do not belong to one and the same Tree, therefore space cannot be a concept, and if it cannot be concept it must be an intuition, since these are the only two sources of human knowledge.[3]

So the conclusion of the argument is that space is not property of things, either as sensation or a concept, but is a necessary part of our experience of the world, for we cannot have an experience of an external without it already been organised through space. Space, therefore, is both a priori, since it is necessary, and synthetic, since it is added something to experience (namely it is spatial). Things are spatial because human consciousness is spatial, and not the other way around. Kant repeats the argument with time, and then in the transcendental logic with logics. It wants also to show through the transcendental deductions that without these pure forms of appearance there would be no object for us at all. As Kant writes,

The a priori conditions of a possible experience in general are at the same time conditions of the possibility of objects of experience. (Kant 2007, p.A111)

So Hume’s argument is that we have an experience and then associated these ideas in our minds. For Kant, on the contrary, we wouldn’t be having an experience at all. Causality is not something that we apply to our experience; it belongs to the very fabric of our experience as something meaningful and coherent from us, and it is on this foundations that the natural sciences are built.

Bibliography

Gardner, S., 2006. Kant and the Critique of pure reason, London; New York: Routledge.

Hume, D. & Buckle, S., 2007. An enquiry concerning human understanding and other writings, Cambridge; New York: Cambridge University Press.

Kant, I., 2007. Critique of Pure Reason 2nd ed., Palgrave Macmillan.

Kant, I. et al., 2004. Immanuel Kant Prolegomena to Any Future Metaphysics., Cambridge: Cambridge University Press.


[1] Of Leibniz-Wolffian kind. Kant writes in Prolegomena, ‘I freely admit that it was the remembrance of David Hume which, many years ago, first interrupted my dogmatic slumber and gave my investigations in the field of speculative philosophy a completely different direction’ (Kant et al. 2004, p.10).

[2] We need to be certain here, as Sebastian Gardner points out, that Kant is not denying that there is a concept of space, but we should not confuse this with the pure intuition of space, which must underlie even this concept (Gardner 2006, p.77).

[3] Kant, in the second edition of The Critique of Pure Reason, also demonstrates the difference between the pure intuition of space and a concept by demonstrating that the infinity of space is not the same as the infinity of a concept.


The Problem of Induction – Lecture 3

October 16, 2015

HumeThe justification of science appears at first glance to be the generalisation of experience. I heat metal x and see that it expands, I heat metal y and see that it expands, I heat metal z and see that it expands, and so on, such that it seems natural that I can claim that all metals expand when I heat them. Most scientists think this is what a scientific argument is, and most would also think this is what we might mean by objectivity. There are, however, two questions we might ask of them. First of all, does the inductive method really produce knowledge, and secondly even if it did is this how science itself operates in its own history?

Let us take the first question first, because it is the more traditional problem of induction, and has its canonical form in the argument of Hume. To understand his problem with induction we first of all need to understand his epistemology. For Hume, there are two kinds of propositions: relations of ideas, and matters of facts. In the first relation, the truth of our ideas is confined to our ideas alone. Thus if you understand the concept ‘bachelor’ you know the idea ‘unmarried man’ is contained within it. When it comes to matters of fact, however, we have to go beyond our concepts to experience. They tell us something new about the world and not just the ideas we already know. A matter of fact would be that Paris is the capital of France, or metals expand when heated. Of course when you know the idea then you know what is contained in it, but to obtain the idea you first of all have to get the knowledge.

There can be false relations of ideas as there can be false matters of fact. Thus if you think that a whale is a fish, then you have made an error about a relation of ideas (you don’t know that a whale is a mammal), and if you think that Plato died in 399 BC, then you have made an error at the level of facts (Ladyman 2002, p.32). Relations of ideas can be proved true by deduction since the negation is a contraction. Basically relations of ideas are tautologies, you cannot assert that Peter is not a bachelor at the same time as asserting that he isn’t married as well, since being unmarried and being a bachelor are one the same thing. On the other hand, matters of fact cannot be proved by deduction, but can only be derived from experience and their contradiction is not a fallacy. If I say that Everest is the tallest mountain on Earth, none of the terms have a logical relation to one another, so I could assume that there is taller mountain. I would have to experience the different tall mountains on Earth to know which one was tallest or not (Ladyman 2002, p.33). For this reason Hume was extremely sceptical about what one could claim to know deductively. All that one could claim are logical relations between concepts that we already known (whose origin anyway would be the senses). What we cannot claim is to produce new knowledge about the world simply through examining our concepts (as theology and metaphysics is wont to do in his opinion).[1]

These distinctions seem very straight forward and at first glance appear to back up the inductivist view of science. The problem for Hume, however, is whether the idea that matters of fact could have the same necessary conclusions as relations of ideas, as the idea of expanding metals as a universal law implies. The key to this problem for Hume is whether I can assert that what happens in the past is a certain kind for what will happen in the future. I have experienced the fact that the sun rises every morning. Does this give me the right to say it will rise again tomorrow, when I haven’t actually experience this dawn yet? If it does rise then I will be certain, and in terms of the past, I know that it did rise, but now can I know that I will rise again tomorrow? It is perfectly possible, even if it were unexpected, that the sun might not rise.

Induction for Hume is based upon causal arguments. Our only knowledge of cause and effect is through experience itself because there is no logical reason why any causal relation should hold or not hold. I know matches cause fires, because I know that from experience, not because matches logically contain fire. Just as we can only infer future behaviour of the world from the actual experience of the world, then we can only understand the category of causality from experience. In other words without experience we would not have the concept of causality as a generality. If I always experience the dawn as the rising of the sun then I conjoin this events. If A always follows B, then I will say that A causes B. This because I believe that the future always follows the same path as the past. So that if A happens, then B will happen. Linked to conjunction is contiguity and precedence. Contiguity means that B follows A in time and space, and precedence is that the effect is always after the cause. (the flame is after the lighted match and not before). It is because of conjunction, contiguity, and precedence, that we feel that we have good reason to say that A causes B, or that the sun will rise tomorrow. Hume assertion, however, is that this can never be a necessary reason, as is suggested by generalisation of a universal law however compelling I feel this causality to be.

Take the example of billiard balls, which seems the most basic relation of causality. The ball X hits the ball Y and causes it to move. But what do we mean by that? Do we mean that the ball X makes the ball Y move or that it produces its movement? We think there is a necessary connection between the two events. X moving and Y moving. What we experience is conjunction, contiguity and precedence, what we do not experience is some mysterious ‘necessary connection’. What we see is ball X and ball Y, what we do not see is some other third thing (like an invisible connection, indeed what we do not see is causality). What does it add to our explanation of the events, even if we were to add this mysterious cause. Wouldn’t the ball X and the ball Y just move in exactly the same way?

The point for Hume is just because two events have always in the past be conjoined, does not mean that we can be universally certain that they will always do so. The conclusion of inductive argument could be false but that would never make it invalid (indeed it might make it more interesting, as if the sun did not rise the next day), but this is never the case with a deductive argument if the premises are true, then the conclusion is necessarily true. What underpins the inductive generalisation is the belief that nature is well ordered spatially and temporally, that what happens many times will happen again in the same way. But that is just an assumption. Why must the future always be the same as the past and it certainly is not a logical contradiction if it were not.

Now of course we make these kind of inferences all the time, and Hume accepts that. I probably would not be able to live if I really though the sun would not rise tomorrow every time I went to bed. But this uniformity is a result of our psychology (perhaps it is an evolutionary trait) rather than reason or logic. We find regularity in nature because our habitual associations of events, and not because these events are necessarily connected.[2]

There is no doubt that Hume’s problem is very profound and does make us look at induction more critically, but we might think that the idea that science itself is inductive in the simple way that inductivism implies is too simplistic. It is important to note that this is a very different critique from the methodological one. In the first case, we investigate the method of induction, and like Hume say that is flawed, or might even argue that Hume’s own account of induction is not a correct description of induction.[3] Whereas in the historical account of science, we are arguing whether the description of method is actually how scientists themselves work. One is a description of the content of scientific knowledge, the other is a description of the activity of scientists themselves. Do scientists really act the way that Hume’s example suggests they do? This is a completely different way of doing philosophy of science. For it does not first of all describe a method of doing science and then apply it to scientists, rather it examines what scientists do and from that derives the method. We shall see that this way of understanding science is going to be very important to Kuhn.

Why might we think that scientists do not use the inductive method in the way that induction has been described so far? Take the example of Newton’s Principia (Ladyman 2002, pp.55–6). Newton presents in this work the three laws of motion and the law of gravity. From these laws in explains natural phenomena like planetary motion. He says that he has inferred these laws through induction from observation. Now it is French philosopher of science Duhem that points out that there is a problem with Newton’s explanation. The data he is using is Kepler’s. His data proves that the planet will move in circles, whereas Newton’s in ellipses. This means that he could not have inferred gravity from Kepler’s data, rather he already the hypothesis of the law of gravity to interpret Kepler’s data. Again Newton’s first law state that bodies will maintain their state of motion unless acted upon by another body, but we have not observed a body that has not been acted upon, so this law could not be obtained through observation. Even Kepler’s theory could not have be derived from observation, because he took his data from Brahe, but could only organise it by already assuming that planets moved in circles, a hypothesis he didn’t receive from data, but from the mystical Pythagorean tradition.

So there are two reasons why we might be sceptical of the simple inductive explanation of science. One is methodological through the problem of induction (though we might come up with a better inductive method to solve this), and the other is historical, that science does not work in the way that theory of induction describes. I think the latter is the more serious issue than the former. For in the end science is what scientists do, and not what philosophers might idealise that they do. If you like, the problem of induction is a problem for philosophers. It isn’t one for scientists.

Works Cited

Ladyman, J., 2002. Understanding Philosophy of Science, London; New York: Routledge.


[1] A group of philosophers from the 20th century called logical positivists also liked this distinction, and differentiated mathematical and logical truths, on the one hand, and science on the other. Anything that didn’t fit this schema was said to be nonsense or meaningless. I am not sure that Hume would have gone that far.

[2] Kant’s argument against Hume is that causality is not merely a habit of the mind but a necessary part of our representation of the world. It would not make sense without it.

[3] This is what Ladyman does when he lists all the different ways in which we might counter Hume, the most telling being induction as the ‘best explanation’ (Ladyman 2002, pp.46–7).


The Problem of Induction – Lecture 3

November 2, 2014

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The justification of science appears at first glance to be the generalisation of experience. I heat metal x and see that it expands, I heat metal y and see that it expands, I heat metal z and see that it expands, and so on, such that it seems natural that I can claim that all metals expand when I heat them. Most scientists think this is what a scientific argument is, and most would also think this is what we might mean by objectivity. There are, however, two questions we might ask of them. First of all, does the inductive method really produce knowledge, and secondly even if it did is this how science itself operates in its own history?

Let us take the first question first, because it is the more traditional problem of induction, and has its canonical form in the argument of Hume. To understand his problem with induction we first of all need to understand his epistemology. For Hume, there are two kinds of propositions: relations of ideas, and matters of facts. In the first relation, the truth of our ideas is confined to our ideas alone. Thus if you understand the concept ‘bachelor’ you know the idea ‘unmarried man’ is contained within it. When it comes to matters of fact, however, we have to go beyond our concepts to experience. They tell us something new about the world and not just the ideas that we already know. A matter of fact would be that Paris is the capital of France, or metals expand when heated. Of course when you know the idea then you know what is contained in it, but to get the idea you first of all have to get the knowledge.

They can be false relations of ideas as there can be false matters of fact. Thus if you think that a whale is a fish, then you have made an error about a relation of ideas (you don’t know that a whale is a mammal), and if you think that Plato died in 399 BC, then you have made an error at the level of facts (Ladyman 2002, p.32). Relations of ideas can be proved true by deduction since the negation is a contraction. Basically relations of ideas are tautologies, you cannot assert that Peter is not a bachelor at the same time as asserting that he isn’t married as well, since being unmarried and being a bachelor are one the same thing. On the other hand, matters of fact cannot be proved by deduction, but can only be derived from experience and their contradiction is not a fallacy. If I say that Everest is the tallest mountain on Earth, none of the terms have a logical relation to one another, so I could assume that there is taller mountain. I would have to experience the different tall mountains on Earth to know which one was tallest or not (Ladyman 2002, p.33). For this reason Hume was extremely sceptical about what one could claim to know deductively. All that one could claim are logical relations between concepts that we already known (whose origin anyway would be the senses). What we cannot claim is to produce new knowledge about the world simply through examining our concepts (as theology and metaphysics is wont to do in his opinion).[1]

These distinctions seem very straight forward and at first glance appear to back up the inductivist view of science. The problem for Hume, however, is whether the idea that matters of fact could have the same necessary conclusions as relations of ideas, as the idea of expanding metals as a universal law implies. The key to this problem for Hume is whether I can assert that what happens in the past is a certain kind for what will happen in the future. I have experienced the fact that the sun rises every morning. Does this give me the right to say it will rise again tomorrow, when I haven’t actually experience this dawn yet? If it does rise then I will be certain, and in terms of the past, I know that it did rise, but now can I know that I will rise again tomorrow? It is perfectly possible, even if it were unexpected, that the sun might not rise.

Induction for Hume is based upon causal arguments. Our only knowledge of cause and effect is through experience itself because there is no logical reason why any causal relation should hold or not hold. I know matches cause fires, because I know that from experience, not because matches logically contain fire. Just as we can only infer future behaviour of the world from the actual experience of the world, then we can only understand the category of causality from experience. In other words without experience we would not have the concept of causality as a generality. If I always experience the dawn as the rising of the sun then I conjoin this events. If A always follows B, then I will say that A causes B. This because I believe that the future always follows the same path as the past. So that if A happens, then B will happen. Linked to conjunction is contiguity and precedence. Contiguity means that B follows A in time and space, and precedence is that the effect is always after the cause. (the flame is after the lighted match and not before). It is because of conjunction, contiguity, and precedence, that we feel that we have good reason to say that A causes B, or that the sun will rise tomorrow. Hume assertion, however, is that this can never be a necessary reason, as is suggested by generalisation of a universal law however compelling I feel this causality to be.

Take the example of billiard balls, which seems the most basic relation of causality. The ball X hits the ball Y and causes it to move. But what do we mean by that? Do we mean that the ball X makes the ball Y move or that it produces its movement? We think there is a necessary connection between the two events. X moving and Y moving. What we experience is conjunction, contiguity and precedence, what we do not experience is some mysterious ‘necessary connection’. What we see is ball X and ball Y, what we do not see is some other third thing (like an invisible connection, indeed what we do not see is causality). What does it add to our explanation of the events, even if we were to add this mysterious cause. Wouldn’t the ball X and the ball Y just move in exactly the same way?

The point for Hume is just because two events have always in the past be conjoined, does not mean that we can be universally certain that they will always do so. The conclusion of inductive argument could be false but that would never make it invalid (indeed it might make it more interesting, as if the sun did not rise the next day), but this is never the case with a deductive argument if the premises are true, then the conclusion is necessarily true. What underpins the inductive generalisation is the belief that nature is well ordered spatially and temporally, that what happens many times will happen again in the same way. But that is just an assumption. Why must the future always be the same as the past and it certainly is not a logical contradiction if it were not.

Now of course we make these kind of inferences all the time, and Hume accepts that. I probably would not be able to live if I really though the sun would not rise tomorrow every time I went to bed. But this uniformity is a result of our psychology (perhaps it is an evolutionary trait) rather than reason or logic. We find regularity in nature because our habitual associations of events, and not because these events are necessarily connected.[2]

There is no doubt that Hume’s problem is very profound and does make us look at induction more critically, but we might think that the idea that science itself is inductive in the simply way that inductivism implies is too simplistic. It is important to note that this is a very different critique from the methodological one. In the first case, we investigate the method of induction, and like Hume say that is flawed, or might even argue that Hume’s own account of induction is not a correct description of induction.[3] Whereas in the historical account of science, we are arguing whether the description of method is actually how scientists themselves work. One is a description of the content of scientific knowledge, the other is a description of the activity of scientists themselves. Do scientists really act the way that Hume’s example suggests they do? This is a completely different way of doing philosophy of science. For it does not first of all describe a method of doing science and then apply it to scientists, rather it examines what scientists do and from that derives the method. We shall see that this way of understanding science is going to be very important to Kuhn.

Why might we think that scientists do not use the inductive method in the way that induction has been described so far? Take the example of Newton’s Principia (Ladyman 2002, pp.55–6). Newton presents in this work the three laws of motion and the law of gravity. From these laws in explains natural phenomena like planetary motion. He says that he has inferred these laws through induction from observation. Now it is French philosopher of science Duhem that points out that there is a problem with Newton’s explanation. The data he is using is Kepler’s. His data proves that the planet will move in circles, whereas Newton’s in ellipses. This means that he could not have inferred gravity from Kepler’s data, rather he already the hypothesis of the law of gravity to interpret Kepler’s data. Again Newton’s first law state that bodies will maintain their state of motion unless acted upon by another body, but we have not observed a body that has not been acted upon, so this law could not be obtained through observation. Even Kepler’s theory could not have be derived from observation, because he took his data from Brahe, but could only organise it by already assuming that planets moved in circles, a hypothesis he didn’t receive from data, but from the mystical Pythagorean tradition.

So there are two reasons why we might be sceptical of the simple inductive explanation of science. One is methodological through the problem of induction (though we might come up with a better inductive method to solve this), and the other is historical, that science does not work in the way that theory of induction describes. I think the latter is the more serious issue than the former. For in the end science is what scientists do, and not what philosophers might idealise that they do. If you like, the problem of induction is a problem for philosophers. It isn’t one for scientists.

Works Cited

Ladyman, J., 2002. Understanding Philosophy of Science, London; New York: Routledge.

 


[1] A group of philosophers from the 20th century called logical positivists also liked this distinction, and differentiated mathematical and logical truths, on the one hand, and science on the other. Anything that didn’t fit this schema was said to be nonsense or meaningless.

[2] Kant’s argument against Hume is that causality is not merely a habit of the mind but a necessary part of our representation of the world. It would not make sense without it.

[3] This is what Ladyman does when he lists all the different ways in which we might counter Hume, the most telling being induction as the ‘best explanation’ (Ladyman 2002, pp.46–7).


Problem of Induction–Lecture 3

October 24, 2013

The justification of science appears at first glance to be the generalisation of experience. I heat metal x and see that it expands, I heat metal y and see that it expands, I heat metal z and see that it expands, and so on, such that it seems natural that I can claim that all metals expand when I heat them. Most scientists think that this is what a scientific argument is, and most would also think this is what we might mean by objectivity. There are, however, two questions we might ask of them. First of all, does the inductive method really produce knowledge, and secondly even if it did is this how science itself operates in its own history?

Let us take the first question first, because it is the more traditional problem of induction, and has its canonical form in the argument of Hume. To understand his problem with induction we first of all need to understand his epistemology. For Hume, there are two kinds of propositions: relations of ideas, and matters of facts. In the first relation, the truth of our ideas is confined to our ideas alone. Thus if you understand the concept ‘bachelor’ you know that the idea ‘unmarried man’ in contained within it. When it comes to matters of fact, however, we have to go beyond our concepts to experience. They tell us something new about the world and not just the ideas that we already know. A matter of fact would be that Paris is the capital of France, or metals expand when heated. Of course when you know the idea then you know what is contained in it, but to get the idea you first of all have to get the knowledge.

They can be false relations of ideas as there can be false matters of fact. Thus if you think that a whale is a fish, then you have made an error about a relation of ideas (you don’t know that a whale is a mammal), and if you think that Plato died in 399 BC, then you have made an error at the level of facts (Ladyman 2002, p.32). Relations of ideas can be proved true by deduction since the negation is a contraction. Basically relations of ideas are tautologies, you cannot assert that Peter is not a bachelor at the same time as asserting that he isn’t married as well, since being unmarried and being a bachelor are one the same thing. On the other hand, matters of fact cannot be proved by deduction, but can only be derived from experience and their contradiction is not a fallacy. If I say that Everest is the tallest mountain on Earth, none of the terms have a logical relation to one another, so I could assume that there is taller mountain. I would have to experience the different tall mountains on Earth to know which one was tallest or not (Ladyman 2002, p.33). For this reason Hume was extremely sceptical about what one could claim to know deductively. All that one could claim are logical relations between concepts that we already known (whose origin anyway would be the senses). What we cannot claim is to produce new knowledge about the world simply through examining our concepts (as theology and metaphysics is wont to do in his opinion).[1]

These distinctions seem very straight forward and at first glance appear to back up the inductivist view of science. The problem for Hume, however, is the idea that matters of fact could have the same necessary conclusions as relations of ideas, as the idea of expanding metals as a universal law implies. The key to this problem for Hume is whether I can assert that what happens in the past is a certain kind for what will happen in the future. I have experienced the fact that the sun rises every morning. Does this give me the right to say that it will rise again tomorrow, when I haven’t actually experience this dawn yet? If it does rise then I will be certain, and in terms of the past, I know that it did rise, but now can I know that I will rise again tomorrow? It is perfectly possible, even if it were unexpected, that the sun might not rise.

Induction for Hume is based upon causal arguments. Our only knowledge of cause and effect is through experience itself because there is no logical reason why any causal relation should hold or not hold. I know that matches cause fires, because I know that from experience, not because matches logically contain fire. Just as we can only infer future behaviour of the world from the actual experience of the world, then we can only understand the category of causality from experience. In other words without experience we would not have the concept of causality as a generality. If I always experience the dawn as the rising of the sun then I conjoin this events. If A always follows B, then I will say that A causes B. This because I believe that the future always follows the same path as the past. So that if A happens, then B will happen. Linked to conjunction is contiguity and precedence. Contiguity means that B follows A in time and space, and precedence is that the effect is always after the cause. (the flame is after the lighted match and not before). It is because of conjunction, contiguity, and precedence, that we feel that we have good reason to say that A causes B, or that the sun will rise tomorrow. Hume assertion, however, is that this can never be a necessary reason, as is suggested by generalisation of a universal law however compelling I feel this causality to be.

Take the example of billiard balls, which seems the most basic relation of causality. The ball X hits the ball Y and causes it to move. But what do we mean by that? Do we mean that the ball X makes the ball Y move or that it produces its movement? We think there is a necessary connection between the two events. X moving and Y moving. What we experience is conjunction, contiguity and precedence, what we do not experience is some mysterious ‘necessary connection’. What we see is ball X and ball Y, what we do not see is some other third thing (like an invisible connection, indeed what we do not see is causality). What does it add to our explanation of the events, even if we were to add this mysterious cause. Wouldn’t the ball X and the ball Y just move in exactly the same way?

The point for Hume is just because two events have always in the past be conjoined, does not mean that we can be universally certain that they will always do so. The conclusion of inductive argument could be false but that would never make it invalid (indeed it might make it more interesting, as if the sun did not rise the next day), but this is never the case with a deductive argument if the premises are true, then the conclusion is necessarily true. What underpins the inductive generalisation is the belief that nature is well ordered spatially and temporally, that what happens many times will happen again in the same way. But that is just an assumption. Why must the future always be the same as the past and it certainly is not a logical contradiction if it were not.

Now of course we make these kind of inferences all the time, and Hume accepts that. I probably would not be able to live if I really though the sun would not rise tomorrow every time I went to bed. But this uniformity is a result of our psychology (perhaps it is an evolutionary trait) rather than reason or logic. We find regularity in nature because our habitual associations of events, and not because these events are necessarily connected.

There is no doubt that Hume’s problem is very profound and does make us look at induction more critically, but we might think that the idea that science itself is inductive in the simply way that inductivism implies is too simplistic. It is important to note that this is a very different critique from the methodological one. In the first case, we investigate the method of induction, and like Hume say that is flawed, or might even argue that Hume’s own account of induction is not a correct description of induction.[2] Whereas in the historical account of science, we are arguing whether the description of method is actually how scientists themselves work. One is a description of the content of scientific knowledge, the other is a description of the activity of scientists themselves. Do scientists really act the way that Hume’s example suggests they do? This is a completely different way of doing philosophy of science. For it does not first of all describe a method of doing science and then apply it to scientists, rather it examines what scientists do and from that derives the method. We shall see that this way of understanding science is going to be very important to Kuhn.

Why might we think that scientists do not use the inductive method in the way that induction has been described so far? Take the example of Newton’s Principia (Ladyman 2002, pp.55–6). Newton presents in this work the three laws of motion and the law of gravity. From these laws in explains natural phenomena like planetary motion. He says that he has inferred these laws through induction from observation. Now it is French philosopher of science Duhem that points out that there is a problem with Newton’s explanation. The data he is using is Kepler’s. His data proves that the planet will move in circles, whereas Newton’s in ellipses. This means that he could not have inferred gravity from Kepler’s data, rather he already the hypothesis of the law of gravity to interpret Kepler’s data. Again Newton’s first law state that bodies will maintain their state of motion unless acted upon by another body, but we have not observed a body that has not been acted upon, so this law could not be obtained through observation. Even Kepler’s theory could not have be derived from observation, because he took his data from Brahe, but could only organise it by already assuming that planets moved in circles, a hypothesis he didn’t receive from data, but from the mystical Pythagorean tradition.

So there are two reasons why we might be sceptical of the simple inductive explanation of science. One is methodological through the problem of induction (though we might come up with a better inductive method to solve this), and the other is historical, that science does not work in the way that theory of induction describes. I think the latter is the more serious issue than the former. For in the end science is what scientists do, and not what philosophers might idealise that they do.

Works Cited

Ladyman, J., 2002. Understanding Philosophy of Science, London; New York: Routledge.


[1] A group of philosophers from the 20th century called logical positivists also liked this distinction, and differentiated mathematical and logical truths, on the one hand, and science on the other. Anything that didn’t fit this schema was said to be nonsense or meaningless.

[2] This is what Ladyman does when he lists all the different ways in which we might counter Hume, the most telling being induction as the ‘best explanation’ (Ladyman 2002, pp.46–7).