Induction – Lecture 2

October 10, 2016

BaconLast week we spoke about the difference between science and religion. We said it could be conceptualised as one between belief and facts. The more, we investigated, however, what a fact is, the less certain we became of its status as a starting point for scientific investigation. Common sense might tell us that facts are just out there and we simply observe them and scientific theories are merely collections of these observations, but when we look at the history of science, however, it is clear that this is not how science works. What we take as facts are already determined by the way we understand and see the world, and our observations are equally shaped by this background conceptuality. In the next two lectures, we are going to investigate the problem of induction, which is probably the classic form of the philosophy of science, and we shall see that we’ll come up against the same barrier again. Moreover, the knowledge that science has of the world cannot itself be infallible, because of the very way that it interprets these facts. In this lecture, however, we’ll give a positive account of induction through Francis Bacon’s method in Novum Organum (1620).[1]

Ordinarily we might think that scientific theories are obtained from facts through observation and this is what makes it different from belief. But what does it exactly mean that theories are obtained or derived from facts? How do we get from the one to the other? What we mean here is something logical rather than temporal. We don’t just mean that first of all there is a collection of facts, and then a theory, as though facts were just pebbles on a beach that we pick up. A theory, on the contrary, is supposed to tell us something about these facts before we have even discovered them. It is about meaning and context, rather than just what comes first or second in a temporal order.

What then do we mean by derivation when we speak about logic? We don’t have to go into the complexities of logic here but just the basic form since all we are interested is how theories originate from facts. Logic is based upon deduction. Here is a valid deductive argument, which comes from Ladyman:

All human beings are mortal

Socrates is a human being

Socrates is mortal. (Ladyman, 2002, p. 19)

1 and 2 are the premises and 3 is the conclusion. You cannot deny the conclusion if you take the premises as true. We can change the premises slightly, however, as Ladyman writes, and the deduction would be wrong.

All human beings are animals

Bess is an animal

Therefore Bess is a human being (Ladyman 2002, p.19)

What is important here is that it’s the form of the argument itself that is wrong. The conclusion does not follow from the premises even if one accepts them. Bess could be any kind of animal. What is positive about deductive arguments is that they are truth preserving. That is, if the premises are true and the argument is valid, then the conclusion is. The problem is that the conclusion does not contain any more information than the premises. It does not tell you anything more about the world and surely this is what science does. Although science uses logic and mathematics, it does tell us something new about the phenomena we observe. If it did not, then there wouldn’t be different theories about the world.

From this is follows that if science is derived from facts then it cannot be done so logically, because logic cannot tell us whether a fact is true or not. If we know there are true facts then we can logically relate them together (logic is ‘truth preserving’), but it is only from experience whether we know they are true or not. Take for example the scientific law that metal expands when it heats. It does not matter how many times that I repeat this, as Chalmers argues, it does not logically follow (as is implied below) that all metals will expand when heated:

metal x expanded when it was heated

metal y expanded when it was heated

metal z expanded when it was heated

All metals expand when heated (Chalmers, 1999, p. 44)

If scientific theories don’t come from facts logically, then how are they derived? The answer must be through experience itself; that is to say, inductively. What do we mean by induction? First of all the difference between deductive and inductive arguments is that in the latter the conclusion always goes beyond what is contained in the premises, as the example above shows. I can never be certain that all metals will expand when heated, because this is precisely what I assert when I move from a singular instances (this metal expands when heated) to the universal judgement that all do so.

How then can I adjudicate between a bad and good inductive argument in the way that I did with deductive ones? It would seem, through common sense, that I might be able to justify my universal judgements if I go through a number of singular observations. In other words, I observe a large number of samples of metal to investigate whether they do expand or not, and if I observe in this large number that they do, then I would be justified in asserting ‘All metals expand when heated’. Thus the laws of induction would be

1) The number of observations should be large

2) They must be repeated under a wide range of conditions

3) There should be no exceptions.

It is precisely for this reason that English philosopher and scientist Francis Bacon can up with his ‘new method’.[2] First of all this method is negative. The point is that we should avoid falling into bad arguments rather than coming up with new deductive ones. Bacon’s method is rules about how to practice science by avoiding some of the worst errors. These errors he called ‘idols of the mind’: that we tend to see order and regularity in nature when there is none is the idol of the tribe; that our judgements and are shaped by our language and concepts rather than what we see is the idol of the marketplace; and finally that are views of nature can be distorted by our philosophical and metaphysical systems of thought is the idol of the theatre.[3] From this follows the positive content of Bacon’s method that we ought to make observations of nature that are free of these idols. It is from the mass of information gained through observation that we should make generalisations, rather than understanding our observations through generalisations, which he accuses the philosophers of doing. This he calls the ‘natural and experimental history’.

It is important to understand what Bacon meant by observation is not just looking at the world, but doing experiments, and it this emphasis on experiments that distinguishes the new method from the old Aristotelian one.[4] It is experiments that preserve the objectivity of observations. First of all, it allows them to be quantified and secondly that they can be repeated by others and thus tested as to their reliability. It is this data from experiments that are then put into tables. To use then example from Bacon of heat: first we have the table of Essence and Presence that lists those things that are directly part of the phenomena of heat; secondly, we have the list of Deviation and Absence, which lists those phenomena that are related to the first but have no heat; and then we have the list of Comparison, where features that have a quantity of heat are listed and quantified. The empirical method is one of elimination. Let us say I argue that the colour white is explanation of heat. Then I would check my tables and I would see that not all the phenomena that hot are white, or that some phenomena that are white are not hot and so on. White, then, could not be part of theory of heat. Through this process of elimination Bacon explained that heat was caused by the ‘extensive motion of parts’, which is not far from the modern kinetic theory of heat.

Bacon believed one can discover the forms that made what we observed possible, even though they were not directly perceivable. These forms where the direct physical cause of what we saw. This was the rejection of final causes, where natural phenomenon where viewed as purposive. The Aristotelian explanation, for example, that stones fall to the ground was because the earthly element sought to fall to the centre of the earth. Teleological explanations such as these are only suitable for human actions (since humans unlike stones do have desires) but not natural phenomena. The ubiquity of physical causes is the major different between new empirical science of the 17th century and the old science of Aristotle’s era that had dominated the explanation of nature for so long.

There are, however, problems with induction. First of all, what is the status of the non-observed forms that are the physical cause of what we observe. How can we make a leap from what is seen to what is not seen? It is possible to see how heat might be explained by Bacon’s method since in fact we can see the motion, but how would we go about explaining radiation? Also we see in science that there can be two competing forms that explain the same visible phenomena such as the two theories of light, for example. Bacon does have an answer for the last problem. He says that we ought to set up two competing experiments that would test what we observe and we could see which was the more successful. But this already demonstrates what we might doubt about Bacon’s new method. In this case are not the theories themselves determining the experiments and not what we observe? Bacon says that science is made from two pillars: observation and induction and that we ought to be able to observe nature without prejudice (the prejudices being the idols of the mind). This is perhaps what most people think that science is. We take many particular instances and then we generalise a law. Yet the problem is how we account for this mysterious leap from the particular to the universal. How many instances make a general law and if there is an exception does this mean that law is no longer a law?

There are, then, two problems with the principle of induction as Bacon describes it. One is that we might doubt that any observation is unprejudiced. This is not just in a negative sense as Bacon describes it, but also positively, that without a theory it is hard to know what one would observe in the first place. Secondly, we might worry about how it is possible to go from many observations to a general law. Just because X has happened many times before, how do we know we know that it will happen again? This problem of induction, as it is called, and was introduced by the Hume, and has for many made naïve ‘inductivism’ untenable. We shall investigate this problem in next week’s lecture.

Works Cited

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

Gaukroger, S., 2001. Francis Bacon and the Transformation of Early-Modern Philosophy. Cambridge University Press.

Harrison, P., 2007. Was there a Scientific Revolution? European Review 15, 445–457.

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


[1] Although Newton had not read Bacon’s work, his scientific method was widely seen as following his account of induction, and through the fame of the former, has become the ‘common sense’ view of science. For a general account of the importance of Bacon for the image of science, see (Gaukroger, 2001).

[2] See (Ladyman, 2002, pp. 22–5) for this summary of Bacon’s method.

[3] As we can see, what Bacon sees as idols, we might see as unavoidable necessities and this precisely prevents us from accepting the inductive explanation of science.

[4] On the importance of experiments to Bacon’s conception of science, and the subsequent transformation of science from a solitary to a communal affair, see (Harrison, 2007).

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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).


Induction – Lecture 2

October 7, 2015

BaconLast week we spoke about the difference between science and religion. We said it could be conceptualised as one between belief and facts. The more, we investigated, however, what a fact is, the less certain we became of its status as a starting point for scientific investigation. Common sense might tell us that facts are just out there and we simply observe them and scientific theories are merely collections of these observations, but when we look at the history of science, however, it is clear that this is not how science works. What we take as facts are already determined by the way we understand and see the world, and our observations are equally shaped by this background conceptuality. In this lecture, we are going to investigate the problem of induction, which is probably the classic form of the philosophy of science, and we shall see that we’ll come up against the same barrier again. Moreover the knowledge that science has of the world cannot itself be infallible, because of the very way that it interprets these facts.

Ordinarily we might think that scientific theories are obtained from facts through observation and this is what makes it different from belief. But what does it exactly mean that theories are obtained or derived from facts? How do we get from the one to the other? What we mean here is something logical rather than temporal. We don’t just mean that first of all there is a collection of facts, and then a theory, as though facts were just pebbles on a beach that we pick up. A theory, on the contrary, is supposed to tell us something about these facts before we have even discovered them. It is about meaning and context, rather than just what comes first or second in a temporal order.

What then do we mean by derivation when we speak about logic? We don’t have to go into the complexities of logic here but just the basic form since all we are interested is how theories originate from facts. Logic is based upon deduction. Here is a valid deductive argument, which comes from Ladyman:

All human beings are mortal

Socrates is a human being

Socrates is mortal. (Ladyman 2002, p.19)

1 and 2 are the premises and 3 is the conclusion. You cannot deny the conclusion if you take the premises as true. We can change the premises slightly, however, as Ladyman writes, and the deduction would be wrong.

All human beings are animals

Bess is an animal

Therefore Bess is a human being (Ladyman 2002, p.19)

What is important here is that it’s the form of the argument itself that is wrong. The conclusion does not follow from the premises even if one accepts them. Bess could be any kind of animal. What is positive about deductive arguments is that they are truth preserving. That is, if the premises are true and the argument is valid, then the conclusion is. The problem is that the conclusion does not contain any more information than the premises. It does not tell you anything more about the world and surely this is what science does.

From this is follows that if science is derived from facts then it cannot be done so logically, because logic cannot tell us whether a fact is true or not. If we know there are true facts then we can logically relate them together (logic is ‘truth preserving’), but it is only from experience whether we know they are true or not. Take for example the scientific law that metal expands when it heats. It does not matter how many times that I repeat this, as Chalmers argues, it does not logically follow (as is implied below) that all metals will expand when heated:

metal x expanded when it was heated

metal y expanded when it was heated

metal z expanded when it was heated

All metals expand when heated (Chalmers 1999, p.44)

If scientific theories don’t come from facts logically, then how are they derived? The answer must be through experience itself; that is to say, inductively. What do we mean by induction? First of all the difference between deductive and inductive arguments is that in the latter the conclusion always goes beyond what is contained in the premises, as the example above shows. I can never be certain that all metals will expand when heated, because this is precisely what I assert when I move from a singular instances (this metal expands when heated) to the universal judgement that all do so.

How then can I adjudicate between a bad and good inductive argument in the way that I did with deductive ones? It would seem, through common sense, that I might be able to justify my universal judgements if I go through a number of singular observations. In other words that I observe a large number of samples of metal to investigate whether they do expand or not, and if I observe in this large number that they do, then I would be justified in asserting ‘All metals expand when heated’. Thus the laws of induction would be

1) The number of observations should be large

2) They must be repeated under a wide range of conditions

3) There should be no exceptions.

It is precisely for this reason that English philosopher and scientist Francis Bacon can up with his ‘new method’.[1] First of all this method is negative. The point is that we should avoid falling into bad arguments rather than coming up with new deductive ones. Bacon’s method is rules about how to practice science by avoiding some of the worst errors. These errors he called ‘idols of the mind’: that we tend to see order and regularity in nature when there is none is the idol of the tribe; that our judgements and are shaped by our language and concepts rather than what we see is the idol of the marketplace; and finally that are views of nature can be distorted by our philosophical and metaphysical systems of thought is the idol of the theatre.[2] From this follows the positive content of Bacon’s method that we ought to make observations of nature that are free of these idols. It is from the mass of information gained through observation that we should make generalisations, rather than understanding our observations through generalisations, which he accuses the philosophers of doing. This he calls the ‘natural and experimental history’.

It is important to understand what Bacon meant by observation is not just looking but experiments, and it this emphasis on experiments that distinguishes the new method from the old Aristotelian one. It is experiments that preserve the objectivity of observations. First of all it allows them to be quantified and secondly that they can be repeated by others and thus tested as to their reliability. It is this data from experiments that are then put into tables. To use then example from Bacon of heat: first we have the table of Essence and Presence that lists those things that are directly part of the phenomena of heat; secondly, we have the list of Deviation and Absence, which lists those phenomena that are related to the first but have no heat; and then we have the list of Comparison, where features that have a quantity of heat are listed and quantified. The empirical method is one of elimination. Let us say I argue that the colour white is explanation of heat. Then I would check my tables and I would see that not all the phenomena that hot are white, or that some phenomena that are white are not hot and so on. White, then, could not be part of theory of heat. Through this process of elimination Bacon explained that heat was caused by the ‘extensive motion of parts’, which is not far from the modern kinetic theory of heat.

Bacon believed one can discover the forms that made what we observed possible, even though they were not directly perceivable. These forms where the direct physical cause of what we saw. This was the rejection of final causes, where natural phenomenon where viewed as purposive. The Aristotelian explanation, for example, that stones fall to the ground was because the earthly element sought to fall to the centre of the earth. Teleological explanations such as these are only suitable for human actions (since humans unlike stones do have desires) but not natural phenomena. The ubiquity of physical causes is the major different between new empirical science of the 17th century and the old science of Aristotle’s era that had dominated the explanation of nature for so long.

There are, however, problems with induction. First of all what is the status of the non-observed forms that are the physical cause of what we observe. How can we make a leap from what is seen to what is not seen? It is possible to see how heat might be explained by Bacon’s method since in fact we can see the motion, but how would we go about explaining radiation? Also we see in science that there can be two competing forms that explain the same visible phenomena such as the two theories of light, for example. Bacon does have an answer for the last problem. He says that we ought to set up two competing experiments that would test what we observe and we could see which was the more successful. But this already demonstrates what we might doubt about Bacon’s new method. In this case are not the theories themselves determining the experiments and not what we observe? Bacon says that science is made from two pillars: observation and induction and that we ought to be able to observe nature without prejudice (the prejudices being the idols of the mind). This is perhaps what most people think that science is. We take many particular instances and then we generalise a law. Yet the problem is how we account for this mysterious leap from the particular to the universal. How many instances make a general law and if there is an exception does this mean that law is no longer a law? There are two problems with the principle of induction as Bacon describes it. One is that we might doubt that any observation is unprejudiced. This is not just in a negative sense as Bacon describes it, but also positively, that without a theory it is hard to know what one would observe in the first place. Secondly, we might worry about how it is possible to go from many observations to a general law. Just because X has happened many times before, how do we know we know that it will happen again? This problem of induction, as it is called, and was introduced by the Hume, and has for many made naïve inductivism untenable. We shall investigate this problem in next week’s lecture.

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.


[1] See (Ladyman 2002, pp.22–5) for this summary of Bacon’s method.

[2] As we can see, what Bacon sees as idols, we might see as unavoidable necessities and this precisely prevents us from accepting the inductive explanation of science.


Induction – Lecture 2

October 13, 2014

MiracleLast week we spoke about the difference between science and religion. We said it could be conceptualised as one between belief and facts. The more, we investigated, however, what a fact is, the less certain we became of its status as a starting point for scientific investigation. Common sense might tell us that facts are just out there and we simply observe them and scientific theories are merely collections of these observations, but when we look at the history of science, however, it is clear that this is not how science works. What we take as facts are already determined by the way we understand and see the world, and our observations are equally shaped by this background conceptuality. In this lecture, we are going to investigate the problem of induction, and we shall see that we’ll come up against the same barrier again. Moreover the knowledge that science has of the world cannot itself be infallible, because of the very way that it interprets these facts.

Ordinarily we might think that scientific theories are obtained from facts through observation and this is what makes it different from belief. But what does it exactly mean that theories are obtained or derived from facts? How do we get from the one to the other? What we mean here is something logical rather than temporal. We don’t just mean that first of all there is a collection of facts, and then a theory, as though facts were just pebbles on a beach that we pick up. A theory, on the contrary, is supposed to tell us something about these facts before we have even discovered them. It is about meaning and context, rather than just what comes first or second in a temporal order.

What then do we mean by derivation when we speak about logic? We don’t have to go into the complexities of logic here but just the basic form since all we are interested is how theories originate from facts. Logic is based upon deduction. Here is a valid deductive argument, which comes from Ladyman:

All human beings are mortal

Socrates is a human being

Socrates is mortal. (Ladyman 2002, p.19)

1 and 2 are the premises and 3 is the conclusion. You cannot deny the conclusion if you take the premises as true. We can change the premises slightly, however, as Ladyman writes, and the deduction would be wrong.

All human beings are animals

Bess is an animal

Therefore Bess is a human being (Ladyman 2002, p.19)

What is important here is that it’s the form of the argument itself that is wrong. The conclusion does not follow from the premises even if one accepts them. Bess could be any kind of animal. What is positive about deductive arguments is that they are truth preserving. That is, if the premises are true and the argument is valid, then the conclusion is. The problem is that the conclusion does not contain any more information than the premises. It does not tell you anything more about the world and surely this is what science does.

From this is follows that if science is derived from facts then it cannot be done so logically, because logic cannot tell us whether a fact is true or not. If we know there are true facts then we can logically relate them together (logic is ‘truth preserving’), but it is only from experience whether we know that they are true. Take for example the scientific law that metal expands when it heats. It does not matter how many times that I repeat this, as Chalmers argues, it does not logically follow (as is implied below) that all metals will expand when heated:

metal x expanded when it was heated

metal y expanded when it was heated

metal z expanded when it was heated

All metals expand when heated (Chalmers 1999, p.44)

If scientific theories don’t come from facts logically, then how are they derived? The answer must be through experience itself; that is to say, inductively. What do we mean by induction? First of all the difference between deductive and inductive arguments is that in the latter the conclusion always goes beyond what is contained in the premises, as the example above shows. I can never be certain that all metals will expand when heated, because this is precisely what I assert when I move from a singular instances (this metal expands when heated) to the universal judgement that all do so.

How then can I adjudicate between a bad and good inductive argument in the way that I did with deductive ones? It would seem, through common sense, that I might be able to justify my universal judgements if I go through a number of singular observations. In other words that I observe a large number of samples of metal to investigate whether they do expand or not, and if I observe in this large number that they do, then I would be justified in asserting ‘All metals expand when heated’. Thus the laws of induction would be

1) The number of observations should be large

2) They must be repeated under a wide range of conditions

3) There should be no exceptions.

It is precisely for this reason that English philosopher and scientist Francis Bacon can up with his ‘new method’.[1] First of all this method is negative. The point is that we should avoid falling into bad arguments rather than coming up with new deductive ones. Bacon’s method is rules about how to practice science by avoiding some of the worst errors. These errors he called ‘idols of the mind’: that we tend to see order and regularity in nature when there is none is the idol of the tribe; that our judgements and are shaped by our language and concepts rather than what we see is the idol of the marketplace; and finally that are views of nature can be distorted by our philosophical and metaphysical systems of thought is the idol of the theatre.[2] From this follows the positive content of Bacon’s method that we ought to make observations of nature that are free of these idols. It is from the mass of information gained through observation that we should make generalisations, rather than understanding our observations through generalisations, which he accuses the philosophers of doing. This he calls the ‘natural and experimental history’.

It is important to understand what he meant by observation is not just looking but experiments and it this emphasis on experiments that distinguishes the new method from the old Aristotelian one. It is experiments that preserve the objectivity of observations. First of all it allows them to be quantified and secondly that they can be repeated by others and thus tested as to their reliability. It is this data from experiments that are then put into tables. To use then example from Bacon of heat: first we have the table of Essence and Presence that lists those things that are directly part of the phenomena of heat; secondly, we have the list of Deviation and Absence, which lists those phenomena that are related to the first but have no heat; and then we have the list of Comparison, where features that have a quantity of heat are listed and quantified. The empirical method is one of elimination. Let us say I argue that the colour white is explanation of heat. Then I would check my tables and I would see that not all the phenomena that hot are white, or that some phenomena that are white are not hot and so on. White, then, could not be part of theory of heat. Through this process of elimination Bacon explained that heat was caused by the ‘extensive motion of parts’, which is not far from the modern kinetic theory of heat.

Bacon believed one can discover the forms that made what we observed possible, even though they were not directly perceivable. These forms where the direct physical cause of what we saw. This was the rejection of final causes, where natural phenomenon where viewed as purposive. The Aristotelian explanation, for example, that stones fall to the ground was because the earthly element sought to fall to the centre of the earth. Teleological explanations such as these are only suitable for human actions (since humans unlike stones do have desires) but not natural phenomena. The ubiquity of physical causes is the major different between new empirical science of the 17th century and the old science of Aristotle’s era that had dominated the explanation of nature for so long.

There are, however, problems with induction. First of all what is the status of the non-observed forms that are the physical cause of what we observe. How can we make a leap from what is seen to what is not seen? It is possible to see how heat might be explained by Bacon’s method since in fact we can see the motion, but how would we go about explaining radiation? Also we see in science that there can be two competing forms that explain the same visible phenomena such as the two theories of light, for example. Bacon does have an answer for the last problem. He says that we ought to set up two competing experiments that would test what we observe and we could see which was the more successful. But this already demonstrates what we might doubt about Bacon’s new method. In this case are not the theories themselves determining the experiments and not what we observe? Bacon says that science is made from two pillars: observation and induction and that we ought to be able to observe nature without prejudice (the prejudices being the idols of the mind). This is perhaps what most people think that science is. We take many particular instances and then we generalise a law. Yet the problem is how we account for this mysterious leap from the particular to the universal. How many instances make a general law and if there is an exception does this mean that law is no longer a law? There are two problems with the principle of induction as Bacon describes it. One is that we might doubt that any observation is unprejudiced. This is not just in a negative sense as Bacon describes it, but also positively, that without a theory it is hard to know what one would observe in the first place. Secondly, we might worry about how it is possible to go from many observations to a general law. Just because X has happened many times before, how do we know we know that it will happen again? This problem of induction, as it is called, and was introduced by the Hume, and has for many made naïve inductivism untenable. We shall investigate this problem in next week’s seminar.

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.

[1] See (Ladyman 2002, pp.22–5) for this summary of Bacon’s method.

[2] As we can see, what Bacon sees as idols, we might see as unavoidable necessities and this precisely prevents us from accepting the inductive explanation of science.


Induction – Lecture 2

October 9, 2013

Last week we spoke about the difference between science and religion. We said that this difference could be conceptualised as one between belief and facts. The more, we investigated, however, what a fact is, the less certain we became of its status. Common sense might tell us that facts are just out there and we simply observe them and scientific theories are merely a collections of these observations. When we look at the history of science, however, it is clear that this is not how science works. What we take as facts are already determined by the way we understand and see the world, and our observations are equally shaped by this background conceptuality. In this lecture, we are going to investigate the problem of induction, and we shall see that we’ll come up against the same barrier again. Science is not just a disinterested observation of facts, but is already predetermined in some way or other to interpret these facts. Moreover the knowledge that science has of the world cannot itself be infallible, because of the very way that it interprets these facts.

Ordinarily we might think that scientific theories are obtained from facts through observation and this is what makes it different from belief. But what does it exactly mean that theories are obtained or derived from facts? How do we get from the one to the other? What we mean here is something logical rather than temporal. We don’t just mean that first of all there is a collection of facts, and then a theory, as though facts were just pebbles on a beach that we pick up. A theory, on the contrary, is supposed to tell us something about these facts before we have even discovered them. It is about meaning and context, rather than just what comes first or second in a temporal order.

What then do we mean by derivation when we speak about logic? We don’t have to go into the complexities of logic here but just the basic form since all we are interested is how theories originate from facts. Logic is based upon deduction. Here is a valid deductive argument, which comes from Ladyman:

All human beings are mortal

Socrates is a human being

Socrates is mortal. (Ladyman 2002, p.19)

1 and 2 are the premises and 3 is the conclusion. You cannot deny the conclusion if you take the premises as true. We can change the premises slightly, however, as Ladyman writes, and the deduction would be wrong.

All human beings are animals

Bess is an animal

Therefore Bess is a human being (Ladyman 2002, p.19)

What is important here is that it’s the form of the argument itself that is wrong. The conclusion does not follow from the premises even if one accepts them. Bess could be any kind of animal. What is positive about deductive arguments is that they are truth preserving. That is, if the premises are true and the argument is valid, then the conclusion is. The problem is that the conclusion does not contain any more information than the premises. It does not tell you anything more about the world and surely this is what science does.

From this is follows that if science is derived from facts then it cannot be done so logically, because logic cannot tell us whether a fact is true or not. If we know that there are true facts then we can logically relate them together (logic is ‘truth preserving’), but it is only from experience whether we know that they are true. Take for example the scientific law that metal expands when it heats. It does not matter how many times that I repeat this, as Chalmers argues, it does not logically follow (as is implied below) that all metals will expand when heated:

metal x expanded when it was heated

metal y expanded when it was heated

metal z expanded when it was heated

All metals expand when heated (Chalmers 1999, p.44)

If scientific theories don’t come from facts logically, then how are they derived? The answer must be through experience itself; that is to say, inductively. What do we mean by induction? First of all the difference between deductive and inductive arguments is that in the latter the conclusion always goes beyond what is contained in the premises, as the example above shows. I can never be certain that all metals will expand when heated, because this is precisely what I assert when I move from a singular instances (this metal expands when heated) to the universal judgement that all do so.

How then can I adjudicate between a bad and good inductive argument in the way that I did with deductive ones? It would seem, through common sense, that I might be able to justify my universal judgements if I go through a number of singular observations. In other words that I observe a large number of samples of metal to investigate whether they do expand or not, and if I observe in this large number that they do, then I would be justified in asserting ‘All metals expand when heated’. Thus the laws of induction would be

1) The number of observations should be large

2) They must be repeated under a wide range of conditions

3) There should be no exceptions.

It is precisely for this reason that English philosopher and scientist Francis Bacon can up with his ‘new method’.[1] First of all this method is negative. The point is that we should avoid falling into bad arguments rather than coming up with new deductive ones. Bacon’s method is rules about how to practice science by avoiding some of the worst errors. These errors he called ‘idols of the mind’: that we tend to see order and regularity in nature when there is none is the idol of the tribe; that our judgements and are shaped by our language and concepts rather than what we see is the idol of the marketplace; and finally that are views of nature can be distorted by our philosophical and metaphysical systems of thought is the idol of the theatre.[2] From this follows the positive content of Bacon’s method that we ought to make observations of nature that are free of these idols. It is from the mass of information gained through observation that we should make generalisations, rather than understanding our observations through generalisations, which he accuses the philosophers of doing. This he calls the ‘natural and experimental history’.

It is important to understand that what he meant by observation is not just looking but experiments and it this emphasis on experiments that distinguishes the new method from the old Aristotelian one. It is experiments that preserve the objectivity of observations. First of all it allows them to be quantified and secondly that they can be repeated by others and thus tested as to their reliability. It is this data from experiments that are then put into tables. To use then example from Bacon of heat: first we have the table of Essence and Presence that lists those things that are directly part of the phenomena of heat; secondly, we have the list of Deviation and Absence, which lists those phenomena that are related to the first but have no heat; and then we have the list of Comparison, where features that have a quantity of heat are listed and quantified. The empirical method is one of elimination. Let us say I argue that the colour white is explanation of heat. Then I would check my tables and I would see that not all the phenomena that hot are white, or that some phenomena that are white are not hot and so on. White, then, could not be part of theory of heat. Through this process of elimination Bacon explained that heat was caused by the ‘extensive motion of parts’, which is not far from the modern kinetic theory of heat.

Bacon believed that one can discover the forms that made what we observed possible, even though they were not directly perceivable. These forms where the direct physical cause of what we saw. This was the rejection of final causes, where natural phenomenon where viewed as purposive. The Aristotelian explanation, for example, that stones fall to the ground was because the earthly element sought to fall to the centre of the earth. Teleological explanations such as these are only suitable for human actions (since humans unlike stones do have desires) but not natural phenomena. The ubiquity of physical causes is the major different between new empirical science of the 17th century and the old science of Aristotle’s era that had dominated the explanation of nature for so long.

There are, however, problems with induction. First of all what is the status of the non-observed forms that are the physical cause of what we observe. How can we make a leap from what is seen to what is not seen? It is possible to see how heat might be explained by Bacon’s method since in fact we can see the motion, but how would we go about explaining radiation? Also we see in science that there can be two competing forms that explain the same visible phenomena such as the two theories of light, for example. Bacon does have an answer for the last problem. He says that we ought to set up two competing experiments that would test what we observe and we could see which was the more successful. But this already demonstrates what we might doubt about Bacon’s new method. In this case are not the theories themselves determining the experiments and not what we observe? Bacon says that science is made from two pillars: observation and induction and that we ought to be able to observe nature without prejudice (the prejudices being the idols of the mind). This is perhaps what most people think that science is. We take many particular instances and then we generalise a law. Yet the problem is how we account for this mysterious leap from the particular to the universal. How many instances make a general law and if there is an exception does this mean that law is no longer a law? There are two problems with the principle of induction as Bacon describes it. One is that we might doubt that any observation is unprejudiced. This is not just in a negative sense as Bacon describes it, but also positively, that without a theory it is hard to know what one would observe in the first place. Secondly, we might worry about how it is possible to go from many observations to a general law. Just because X has happened many times before, how do we know we know that it will happen again? This problem of induction, as it is called, and was introduced by the Scottish philosopher Hume, has for many made naïve inductivism untenable. We shall investigate this problem in next week’s lecture.

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.


[1] See (Ladyman 2002, pp.22–5) for this summary of Bacon’s method.

[2] As we can see, what Bacon sees as idols, we might see as unavoidable necessities and this precisely prevents us from accepting the inductive explanation of science.