Philosophy Essay 2
Does the Retreat to Probability Give us an Adequate Reply to the Sceptic about Induction?
In this essay, I will examine whether the retreat to probability solves the problem of induction. I will do this by firstly looking at ‘induction’ as a method of reasoning, and David Hume’s ‘problem of induction’ in two ways: descriptive and normative, and how this problem leads to a sceptical conclusion in both cases. I will then consider one of the solutions to the problem of induction- the ‘retreat to probable knowledge’, the notion that a conclusion is probable. However, this does not solve the problem as it does at first glance- there can be no solution that is not circular or question-begging. In this way, I will show that the retreat to probable knowledge fails to fulfil the problem of induction.
The Descriptive Problem of Induction
How do we gain knowledge about the world? Philosopher David Hume (1711-1776) divided propositions into two kinds: ‘relations of ideas’, and ‘matters of fact’ . An example of the former is ‘a triangle has 3 sides’. If I attempt to imagine its falsity, ‘I notice I am involved with some sort of contradiction or incoherence.’ Relations of ideas give us knowledge as I know that every triangle has 3 sides in advance of having to observe them. Therefore, relations of ideas can be known a priori (without observational evidence) and the denial of it is impossible or self-contradictory.
In contrast, matters of fact involve propositions where both it and its denial can easily be imagined and do not imply a contradiction, e.g. ‘the sun will rise tomorrow’. The contrary to this proposition is conceivable and the only way we come to have knowledge about matters of fact is through experience. Matters of fact give us information about the world as it is, as propositions of this kind do not rely on only the nature of our concepts. As ‘there are no innate concepts that our knowledge of the world is derived from’ , empiricists such as John Locke and George Berkeley deny that we can have knowledge of matters of fact a priori.
But if knowledge of propositions of this kind depends on observed evidence, then is it possible to have knowledge of unobserved matters of fact? It is true that we all have beliefs of this kind; for example, the belief that snow is cold. Hume explains that all reasoning that goes beyond what we have already experienced as based on ‘cause and effect’; any connection between logically unrelated ideas is based on a ‘causal connection’ between them. This is now known as ‘induction’- and is essentially the belief that the future will resemble the past (all snow we have ever observed has been cold so we infer that all snow is cold; the concepts of ‘cold’ and ‘snow’ are connected only by our reasoning that the future will resemble the past).
The Normative Problem of Induction
Induction is defined as the process of deriving a general law from particular instances. In a broad sense, induction is non-deductive inference, i.e. where the premises don’t logically entail the conclusion. For example,
P1. All Fs observed so far are also Gs
C. All Fs are Gs
This argument is non-deductive, as the conclusion is not necessary- simply because all Fs up to now have also been Gs, does not logically entail that all Fs in the future will also be Gs. In the narrow sense then, induction is generalisation from experience, but it should be thought of as extrapolating from the observed to the unobserved. Philosopher and logician, Charles Sanders Pierce called induction ‘ampliative’ as it can amplify or generalise our experience in order to broaden our empirical knowledge, whereas deduction is ‘explicative’ as it does not add to our knowledge- it only orders and rearranges it.
As opposed to deductive inferences then, inductive inferences are contingent (non-necessary); we can easily conceive the conclusion to be true or false without giving a contradiction. This means there can be no deductive argument that can justify induction, because induction as a method of reasoning involves ideas that are not logically related. In addition, any inductive argument for induction would be circular or question-begging- it is illegitimate to use an inductive argument to support induction as an inductive argument will only persuade us it is justified if we already accept that inductive arguments support their conclusions.
The problem is that good inductive reasoning can lead from true premises to a false conclusion by definition. So what grounds do we have for believing conclusions from inductive reasoning are justified? Hume was the first person to suggest that induction cannot be justified.
Perhaps induction fails on the basis it is non-deductive, i.e. that the argument is invalid as the conclusion does not follow from the premises. Hume suggests the inclusion of a further premise will make induction valid: that ‘the future will resemble the past’ (often called the Uniformity of Nature post-Hume).
Therefore, the inductive argument is as follows:
P1. All Fs observed so far are also Gs
P2. The future will resemble the past
C. All Fs are Gs (the next F will be a G)
The argument is now valid. The sceptic’s response is simply that we have no grounds for believing that the future will resemble the past (P2).
Effects are distinct from their causes; we can always conceive of one event occurring and the other not. This implies that causal reasoning or induction can't be a priori reasoning- it must be based on observation. However, there is no ‘self-evident’ relation between cause and effect; causal connections between events can only be observed from similar cases, but they can always be different in the future. The ‘crucial question in epistemology’ is to ask how it is possible for us to have any knowledge based on experience. If we base our knowledge on causal reasoning, which has no foundation other than the supposition that the future will resemble the past, then we have no reason to support rather than reject it.
The Sceptical Problem
What grounds can we have for believing the uniformity of nature? Its denial is perfectly conceivable- any law of nature could be violated tomorrow. Bertrand Russell’s famous example says that inductive reasoning may be as simple as that of a chicken whose owner ‘has fed [it] every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to [it].’ We justify the uniformity of nature by past experience (inductively), but induction is what we are trying to justify. No claims can be made on the basis of observation about the future, so the uniformity of nature can’t be known in this way. As explained above, all unobserved matters of fact are known by induction. However, any inductive argument includes the uniformity of nature as a premise; hence an inductive argument would be viciously circular.
The Retreat to Probable Knowledge
If induction has been proven to work most of the time, then we can say that it is very likely that it is a viable method of reasoning. For example, if every raven we have observed so far is black, then it is very likely that all ravens are black. Scientific knowledge is never completely certain, but ‘the more evidence we accumulate, the more certain we become’ . The argument is now as follows:
P1. The proportion p of observed Fs have also been Gs.
P2. a, not yet observed, is an F
C. It is probable that a is also a G
However, there is no end point for the process of gathering evidence for a statement. Having 100 percent certainty about a statement holding in the future is unattainable; any hypothesis- with any amount of evidence supporting it- may nevertheless be false. In response, some philosophers and probabilists would argue that we can come close enough to certainty to justify scientific knowledge. This is what is known as the ‘retreat to probable knowledge’.
But this method still extrapolates from the observed to the unobserved, so remains the same argument as the original. The inclusion of the unjustified ‘uniformity of nature’ as a premise is also still necessary, leaving us in the exact same position as before- we simply have no reason to believe this indispensable premise is true rather than false.
‘The retreat to probable knowledge does not give us any new grounds to believe [the uniformity of nature], so it does not seem to solve Hume’s problem.’6
The other problem with the retreat to probability is that any sample we observe is still a finite number, in comparison to the infinite number of cases in nature (in the total population). Therefore, the proportion of the sample to the population is always going to be negligible; the retreat to probability is insufficient to solve the problem of induction.
In conclusion, I have examined the problem of induction in Humean terms, and a particular solution to it: the retreat to probable knowledge. This does not lead us to any new information for how to solve the problem of induction. Hume does not seem threatened by this conclusion, as he says we all reason inductively by ‘custom’ as it seems to be part of our psychological disposition to do so. It seems that we have no justification for inductive reasoning- and the retreat to probability is certainly not sufficient to solve the problem of induction.
In this essay, I will examine whether the retreat to probability solves the problem of induction. I will do this by firstly looking at ‘induction’ as a method of reasoning, and David Hume’s ‘problem of induction’ in two ways: descriptive and normative, and how this problem leads to a sceptical conclusion in both cases. I will then consider one of the solutions to the problem of induction- the ‘retreat to probable knowledge’, the notion that a conclusion is probable. However, this does not solve the problem as it does at first glance- there can be no solution that is not circular or question-begging. In this way, I will show that the retreat to probable knowledge fails to fulfil the problem of induction.
The Descriptive Problem of Induction
How do we gain knowledge about the world? Philosopher David Hume (1711-1776) divided propositions into two kinds: ‘relations of ideas’, and ‘matters of fact’ . An example of the former is ‘a triangle has 3 sides’. If I attempt to imagine its falsity, ‘I notice I am involved with some sort of contradiction or incoherence.’ Relations of ideas give us knowledge as I know that every triangle has 3 sides in advance of having to observe them. Therefore, relations of ideas can be known a priori (without observational evidence) and the denial of it is impossible or self-contradictory.
In contrast, matters of fact involve propositions where both it and its denial can easily be imagined and do not imply a contradiction, e.g. ‘the sun will rise tomorrow’. The contrary to this proposition is conceivable and the only way we come to have knowledge about matters of fact is through experience. Matters of fact give us information about the world as it is, as propositions of this kind do not rely on only the nature of our concepts. As ‘there are no innate concepts that our knowledge of the world is derived from’ , empiricists such as John Locke and George Berkeley deny that we can have knowledge of matters of fact a priori.
But if knowledge of propositions of this kind depends on observed evidence, then is it possible to have knowledge of unobserved matters of fact? It is true that we all have beliefs of this kind; for example, the belief that snow is cold. Hume explains that all reasoning that goes beyond what we have already experienced as based on ‘cause and effect’; any connection between logically unrelated ideas is based on a ‘causal connection’ between them. This is now known as ‘induction’- and is essentially the belief that the future will resemble the past (all snow we have ever observed has been cold so we infer that all snow is cold; the concepts of ‘cold’ and ‘snow’ are connected only by our reasoning that the future will resemble the past).
The Normative Problem of Induction
Induction is defined as the process of deriving a general law from particular instances. In a broad sense, induction is non-deductive inference, i.e. where the premises don’t logically entail the conclusion. For example,
P1. All Fs observed so far are also Gs
C. All Fs are Gs
This argument is non-deductive, as the conclusion is not necessary- simply because all Fs up to now have also been Gs, does not logically entail that all Fs in the future will also be Gs. In the narrow sense then, induction is generalisation from experience, but it should be thought of as extrapolating from the observed to the unobserved. Philosopher and logician, Charles Sanders Pierce called induction ‘ampliative’ as it can amplify or generalise our experience in order to broaden our empirical knowledge, whereas deduction is ‘explicative’ as it does not add to our knowledge- it only orders and rearranges it.
As opposed to deductive inferences then, inductive inferences are contingent (non-necessary); we can easily conceive the conclusion to be true or false without giving a contradiction. This means there can be no deductive argument that can justify induction, because induction as a method of reasoning involves ideas that are not logically related. In addition, any inductive argument for induction would be circular or question-begging- it is illegitimate to use an inductive argument to support induction as an inductive argument will only persuade us it is justified if we already accept that inductive arguments support their conclusions.
The problem is that good inductive reasoning can lead from true premises to a false conclusion by definition. So what grounds do we have for believing conclusions from inductive reasoning are justified? Hume was the first person to suggest that induction cannot be justified.
Perhaps induction fails on the basis it is non-deductive, i.e. that the argument is invalid as the conclusion does not follow from the premises. Hume suggests the inclusion of a further premise will make induction valid: that ‘the future will resemble the past’ (often called the Uniformity of Nature post-Hume).
Therefore, the inductive argument is as follows:
P1. All Fs observed so far are also Gs
P2. The future will resemble the past
C. All Fs are Gs (the next F will be a G)
The argument is now valid. The sceptic’s response is simply that we have no grounds for believing that the future will resemble the past (P2).
Effects are distinct from their causes; we can always conceive of one event occurring and the other not. This implies that causal reasoning or induction can't be a priori reasoning- it must be based on observation. However, there is no ‘self-evident’ relation between cause and effect; causal connections between events can only be observed from similar cases, but they can always be different in the future. The ‘crucial question in epistemology’ is to ask how it is possible for us to have any knowledge based on experience. If we base our knowledge on causal reasoning, which has no foundation other than the supposition that the future will resemble the past, then we have no reason to support rather than reject it.
The Sceptical Problem
What grounds can we have for believing the uniformity of nature? Its denial is perfectly conceivable- any law of nature could be violated tomorrow. Bertrand Russell’s famous example says that inductive reasoning may be as simple as that of a chicken whose owner ‘has fed [it] every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to [it].’ We justify the uniformity of nature by past experience (inductively), but induction is what we are trying to justify. No claims can be made on the basis of observation about the future, so the uniformity of nature can’t be known in this way. As explained above, all unobserved matters of fact are known by induction. However, any inductive argument includes the uniformity of nature as a premise; hence an inductive argument would be viciously circular.
The Retreat to Probable Knowledge
If induction has been proven to work most of the time, then we can say that it is very likely that it is a viable method of reasoning. For example, if every raven we have observed so far is black, then it is very likely that all ravens are black. Scientific knowledge is never completely certain, but ‘the more evidence we accumulate, the more certain we become’ . The argument is now as follows:
P1. The proportion p of observed Fs have also been Gs.
P2. a, not yet observed, is an F
C. It is probable that a is also a G
However, there is no end point for the process of gathering evidence for a statement. Having 100 percent certainty about a statement holding in the future is unattainable; any hypothesis- with any amount of evidence supporting it- may nevertheless be false. In response, some philosophers and probabilists would argue that we can come close enough to certainty to justify scientific knowledge. This is what is known as the ‘retreat to probable knowledge’.
But this method still extrapolates from the observed to the unobserved, so remains the same argument as the original. The inclusion of the unjustified ‘uniformity of nature’ as a premise is also still necessary, leaving us in the exact same position as before- we simply have no reason to believe this indispensable premise is true rather than false.
‘The retreat to probable knowledge does not give us any new grounds to believe [the uniformity of nature], so it does not seem to solve Hume’s problem.’6
The other problem with the retreat to probability is that any sample we observe is still a finite number, in comparison to the infinite number of cases in nature (in the total population). Therefore, the proportion of the sample to the population is always going to be negligible; the retreat to probability is insufficient to solve the problem of induction.
In conclusion, I have examined the problem of induction in Humean terms, and a particular solution to it: the retreat to probable knowledge. This does not lead us to any new information for how to solve the problem of induction. Hume does not seem threatened by this conclusion, as he says we all reason inductively by ‘custom’ as it seems to be part of our psychological disposition to do so. It seems that we have no justification for inductive reasoning- and the retreat to probability is certainly not sufficient to solve the problem of induction.