Falsification – Lecture 4

November 30, 2014

Karl_PopperWhat we want is some criterion which will allow us to distinguish science from any other discourse. In other words what makes science, science, as opposed to religion? What is specific to the method of science? Our simplest response to this question is that science deals with facts that are objective (out there in some way) and that religion has to do with belief and is subjective. We might want to say, then, that science is true, and religion is not. When we looked at this simple definition, however, the less certain and clear it seemed. For the idea that science is made up of many observations of facts that are then converted into theories breaks down in the problem of induction, which, in its most succinct form, is the impossibility of leaping from a singular judgement to a universal one. No amount of logical finessing will get you from a particular to a universal. This would seem to imply that science is no more objective than religion, and that a theory is as much a belief as any faith.[1]

Moreover, it was also clear that the inductionist picture of science was not accurate at all, since facts are not just littered throughout the world such that we pick them up and notice common characteristics from which we then construct some universal law. On the contrary, we already come to facts with a pre-existing theory, which determines which fact we take as relevant or not (or even which fact we can see). As Ladyman explained, Newton did not find the law of gravity in Kepler’s data, he already had to have it in order to interpret the data (Ladyman 2002, pp.55–6).

This reversal of the relation between theory and facts, that theory is first and facts second, is the basis of the next philosophy of science that we shall look at, Popper’s theory of falsification, and indeed rose out of the insurmountable problems of ‘inductionism’. His argument is that we should give up induction as the basis of science, but such a rejection would not lead to irrationalism. Rather we substitute for induction, deduction. But did we not argue already in last lecture that deduction could not be the basis of science, since deduction is merely tautological? Deductive logic tells us nothing new about the world, but only analyses what we already know, whereas as would say that science actually tells us something about nature that we didn’t know before.

Deduction does not work as a basis of science only if we move from the singular to the universal, but if we go from the universal back to the singular then deduction does work. Indeed, this move from the universal back to the singular is exactly, Popper argues, how science operates. We do not start with facts and then make laws, rather we start with laws and then we attempt to test them with facts. The logical point is that we can’t go from observations to theories, even if the observations themselves are true, but it is possible the other way around. We can go from theories then back to observational statements to show that the theory is false. Thus to use Chalmers example, if someone was to see a white raven outside the lecture room today, then this would prove deductively that the statement ‘All Ravens are black’ is false. Such deductive arguments are known as modus tollens, which take the form if P, then Q. ⌐Q, therefore ⌐P (Chalmers 1999, p.61).

When we look at the history of science, this seems exactly what happens. Take for the example, Eddington’s proof of Einstein’s theory that gravity bends light. If the theory was correct then a star that was beyond the sun should be displaced from the direction of the observer so that we could see it. Normally the light from the sun would mean that these starts would not be visible to us, but would be if the light of the sun was blocked. Eddington managed to measure just such a displacement with the eclipse of the sun in 1919. For Popper, the point of this story is that he could have proved otherwise. In other words, Einstein’s theory could have been falsified, if there had not been any displacement.

The real difference between science and religion or any other discourse is not the theories or hypotheses that they put forward, but how they test them. Popper is adamant that science is creative as any other human discourse and that the origin of this creativity is outside any logical explanation. That someone comes up with such an idea at such a time cannot be rationally explained. Thus we don’t know how Galileo or Einstein came up with their ideas, and why not someone else, or at different time and place, but what we do know that what makes these creations scientific, as opposed to anything else is that they can be falsified (this is the difference between context of discovery and context of justification). In the opposite case, it does not seem possible to falsify a religion logically. I can always find a reason to believe something. Think for example of the classic problem of evil in theology. How do I justify the existence of God with evil in the world? It is perfectly possible to find such a reason, as Leibniz did that this is the ‘best of all possible worlds’, and it is just our lack of human understanding that prevents us from seeing it so.

Here we might need to know a little of the story of Popper’s life. When he was young he was a communist and of course Marxism was treated as a science. He says that one day in went on a march with his friends and they were attacked by the police and some of them were killed. He was so shaken by this incident that he had to speak about to his political leaders. They told him that these deaths were necessary for the political emancipation of the workers as was explained by scientific Marxism. But what then would falsify Marxism, for they did not seem to be any instance, including the death of his friends that could not be explained by it.[2]

This is precisely the difference between a science and a pseudo-science (religion is only a pseudo-science when it takes itself to be answering scientific questions, otherwise it is perfectly meaningful for Popper): a pseudo-science has the answer to everything and can never not be true, whereas a science does not have the answer to everything and can always be false. It is this that demarcates, to use Popper’s word, empirical science, from anything else and it is a question of method, rather than logical form, by which he means the positivist obsession with the correlation of statements with aspects of reality. Metaphysics and religion are only pseudo sciences when they pretend to be sciences. If they do not, then there is nothing intrinsically wrong with them. They are certainly not meaningless which is just derogatory word, rather than having any useful philosophical sense.

If what makes a scientific theory scientific is falsification, what exactly makes a falsification? Can any falsification be scientific? Such a broad generalisation does not seem to be correct because just to falsify something would not make it a scientific theory. I could falsify physics, by quoting Genesis but no one would think that I was being scientific. The answer here is intersubjective testability. One cannot conceive of how it would be possible to set up an experiment that would test my falsification of physics that claimed God had created the universe in the way that it is described in Genesis. One can imagine, however how it might be possible to test the falsification of Newtonian science through the prediction made by Einstein, which is entirely what the example from Eddington proves, and it is perfectly possible that other scientists could conceive of such an experiment, whether in principal or in practice.[3]

Could a theory always secure itself by simple adding an ad hoc modification every time a falsification was produced? Thus, to use Chalmers’s example, we could take the generalisation that all bread was nutritious to be falsified by the death all the members of French village who ate bread. We could then qualify our theory by saying that all bread is nutritious except when it is eaten by these members of the French village and we could do this every time any falsification was discovered. Such ad hoc modification would completely destroy any progress in scientific discovery. How then can we distinguish between an authentic and inauthentic ad hoc modification (Chalmers 1999, p.75). In this example, the modification cannot be falsified, so it does not tell us anything new about the world. It in fact tells us less than the original theory that all bread nourishes. So an authentic modification must be one that is also falsifiable. If we had said instead that all bread nourishes except one that is contaminated by certain fungus called Claviceps purpurea, then this would be an authentic ad hoc modification, since it could be tested and falsified, and thus does tell us something new about the world.

This distinction between authentic and inauthentic ad hoc modifications of scientific theories, however, tells us that we should not over-estimate falsifications of theories. When we look at the history of science we can see that ad hoc modifications can confirm rather than deny a theory. Take the case of the discovery of Neptune. Irregularities in the orbit of Uranus predicted that there must be another planet that had not be observed. Rather than reject Newton’s theory, scientists argued that a planet must exist that would explain it. Thus, the fact that Neptune was found in 1846 confirmed Newton’s theory rather than falsified it. Rather than seeing science as just a series of falsifications which lead from theory to the next, Aristotelianism to Newtonism to Einstein, we should see it as the confirmation of bold conjectures and the falsification of cautious ones. For what difference does it make to science if one falsifies conjectures such as the universe is made of porridge or confirms a cautious one? But how then do we determine what make a bold conjecture? The only answer to this must be background theories themselves, for only in relation to them could we know what would be bold or timid. The background knowledge is therefore the cautious conjecture (what we take to be correct) and the bold conjecture flies in the face of what everyone thinks is the case. We can see, then, what the real fundamental difference between the falsificationist and inductionist is. The first takes the history of science seriously, and the second has no conception of the history of science at all. There is no background knowledge. Rather facts are accumulated as though there were no context at all and science existed in the eternal present.

Is falsification immune to criticism then? The answer must be unfortunately not. The real problem is still the relation to the theory and the observation. All we can say deductively is that if there is O, then the falsity of T follows if the O is not given, but it tells us nothing about the standard of the evidence itself. What if the evidence is incorrect? Perhaps when person who said that the raven was white and no idea what white was. Perhaps the photograph of the white raven was created in Photoshop, and no such evidence exists.  Popper does not have a better story about the correctness of evidence than the positivist.

Moreover, when we actually look at science, it does not take the simple form of ‘All swans are White’…. Rather, sciences are made up of complex collection of universal statements which are interrelated to one another.  Now if a prediction tells us the theory is false it tells is that one of the premises might be wrong but not which one or even that our own experience might be the problem.  It might not the theory that is out, but the ‘test situation’ itself, because we cannot isolate the premise which allows us to falsify the theory (this is known as the Duhem/Quine thesis). So to use Ladyman’s example, if we were to try and predict the path of a comet, the law of gravity would not be sufficient, so if the predication were incorrect we would not know that it was the theory of gravity that was being falsified or something else (Ladyman 2002, pp.77–8).

Even if such an isolation were possible, falsification does not seem to capture actually what science and scientists do, for when we look at the history of science we do not find one great conjecture following another, but that scientists stick to their theories despite the fact that they can be falsified or they adopt a new hypothesis even though all the known evidence at the time should have killed them off at birth. This is what we find when we look at the detail of the eventual transition from the Aristotelian to the Copernican view of the world as Feyerabend and Kuhn describe it. It is certainly was not the simple falsification of the one by the other. Science works, to some extent, because scientists are dogmatic and not open to falsification. If that is the case, how is it possible to differentiate, or demarcate, science from any other dogma? Will we not have to use different criteria?

Works Cited

Chalmers, A.F., 1999. What is this Thing Called Science?, St. Lucia, Qld.: University of Queensland.

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

Popper, K.R., 2002. Unended quest, London; New York: Routledge.


[1] When we look at science as a method this is a problem. We might ask, however, if we think of science as an activity, whether it is such a problem.

[2] The source of this story can be found in Popper’s autobiography (Popper 2002, pp.30–8).

[3] Does this open Popper to a more pragmatic account of science than an epistemological one? For if testability is inter-subjective how are we to describe it? Popper appears to want to separate questions of method from question of practice, but later criticisms will in turn want to question this distinction by asking whether it is really the case, when we look at the history of science, that scientist really are committed to the principle of falsifiability.



November 8, 2014

DescartesOne of the difficulties of reading Descartes’ Meditations is that it has become such a part of our philosophical culture, indeed our culture as a whole (who has not heart of the famous cogito ego sum), that we can just read the text without really making any attempt to understand it. Moreover, the apparent ease of our interpretation means we can even think that we can easily dismiss these arguments, because everyone knows them and they hardly require any thought whatsoever.

The simplicity of this reading has more to do with our ignorance, however, rather than our deep understanding. It is because we are unaware of the context of Descartes’ argument, why he wrote the Meditations as he did, and especially their revolutionary nature, that we can easily be misled as to their depth and originality. The most important element of this context is the rise of the new sciences in the 16th and 17th century. Before he saw himself as a philosopher, Descartes viewed himself (if these different functions were really as separable to him and his contemporaries, as they might be to us), as a scientist and a mathematician. He wrote a philosophy as a defence of the new science, and the importance of the mathematical method, rather than just a work of philosophy in itself.

If we are going to understand how revolutionary the new science was, and why Descartes believed it required a different metaphysics to support it, then we have to recognise, if however succinctly and briefly, that metaphysics it rejected, which was Aristotelianism. Aristotle’s understanding of nature was the dominant picture of reality. The problem of dislodging this picture was not just that the new science rejected it, but that its hold on people’s imaginations was so prevalent and dominant. This is because Aristotle’s philosophy is the philosophy of common sense. It describes what we see around us, and thus to reject it is to reject everything we know around us. We can see why Descartes’ method in the Meditations is sceptical, because before he can reinstitute the new science on a secure ground, he must first of all get us to reject what we ordinarily take to be knowledge of the world.

Let us compare, therefore, an Aristotelian account of vision from a Cartesian one (Hatfield 2014, pp.291–4). We today might be very blasé about Descartes’ mechanical explanation of colour, because we take for granted the physiological explanation of colour (colour is nothing but the interaction of the spectrum of light with the retina), but it would have sounded strange to his contemporaries. In the Aristotelian conception of sensation, my perception of external objects is caused by the real qualities of those objects. Thus if I see a red rose then my perception of ‘red’ is caused by the red qualities of that rose. The red exists in the rose, travels to my eye, and thereby causes my sensation of red. As we can see, this seems to be a very common sense view of what happens when we see things (and there are probably people who still think that this is what it means to physically ‘see’ the colour red). For Descartes, on the contrary, there are no ‘red’ things as such. On the contrary, for Descartes, nature is nothing but matter in motion. Matter is corpuscular (infinitely divisible particles). The quality of red in the object, therefore, and its interaction with the eye, can be explained by the shape, size and motion of these particles. Colour is caused by the surface of the object I am looking at, which refracts light particles that interact with the eye. Descartes is not denying that we see red, but that red cannot be explained by a real quality called red. Rather the phenomenon ‘red’ requires a deeper explanation that can only be provided scientifically through the kind of mechanical model that Descartes describes

Although there are specific problems with Descartes’ explanation of colour, which will wait for the modern developments in optics, we can see that we are in two totally different scientific worlds. Fundamentally for Aristotle, everything that exists is explained through form and matter. It is the form of something that explains what it is. Thus to understand what it a tree is one has to understand the ‘form’ tree. If we are looking at an oak tree, then the form would be contained in the acorn. This is true, just as much for animate as well as inanimate things. So to explain the sun, we also have to understand the form of the sun, as well as its material existence (which for Aristotle was the four elements, plus the mysterious fifth one, aether). For Descartes, there is only a material explanation of nature. If one wants to understand the sun, then one needs to understand the nuclear fusion of hydrogen to helium. Moreover, these material laws are the same for all objects in nature and the whole of nature itself. The explanation of our sun would be the same as for all suns in the universe, and these explanations would be would be the same for everything that exists (that is, matter in motion, which can be mathematical defined).

The different physics of Aristotle and Descartes means that they have completely different metaphysics. The basis of the universe for Aristotle is individual substances. Because matter is not sufficient to explain what it is to be something, there cannot be a material explanation of nature. Each thing is an individual substance, which is the specific conjunction of form and matter, whether we are speaking of a tree or animal, me or you, the sun and the other stars. For Descartes, there is only one thing that exists and that is matter in motion, and every individual thing we see is only a property or a mode of this one material substance. Things differ only because matter differs (there is a difference is shape, size and motion of particles), not because there is an extrinsic difference between them. We can see in Aristotle’s metaphysics, that we need an explanation for each thing, whereas for Descartes, we only need a few simple laws of motion (three), in order to explain everything that we see, and that these simple laws of motion, since they have to only to do with shape, size and motion, can be explained quantitatively (that is mathematically) other than qualitatively in the Aristotelian system.

Only now with this scientific background, can we really begin to understand the Meditations. Descartes’ scepticism, at the beginning, then, is not merely an amusing thought experiment, which will later become the plot of the film Matrix, but presupposes the fundamental break that modern science has taken with the common sense perception of the world. For the hypothesis that nature is matter in motion is precisely that a hypothesis, which one can quite literally not see, and thus what I see cannot itself be true. Thus, the task for Descartes is not to destroy our knowledge of the world, but to rebuild it, but where the foundations will be more secure, no longer resting on our fallible senses, but reliable understanding and reason. Scepticism is not employed for its own sake, or even to make philosophy impossible, but on the contrary, to make our knowledge of the world even more certain, by showing that sceptical arguments can be defeated if our metaphysics is robust enough.

It is for this reason why we can Descartes’ takes his doubt much further than classical scepticsm. We should not only doubt our senses, for we know that they tell us lies about the world (is that pencil really bent that I see in the glass of water), but also the world of mathematics and even the status of reality itself. How do I know that this is not all a dream, since my dreams have been as vivid as my perception of the world right now, and why it is not possible that a malicious demon hasn’t put into my head the idea that 4+4 = 8, when it really is 9?. Now all these sound a bit excessive if we don’t know the scientific context of these doubts. If the truth of reality is in fact mathematical, then the question Descartes is really asking is how I know that this mathematical reality is real, when there is nothing in my ordinary experience that would verify it.

If I can doubt everything in reality, even that my mathematical ideas are a true representation of what is real, then there is one thing, Descartes argues, that I cannot doubt, and that I am thinking. For even if I doubt everything, there is one thing I cannot doubt and that is in the very act of doubting, I am in fact doubting. What is important at this point in Descartes’ argument is not to confuse the status of the ‘I’ in the statement ‘I think therefore I am’. This I is not me as physical being. The ‘I’ that stands before you know, the ‘I’ that is writing this lecture on the computer. My physical reality is just as doubtful as the reality of the rest of physical nature. Also this ‘I’ only exist in the very moment of thinking. Only in the very act of thinking can the ‘I’ be said to exist, because it is self-refuting to argue otherwise. Even if I say, ‘I do not exist’, it is I who am thinking this, and so must exist in the moment I think it.

Though the cogito is very limited in one sense, it also includes a lot more than one might first assume. First of all Descartes includes all acts of consciousness, such remembering, desires, and most importantly for us, perceiving. Thus when I desire something, I exist in the moment of desiring, when I remember something I exist in the moment of remembering it, and when I perceive something, I exist in the moment of perceiving it. When I perceive a something I exist in perceiving it. Of course, following from radical doubt of the first meditation, I don’t know whether what I perceive is the same as what is in reality (it really could be all a dream, or mathematical code as in the film Matrix), but I cannot doubt that I am perceiving the chair. Secondly, and this is going to be very important when we come to look at the wax example, the content of what I think, desire, remember and perceive is also real Again, it is not real, as in ‘out there’, but real in my mind. So when, I am thinking, remembering, desiring, perceiving a chair, I really am thinking, remember, desiring, perceiving a chair, even though I don’t know whether a chair real exists.

What is going here, which is very important for understanding Descartes’ metaphysics, is that he is totally changing our idea of truth. Normally when we think of truth (and it should not surprise us, when we think of what we said about science above, that this too has a long Aristotelian heritage), we think of it as adequation. That is, we think that truth is about how we speak about the external world. When I say to you ‘There is chair’, you take this statement to be true, because there is a chair in the real world that corresponds to the statement. Now Descartes’ cannot appeal to this notion of truth, because at the moment of the status of the real world has been bracketed (I don’t know whether the world is true or not). He therefore replaces the truth as adequation, with truth as coherence. An idea is true because it is clear and distinct in my mind. The cogito is therefore a measure of what it is to be true since is self-evident that to have a thought there must be an ‘I’ that thinks it. But we can also say that the idea of triangle as a three sided figure is true, whereas the idea of square circle is not. Not because there are no square circle in the world, but because the idea itself does not make sense since it is incoherent.

When we come to the example of the wax in the third mediation, therefore, we can become completely confused if we think Descartes is talking about the external perception of the wax, because this is precisely what he has given up (we don’t know what the real wax is, because we don’t even know if reality is real). What he is describing is our idea of the wax, how the wax appears to us, even if we don’t whether the wax is real or not. His first description, then, is how the idea of wax appear to us when we take the wax as something we perceive, but perception means here, perception as an action of thought (I am thinking about how the wax is perceived by me), and not perception as the sensation of an external object that I take to exist really outside of me and which effects my sense and which I then think of as was (our example of real qualities and the red flower above). If we were to take that Descartes was doing the latter, then we would be confusing him with Aristotelian account of perception.

What then do I think I perceive when I think that the idea of wax is sensation? I have a list of properties that describe the wax. It smells of flowers; it tastes of honey; it makes a sound when you tap it; it is hard and cold to the touch; and it is white and the shape of a cube. Doesn’t this, then, tell us exactly what the wax is. Why would we need to know anymore? We remember, though that Descartes is sitting in a warm room (it tells us at the beginning of the Meditations). With the heat of the room, all the properties of the wax change: there is no fragrance of flowers; no sweetness of honey; no sound when a hit it; it is not hard and cold; it is no longer white and shaped like a cup. How, therefore, can the sense tell us what the wax is, since now it is completely change. The idea of the wax under the thought of perception is a completely confused idea. However, even though I know the wax has completely changed, it is nonetheless the same piece of wax that remained the same throughout this transformation. What is this wax? It can’t be the list of properties of the sensation because these are completely different. It must be what remains when we strip away all these properties that have changed in our idea of the wax itself. What is it that remains? It is the idea of the body in general as ‘something extended, flexible and changeable’. [AT VII, 30] Although I cannot experience this body, since it would have innumerable shapes that I cannot imagine, I nonetheless can think it, and the idea of this body is less confused and incoherent understanding of the wax in general, than what is present by the idea of sensation. Going back to Descartes’ definition of truth, it is, therefore more true.

At this point we haven’t got outside the cogito itself. I can say that the idea of extension as the correct understanding of bodies, rather than their real qualities, might make more sense, but it does not mean that the what the wax is in the real world is anything like that at all. At this stage, extension (that matter is extended in three dimensions) as the explanation of all the phenomena we see, including the secondary phenomena of the senses, is merely a hypothesis. To prove that nature in itself is like that, we need to get outside of our minds. But how are going to do that? Through the proof of the existence of God, because the idea of God is a very strange idea, and necessitates the actual existence of the content of the idea, in the way that no other idea I have does.

Descartes is not the first philosopher to use the ontological proof for the existence of God, but it does have a particular form in his philosophy, so it is worth going into it in a little more detail. Also, we need to remember what kind of work the proof is doing. Descartes is not proving the existence of God because he lacks faith. He already believes in God. He does not need a proof. We are speaking here of a philosophical concept of God and not a religious one (although as we shall see with Spinoza’s criticism of Descartes, he might sneak a theological notion within this concept). The concept of God is solving a philosophical problem for Descartes, how do we know that are scientific hypothesis that we cannot see with our senses, is actually telling us the truth about the world, and not a crisis of faith.

One of the problems for the modern reader following Descartes proof is that he uses Scholastic terminology that they might not know.[1] Let us briefly explain this jargon before we look at the argument itself. When it comes to ideas in our minds, Descartes makes three important distinctions: objective reality, formal reality and eminent reality. The objective idea of the triangle is the idea of the triangle insofar as it represents a thing. The objective reality is not the thing represented, but the representation. One of the best ways to think of this is in terms of the operation of an image, though we should be careful here not thinking that Descartes thought that all representation were images. Thus when we say that a picture is a picture of something we can distinguish between what the picture is and what the picture represents. In the case of a picture of a tree for example, we can distinguish between the picture and the tree that is represented in the picture.

What is much more difficult is the idea of formal reality in Descartes. It is much more difficult because Descartes himself seems to be confused about it. We could interpret formal reality to be the actual existence of the thing that is represented in the idea. But this would admit the existence of external things, whereas we are only talking about the nature of ideas. Formal reality is the part of the definition of the idea and not the description of a thing. Many misunderstandings of Descartes have to do with confusing the formal reality of the idea with the reality of a thing. On the contrary, the formal reality of the idea describes the status of the idea itself. Whatever idea we speak of and whatever this idea might represent, the idea itself exists. Again if we go back to our picture example, being mindful that ideas are not pictures for Descartes, so that this is only an analogy, then we can make a distinction between the picture, on the one hand, and what the picture represents on the other. Now the picture, on this analogy, is the formal idea. That is to say idea of the tree itself, and not the tree that is represented in the idea.

Now for Descartes ideas themselves and not just what they represent in the idea, have degrees of reality. The best way to understand what Descartes means by ‘degrees of reality’ here is degree of perfection, otherwise again you are going to get confused and think that he is speaking about real external things. Now for Descartes it is possible to say that some ideas, formally speaking are more perfect than other’s. The idea itself is more perfect and not just what is represented in the idea (though it is true to say that when we are speaking about perfection these two are connected). Thus to use Deleuze’s example from his own lectures, the idea of frog is less perfect than the idea of God (Deleuze 1978). It is the idea itself that is more perfect, that is to say its formal reality, and not just what is represented in the idea, that is to say its objective reality. The idea of God does not just have more objective reality than the idea of frog; rather it has more formal reality than any other idea. The idea of God, therefore, for Descartes, has eminent reality. Of course the immediate question we need to ask is why is the idea of God more perfect than any other idea? But before we get to this question we need to think about how Descartes explains the relation between objective and formal reality, for this is the basis of the proof of the existence of God

This relation is essentially causal for Descartes. That is to say that the formal idea is the cause of the objective idea. We might put it this way. In the absence of the idea of the frog, they would be no ‘frog’ as an object of the idea. This means for Descartes that the idea of the frog, it formal reality, is the cause of the objective reality of the frog. It is not just the causality of ideas that we need to be aware of, but also, as we have already seen, that reality means for Descartes ‘degrees of perfection’. The proof for the existence of God is a combination of causality and perfection. Thus the formal reality not only causes the objective reality to exist, but also the degree of perfection that this idea has. Descartes regards it as a fundamental axiom that more cannot come from less. If the formal reality is the cause of the objective reality, then there must be as much reality in the formal reality as there is in the objective reality. We need to be very careful that we are speaking about ideas and not objects, and the best way to thing about it is again in terms of a picture. Descartes’ argument is that a picture will have more reality than any other one the more reality that the object of the picture has. Thus to use Bernard William’s example: a picture of a pile of sticks will have less reality than a picture of a complex machine, precisely because the complex machine, as an objective reality, has more reality than a pile of sticks (Williams 2005, p.124). The best way to think of think of the relation between objective and formal relations, when it comes causality and perfection, is therefore backwards. From the complexity of the object of thought we go back to the complexity of the idea which is the origin of this thought.

The question, then, is how I get from this relation between formal and objective reality of ideas to the proof of the existence of God. Again we need to remember that this is a causal relation for Descartes. The idea must have as much reality, perfection or complexity, as the object that it represents. In Descartes language, it contains formally as much reality as the object contains objectively. But this does not present it having more reality than the object it represents. In this instance, Descartes says it contains eminently what the object of thought only contains formally. But how does this further distinction get us any closer to the idea of God? Descartes asks whether it is possible that there is one idea that contains formally what I cannot be the cause of objectively; that is to say, whether there is an idea whose objectively reality, whose object of thought cannot have its origin in me.

Thus if I look at all the content of my ideas, I can see that they can all have their origin in me, but the objective reality of the formal idea of God cannot. Why is that? What is it about the idea of God that means that its objective reality cannot be inside of me and that it must exist outside of me? It is because the very formal idea of God, the definition of God, contains an objective reality that I could not be the cause of because I know that I myself am an imperfect being. We have already agreed that what has less perfection cannot be the cause of something that has more perfection. I could be, Descartes argues, the cause of all my other ideas, since objectively they contain nothing more than I contain formally, but I cannot be the origin of the content of the formal idea of God, the objective reality of God, since this objective reality contains more perfection than I do. That is to say my picture of God is less than the objective reality of the idea, and thus could not be its cause. This idea must be caused by something that existed outside of me, and it must contain formally speaking as much reality as the objective reality of the idea of God. Only God could be the cause of the idea of God.

So the idea of God necessarily proves that God exists and we have a little chink in the armour of the cogito. There is one thing I know that exist outside of my idea of it, and that is God. But why would that solve my problem with the wax. Why would the existence of God demonstrate that my idea of wax must be what the wax is in nature? It is the existence of God that guarantees the existence of external objects, and also that my idea of these objects correspond to the true nature of external objects. What I can clearly and distinctly perceive is true, but without God this truth would not be sufficient, since although I am perceiving this truth in my mind, there might be nothing like it in the outside world. If I can prove that God exists, then it follows that everything depends upon him, since God is the only perfection, and such a God could not deceive me. It follows, therefore, what I clearly and distinctly perceive, and I can remember having done so, must be actually true.

The success of Descartes’ metaphysical project rests on the existence of God. It would not surprise many readers that no manner philosophers, even immediately so, were convinced by it. Cartesian science itself was pretty much left behind with the success of Newton (though he was clearly influenced by Descartes). However, I want to refer to one important critique of Descartes, which is Spinoza. He was as rationalist as Descartes (and thus his critique is very different from the empiricists and Kant that we will look at next week), but his argument with Descartes is that he did not take his ideas seriously enough. In other words, Spinoza want to out Descartes Descartes.

Spinoza issue with Descartes is that he smuggles a theological conception of God into his philosophical idea of God, and that is the idea of creation. There are in fact three substances in Descartes: the two finite substances, mind and matter, and the infinite substance God. This mirrors the theological distinction in the idea of creation of the difference between transcendence and immanence. Now the transcendent God is beyond the comprehension of the finite mind (this is the turning point of the ontological proof for Descartes, I know that God exists, but I don’t know what God is, and God in his absolute power could have created a world in which triangles have 4 sides and 2+2=5. For Spinoza this is absurd. If there were a difference between an infinite God and a finite world, then God would not be infinite, since God would lack something; that is the finite world that is different from him. Also God could not be governed by different laws (as though God were a capricious tyrant), because this would mean that laws that came from God could have been different, but this too would mean that God would lack something, which would be the laws that he did not create. If God is infinite, and we start with this infinite, then the idea of transcendent wilful God that is still at the heart of Descartes’ project (which Spinoza will explain is only anthropomorphic idea of God), must be a fiction. ‘God,’ Spinoza writes, is the immanent, not the transitive, cause of all things’ (1P18).

Rather than explaining attributes in relation to infinite substance, Descartes has explained substance in relation to attributes, and this is why he has ended up with three substances, rather than one unique substance, God, whose essence must infinite attributes (not just two) that express themselves through infinitely many things and ideas. We must begin, Spinoza is saying, with the infinite universe and explain are place within it, rather than projecting an image of ourselves onto this infinite universe.


Deleuze, G., 1978. Les Cours de Gilles Deleuze. Sur Spinoza. Available at: http://www.webdeleuze.com/php/texte.php?cle=14&groupe=Spinoza&langue=2 [Accessed October 9, 2014].

Hatfield, G.C., 2014. The Routledge guidebook to Descartes’ Meditations,

Williams, B., 2005. Descartes: The Project of Pure Enquiry, Psychology Press.

[1] This shows that Descartes was not as far from the Scholastics as some have presented him, and indeed, how he sometimes presents himself.

The Problem of Induction – Lecture 3

November 2, 2014


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).