The history of philosophy is intertwined with the history of the natural sciences. Long before the 19th century, when the term science began to be used with its modern meaning, Aristotle (384–322 BC) was the first great biologist. René Descartes (1596-1650) formulated analytic geometry (“Cartesian geometry”) and discovered the laws of reflection and refraction of light. Gottfried Wilhelm Leibniz (1646-1716) claimed priority in inventing the calculus. Finally, Immanuel Kant (1724–1804) provided the basis for a still current hypothesis about the formation of the solar system (the Kant-Laplace nebular hypothesis).

Background of the Philosophy of Science

Reflecting on human knowledge, the great philosophers also offered accounts of the aims and methods of the sciences. These range from Aristotle’s studies in logic to the proposals of Francis Bacon (1561-1626) and Descartes. They were fundamental in the configuration of science in the seventeenth century. These reflections were joined by the most eminent natural scientists.

Galileo (1564-1642) supplemented his arguments on the motions of the heavenly and earthly bodies with statements about the role of mathematics. In the same way, he experimented to discover facts about nature. Similarly, Isaac Newton’s (1642-1727) account of his natural world system is marked by a defense of his methods and an outline of a positive program for scientific inquiry. Antoine-Laurent Lavoisier (1743–94), James Clerk Maxwell (1831–79), Charles Darwin (1809–82), and Albert Einstein (1879–1955) continued this tradition, offering their own insights into the character of scientists.

The early 20th century

Since the beginning of the 20th century, the philosophy of science has been more aware of its proper role. Some philosophers continue to work on problems that are continuous with the natural sciences. They have continued to explore, for example, the character of space and time or the fundamental characteristics of life. They contribute to the philosophy of the special sciences, a field with a long tradition of distinguished work in the philosophy of physics. More recent contributions have been made in the philosophy of biology and the philosophy of psychology and neuroscience. The general philosophy of science, on the contrary, seeks to illuminate broad characteristics of the sciences, continuing the inquiries begun in Aristotle’s discussions of logic and method.

Logical positivism and logical empiricism

A series of developments in philosophy in the early 20th century made the general philosophy of science central to philosophy in the English-speaking world. They were inspired by the articulation of mathematical logic, or formal logic. For example, in the work of the philosophers Gottlob Frege (1848-1925) and Bertrand Russell (1872-1970) and the mathematician David Hilbert (1862-1943).

In this regard, a group of known European philosophers while the Vienna Circle tried to diagnose the difference between the inconclusive debates that mark the history of philosophy and the steadfast achievements of the sciences that they admired. They offered criteria of significance, or “cognitive significance,” with the aim of showing that traditional philosophical questions (and their proposed answers) are meaningless.

The correct task of philosophy, they suggested, is to formulate a “logic of science” that would be analogous to the logic of pure mathematics formulated by Frege, Russell, and Hilbert. In the light of logic, they thought, genuinely fruitful investigations could free themselves from the obstacles of traditional philosophy. To carry out this daring program, a strict criterion of significance was required. Unfortunately, when they tried to use the tools of mathematical logic to specify the criteria, the logical positivists (as they came to be known) encountered unexpected difficulties.

Faced with these disappointing results, logical positivism evolved into a more moderate movement, logical empiricism. Many historians of philosophy treat this movement as a late version of logical positivism and consequently do not refer to it by any other name. The logical empiricists took as a central task the understanding of the distinctive virtues of the natural sciences.

Discovery and Justification Logics

Following Hans Reichenbach (1891-1953), philosophers often distinguished between the “context of discovery” and the “context of justification.” Once a hypothesis has been proposed, there are canons of logic that determine whether it should be accepted or not. That is, there are rules of method that are maintained in the context of justification.

However, there are no such rules that guide someone to formulate the correct hypothesis, or even hypotheses that are plausible or fruitful. Logical empiricists reached this conclusion by reflecting on cases in which scientific discoveries were made by leaps and bounds or by lucky accidents. A favorite example was the hypothesis by August Kekulé (1829-1896) that benzene molecules have a hexagonal structure. They were supposedly formed while he was dozing in front of a fire in which the embers seemed to resemble a snake that devoured its tail.

Thomas Kuhn’s work

Although the idea that there can be no logic of scientific discovery often assumed the status of orthodoxy, it was not unquestionable. As will become clear later, one of the implications of Thomas Kuhn’s (1922-1996) influential work on the philosophy of science was that considerations about the probability of future discoveries of particular types are sometimes intertwined with judgments of evidence.

In this way, discovery can be dismissed as an irrational process only if one is willing to admit that irrationality also infects the context of justification itself. The most ambitious response to empiricist orthodoxy attempted to do exactly what was abandoned as desperate. That is, specifying formal procedures for producing hypotheses in response to a set of available tests. These programs were applied in several traditionally difficult areas of natural and social scientific research. Perhaps, then, logical empiricism was premature in dismissing the context of discovery as beyond the scope of philosophical analysis.

The philosophy of science and the logical empiricists

In contrast, the logical empiricists worked vigorously on the problem of understanding scientific justification. Inspired by the thought that Frege, Russell, and Hilbert had given a completely precise specification of the conditions under which the premises deductively imply a conclusion.

Philosophers of science hoped to offer a “confirmatory logic” that would identify, with equal precision, the conditions under which a body of evidence supported a scientific hypothesis. They recognized, of course, that a series of experimental reports on the expansion of metals under heat would not deductively imply the general conclusion that all metals expand when heated.

Even if all reports were correct, it would still be possible that the next metal to examine itself did not expand under the heat. However, it seemed that a sufficiently large and varied collection of reports would provide some support, even strong support, for generalization. The philosophical task was to pin down this intuitive judgment about support.

The work of Carnap and Hempel

During the 1940s, two prominent logical empiricists, Rudolf Carnap (1891-1970) and Carl Hempel (1905-1997), made influential attempts to solve this problem. Carnap offered a valuable distinction between various versions of the question. The “qualitative” confirmation problem seeks to specify the conditions under which a body of evidence E supports, to some extent, a hypothesis H. The “comparative” problem seeks to determine when a body of evidence E supports a hypothesis H rather than a set The evidence E * supports a hypothesis H * (here E and E * could be the same, or H and H * could be the same). Finally, the “quantitative” problem seeks a function that assigns a numerical measure of the degree to which E supports H. The comparative problem attracted little attention, but Hempel attacked the qualitative problem while Carnap concentrated on the quantitative problem.

What is science?

The Qualitative Problem

It would be natural to assume that the qualitative problem is the easier of the two, and even that it is quite simple. Many scientists (and philosophers) were attracted to the idea of ​​hypothetical-deductivism, or the hypothetico-deductive method. Scientific hypotheses are confirmed by deducing from them predictions about empirically determinable phenomena. When the predictions are valid, support accumulates for the hypotheses. from where these predictions derive.

A seemingly innocuous point about the support seems to be that if E confirms H, then E confirms any statement that can be deduced from H. Suppose, then, that H deductively implies E, and E has been determined by observation or experiment. If H is now joined with any arbitrary statement, the resulting conjunction will also deductively imply E. Hypothetical deductivism says that this conjunction is confirmed by the evidence. By the innocuous point, E confirms any deductive consequences of the conjunction. One of those deductive consequences is the arbitrary declaration. Then one comes to the conclusion that E, which could be anything, confirms any arbitrary statement.

Hypothetical deductivism

To see how bad this is, consider one of the great predictive theories, for example Newton’s explanation of the motions of celestial bodies. Hypothetical deductivism looks promising in cases like this, precisely because Newton’s theory seems to produce many predictions that can be tested and found to be correct. But if one adds whatever doctrine he pleases to Newtonian theory — perhaps the claim that global warming is the result of elven activities at the North Pole — then the expanded theory will throw up the old predictions as well.

The philosophy of science and Hempel’s work

Hempel’s work showed that this was only the beginning of the complexities of the qualitative confirmation problem. Although he and later philosophers made progress in dealing with the difficulties, it seemed to many confirmation theorists that the quantitative problem was more manageable.

Carnap’s own attempts to address this problem, carried out in the 1940s and 1950s, were aimed at emulating the achievements of deductive logic. Carnap considered artificial systems whose expressive power lags dramatically below the languages ​​actually used in the practice of science. His meticulous investigation made it clear that there were infinite functions (in fact, many continuous, one “greater” infinity corresponding to the size of the set of real numbers) that satisfied the criteria that he considered admissible.

Despite the failure of the official project, however, he argued in detail in favor of a connection between confirmation and probability. In this way, he shows that, given certain apparently reasonable assumptions, the degree of confirmation function must satisfy the axioms of the probability calculus.

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