Introduction:the nature of science 9 justified by the evidence,but this justification is inductive only in the former,broader sense.We need to distinguish between these two senses:I am happy to keep using the word "induction"with the broader sense;the narrow sense I will indicate by the phrase "Humean induction",for reasons that will become clear shortly. We saw earlier on that some forms of knowledge seem to be obtainable just by pure thinking while others require the making of observations and the gathering of data. Philosophers mark this distinction by the use of the terms a priori and a posteriori.A priori knowledge is knowledge that can be gained without the need for experience.(To be precise,a priori knowledge is knowledge that can be gained without any experience beyond that reguired to acguire the relevant concepts.This additional proviso is required because,without some experience,one may not be able to have the thought in question.) A posteriori knowledge is knowledge that is not a priori.So to have a posteriori knowledge experience is required.Pure mathematics and logic are usually taken to be examples of a priori knowledge,whereas most of chemistry and biology are a posteriori. Another concept used in this connection is that of an empirical proposition.Empirical propositions are those the truth or falsity of which can only be known a posterifori. If we take a typical generalization of science-all mammals possess a muscular diaphragm-we can see that it is empirical.Knowing what this proposition means is not sufficient for knowing whether it is true or false.To know that,we would have to go and examine at least some mammals.Then we would have to infer from our observations of a limited range of mammals that all,not just the ones we have seen,possess a muscular diaphragm.This is an inductive inference. It is often said that a priori knowledge is certain,and by implication empirical propositions like those discussed cannot be known with certainty."Certainty"is a slippery concept and is related to an equally slippery concept,"probability",which I will discuss in Chapter 6.One reason why a priori knowledge is thought to be certain in a way that a posteriori knowledge of empirical generalizations is not,is that the former is gained through deductive reasoning while the latter requires inductive reasoning.As we saw above,if the premises of a deductively valid argument are true,the conclusion must be true too,while the premises of an inductive argument might be true yet the conclusion still false.But we need to be careful here,for as we use the word "certain",we are certain of many empirical propositions:that we are mortal,that the water at 30C in my bath tonight will be liquid,and that this book will not turn into a pigeon and fly away.If someone asks why we are certain we may appeal to our past experience.But past experience does not entail these claims about the future.Whatever the past has been like, it is logically possible that the future will be different.One might argue from some natural law.It is a law of nature that people will die and that water at 30C is liquid.How are we certain about these laws of nature?Here again it is because we have reasoned on the basis of our experience that these are among the laws of nature.But this experience does not entail the existence of a law.For it may have been sheer chance that so many people have died,not a matter of law.So to reason that there is such a law and that we too are mortal is to reason inductively,not deductively.Yet it is still something of which we are certain,and in this sense induction can give us inductive certainty. So far I have said nothing to impugn the integrity of inductive argument;all I have done is to draw some rough distinctions between deductive and inductive reasoning.The fact that deductively valid arguments entail their conclusions in a way that inductivejustified by the evidence, but this justification is inductive only in the former, broader sense. We need to distinguish between these two senses: I am happy to keep using the word “induction” with the broader sense; the narrow sense I will indicate by the phrase “Humean induction”, for reasons that will become clear shortly. We saw earlier on that some forms of knowledge seem to be obtainable just by pure thinking while others require the making of observations and the gathering of data. Philosophers mark this distinction by the use of the terms a priori and a posteriori. A priori knowledge is knowledge that can be gained without the need for experience. (To be precise, a priori knowledge is knowledge that can be gained without any experience beyond that required to acquire the relevant concepts. This additional proviso is required because, without some experience, one may not be able to have the thought in question.) A posteriori knowledge is knowledge that is not a priori. So to have a posteriori knowledge experience is required. Pure mathematics and logic are usually taken to be examples of a priori knowledge, whereas most of chemistry and biology are a posteriori. Another concept used in this connection is that of an empirical proposition. Empirical propositions are those the truth or falsity of which can only be known a posteriori. If we take a typical generalization of science—all mammals possess a muscular diaphragm—we can see that it is empirical. Knowing what this proposition means is not sufficient for knowing whether it is true or false. To know that, we would have to go and examine at least some mammals. Then we would have to infer from our observations of a limited range of mammals that all, not just the ones we have seen, possess a muscular diaphragm. This is an inductive inference. It is often said that a priori knowledge is certain, and by implication empirical propositions like those discussed cannot be known with certainty. “Certainty” is a slippery concept and is related to an equally slippery concept, “probability”, which I will discuss in Chapter 6. One reason why a priori knowledge is thought to be certain in a way that a posteriori knowledge of empirical generalizations is not, is that the former is gained through deductive reasoning while the latter requires inductive reasoning. As we saw above, if the premises of a deductively valid argument are true, the conclusion must be true too, while the premises of an inductive argument might be true yet the conclusion still false. But we need to be careful here, for as we use the word “certain”, we are certain of many empirical propositions: that we are mortal, that the water at 30°C in my bath tonight will be liquid, and that this book will not turn into a pigeon and fly away. If someone asks why we are certain we may appeal to our past experience. But past experience does not entail these claims about the future. Whatever the past has been like, it is logically possible that the future will be different. One might argue from some natural law. It is a law of nature that people will die and that water at 30°C is liquid. How are we certain about these laws of nature? Here again it is because we have reasoned on the basis of our experience that these are among the laws of nature. But this experience does not entail the existence of a law. For it may have been sheer chance that so many people have died, not a matter of law. So to reason that there is such a law and that we too are mortal is to reason inductively, not deductively. Yet it is still something of which we are certain, and in this sense induction can give us inductive certainty. So far I have said nothing to impugn the integrity of inductive argument; all I have done is to draw some rough distinctions between deductive and inductive reasoning. The fact that deductively valid arguments entail their conclusions in a way that inductive Introduction: the nature of science 9