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Logic and Philosophy of Science

Modern day philosophy of science is, for better or worse, impossible without some grasp of logic. Many of its key ingredients are couched in logic. For this we have our old friends the logical positivists (or logical empiricists) to thank. This in fact provides us with a very nice, unified account of a whole bunch of key concepts which view various facets of science in terms of logical relationships. To a large extent, this kind of treatment pushed the more non-mathematical sciences to the margins for several decades, with physics taking pride of place. The demise of logical positivism brought with it a greater focus on sciences other than physics, especially biology which is now, within the philosophy of science, perhaps even more dominant than physics.

Making Inferences

A common mythical picture of scientists has them deducing theories about the world from the gathering of facts. This is the way of Sherlock Holmes, who was created precisely to be a "scientific detective" by Arthur Conan Doyle. A famous image has Holmes performing chemical tasks, with Watson looking on (figure 2.1). It is perfectly true that several of the practical methods used by Holmes made their way into forensics (e.g. fingerprinting and footprint analysis), but the methods he employed were not deductive as is claimed. If anything, they were what philosophers would call "abductive," or "inferences to the best explanation." There is no unique logical link between Holmes' theories and the evidence. For example, in Silver Blaze there appears the famous "curious incident of the dog in the night-time": despite what should have been a noisy event of the horse being led out of the stable block, the nearby dog did nothing - a null fact that leads Holmes to his suspicions that the horse was not stolen by a stranger, for the dog should surely have barked. This is, then, at best an inductive inference rather than a deduction - though, at the time of Doyle's writing, "deduction" referred to inference more generally. It is based on facts about dogs and what they usually do. This style of reasoning is nicely encapsulated in Holmes' dictum: "when you have excluded the impossible, whatever remains, however improbable, must be the truth" (eliminative induction).

Figure 2.1 Picture from the Sherlock Holmes story "The Adventure of the Naval Treaty," by Arthur Conan Doyle (illustration by Sidney Paget). The image caption reads: "Holmes was working hard over a chemical investigation."

Source: Wikimedia Commons

Much of science takes a similar form of inferences from evidence to theory. However, the approach of the Vienna Circle and its descendants did involve deductive logical relations (in the modern sense), though between statements of fact, rather than evidence and theory. Note also that often scientific discoveries are made in a way seemingly at odds with this Holmesian approach, and can involve guesswork and all manner of intuitive approaches to come up with a theory. The logical positivists would then detach this theory from its context of discovery and focus their attention only on how it was justified. Holmes' method, and indeed other inductive methods, assume that hypotheses themselves must also be subject to the rigors of the scientific method, just as much as their justification.

Scientists tell us lots of things that go against common sense, that we would not otherwise believe. They tell us that we are related to apes; that the universe is expanding; that there is no single Now separating past, present, and future; that the continents used to be locked together in a giant super-continent known as Pangaea (see figure 2.2). Why do we believe them? How did the scientists themselves come to these conclusions? After all, these are not the kinds of thing one can directly observe. They do it, of course, by employing a method: the fabled "scientific method." They arrive at their beliefs by a process of reasoning or inference, much as with Holmes, though with greater attention to the reliability and bias-free nature of the inferences. But what exactly is this process, and why is such confidence placed in it? In this chapter we answer these questions and show that, according to David Hume, our confidence in such an inferential picture is badly misplaced!

Figure 2.2 Alfred Wegener's reconstruction of the supercontinent of Pangaea as based on his theory of plate tectonics: Die Entstehung der Kontinente und Ozeane (The origin of continents and oceans), 1929, 4th edn

Source: Wikimedia Commons

Problems of Induction

According to empiricists, all of our information comes from observation (Nihil in intellectu nisi prius in sensu - "nothing in the understanding that did not get in there through the senses"). Inductivism is based on observation: this is the foundation-stone of inductive approaches. According to what we might call "naive inductivism," science starts with observation, this observation provides a secure base on which scientific knowledge is supported, and scientific knowledge is derived from observation using induction (inductive inferences). Rationalists, on the other hand, are not wedded to observation: some knowledge (about the world) can come from pure reason alone. So, according to empiricists, our knowledge is justified by our experience (observation, data, experiment). The objectivity and rationality of science is taken to rest on the role experience plays in choosing between hypotheses and in justifying those hypotheses.

Empirical observations, in the context of science, are explained by hypotheses of a general kind: the hypotheses apply to all of a class of events or phenomena, only a sample of which have or will ever be observed. Given this, how can we be sure that some theory that performs this explanatory function is the right one? There are surely many such possible theories that would do the job as well.

This is the problem of induction: how do we get from empirical observations to scientific theories? The Cambridge philosopher C. D. Broad called induction "the glory of science and the scandal of philosophy." We will see why that is still the case. Before we get to it, we have some initial material to review. (Note that this is by far the longest chapter in this book, since it contains most of the core issues that forged philosophy of science into what it is today. They are treated as a unity since the problems come from the same source, in the specific logical setup of central scientific concepts.)

Some Words on Logic

Since the problems we are going to deal with have a distinctly logical aspect (though the problem is really epistemological), let's now say something about logic and, especially, the difference between deduction and induction. Logic, in a nutshell, is about good and bad reasoning. Since ordinary language is often imprecise, it is difficult to assess reasoning in terms of it: so we (us philosophers) have to resort to formalism or, sometimes, just supplying very precise meanings to certain words. Here we simply review some of the more basic elements.

Firstly, what is an argument? This is one of the most basic notions in (scientific) reasoning. An argument consists of a set of premises (one or more) and a conclusion. The idea is that the premises give reasons for the conclusion. The premises are propositions: they can be either true or false. Good arguments are those such that the premises give good reasons for the conclusion and the premises are known to be true. Things go wrong, and we have a bad case of reasoning, when the premises do not support the conclusion.

Serious errors in logic are called "fallacies." A classic example is affirming the consequent. We will see this in action in the next chapter, when we look at ways of demarcating science and pseudoscience. One response to this latter problem is that science follows a "method." In particular, a popular account says it follows an inductive method: gather data and generalize from the data to make general laws; if an instance is found that backs the law, then we have confirmed the law. This is wrong, since the instance could have occurred in many ways, regardless of the law. An everyday example: "If it is raining, then the road will be wet," "the road is wet," therefore "it is raining." This is false: the road could be wet for any number of reasons (a hose-pipe, a water fight, a broken fire hydrant, etc.). Here "it is raining" is known as the "antecedent" and "the road will be wet" is known as the "consequent." If we'd have said: "If it is raining, then the road will be wet," "it is raining," therefore "the road is wet," then that would have been a good argument (it has its own fancy name: modus ponens): if the premises are true, then the conclusion has to be true.

Though the argument is rock-solid in terms of validity (i.e. the conclusion must be true if the premises are - this is a logician's term; it should not be confused with the ordinary-language usage of "valid"), we might still question the premises: and this would be a...