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[A lecture given at Fermilab on June 27, 2018]
The notion of a physical law is perhaps the central concept of modern science. In their book The Grand Design, Stephen Hawking and Leonard Mlodinow characterize the history of science as “the long process of replacing the notion of the reign of gods with the concept of a universe that is governed by laws of nature.”[1] They quote Alexander Pope’s famous couplet:
Nature and Nature’s laws lay hid in night:
God said, Let Newton Be! and all was light.
The idea is that it is Newton’s discovery of physical law that made nature at last intelligible, and that Newton’s successors have increased this intelligibility insofar as they have improved upon Newton’s laws and discovered further ones. Hawking and Mlodinow are, of course, expressing a view that is very common among scientists and admirers of science.
But what exactly is a law of nature? Hawking and Mlodinow characterize a law as “a rule that is based upon an observed regularity and provides predictions that go beyond the immediate situations upon which it is based.”[2] Here too their position is no doubt a common one. But their answer is not terribly informative, because the terms “law” and “rule” are often used synonymously. Suppose you asked a political philosopher what liberty is and he told you that liberty is freedom. You would probably respond: “Yes, I already know that much, because the terms are more or less interchangeable. I wasn’t asking you for a synonym, though. I want to know the nature of the thing that the words ‘liberty’ and ‘freedom’ refer to.” In the same way, since the words “law” and “rule” are often used interchangeably, it isn’t very helpful to say that a physical law is a kind of rule. What we need to know is the nature of the laws or rules that are said to govern the physical world.
To be sure, Hawking and Mlodinow do say more than merely that a law of nature is a kind of rule. Again, they tell us that laws are inferred from observed regularities, and that we can derive predictions from them. They also tell us that “in modern science laws of nature are usually phrased in mathematics,” and that “they must have been observed to hold without exception… at least under a stipulated set of conditions.”[3] And they tell us that physical laws are “consistent principles,” in contrast with the arbitrary and “inscrutable” whims of the gods in terms of which pre-scientific cultures explain natural phenomena.[4]
But while somewhat informative, even these remarks still don’t really answer our question. Suppose you asked a geometer what a triangle is, and he told you that in Euclidean geometry the angles of a triangle summed to 180 degrees, that you could discover various features of triangles by constructing proofs, and so on. All of that is true, but it doesn’t really answer your question. What the geometer would be telling you about is a certain property of triangles, and a method for coming to know things about them. But what you asked about was the nature of the thing that has these properties, and the nature of the thing that can be known in this way. What you need is what is captured in a definition like: “A triangle is a closed plane figure with three straight sides.” That tells you what a triangle is, and not merely certain properties of triangles or facts about them. Similarly, to say that physical laws make natural phenomena intelligible, or that they are stated in mathematical terms, or that we infer them from observed regularities, or that we can derive predictions from them, only tells us about certain properties of laws or facts about them. It does not tell us what a physical law is, does not tell us the nature of the thing of which these various claims are true.
Continued below.
The notion of a physical law is perhaps the central concept of modern science. In their book The Grand Design, Stephen Hawking and Leonard Mlodinow characterize the history of science as “the long process of replacing the notion of the reign of gods with the concept of a universe that is governed by laws of nature.”[1] They quote Alexander Pope’s famous couplet:
Nature and Nature’s laws lay hid in night:
God said, Let Newton Be! and all was light.
The idea is that it is Newton’s discovery of physical law that made nature at last intelligible, and that Newton’s successors have increased this intelligibility insofar as they have improved upon Newton’s laws and discovered further ones. Hawking and Mlodinow are, of course, expressing a view that is very common among scientists and admirers of science.
But what exactly is a law of nature? Hawking and Mlodinow characterize a law as “a rule that is based upon an observed regularity and provides predictions that go beyond the immediate situations upon which it is based.”[2] Here too their position is no doubt a common one. But their answer is not terribly informative, because the terms “law” and “rule” are often used synonymously. Suppose you asked a political philosopher what liberty is and he told you that liberty is freedom. You would probably respond: “Yes, I already know that much, because the terms are more or less interchangeable. I wasn’t asking you for a synonym, though. I want to know the nature of the thing that the words ‘liberty’ and ‘freedom’ refer to.” In the same way, since the words “law” and “rule” are often used interchangeably, it isn’t very helpful to say that a physical law is a kind of rule. What we need to know is the nature of the laws or rules that are said to govern the physical world.
To be sure, Hawking and Mlodinow do say more than merely that a law of nature is a kind of rule. Again, they tell us that laws are inferred from observed regularities, and that we can derive predictions from them. They also tell us that “in modern science laws of nature are usually phrased in mathematics,” and that “they must have been observed to hold without exception… at least under a stipulated set of conditions.”[3] And they tell us that physical laws are “consistent principles,” in contrast with the arbitrary and “inscrutable” whims of the gods in terms of which pre-scientific cultures explain natural phenomena.[4]
But while somewhat informative, even these remarks still don’t really answer our question. Suppose you asked a geometer what a triangle is, and he told you that in Euclidean geometry the angles of a triangle summed to 180 degrees, that you could discover various features of triangles by constructing proofs, and so on. All of that is true, but it doesn’t really answer your question. What the geometer would be telling you about is a certain property of triangles, and a method for coming to know things about them. But what you asked about was the nature of the thing that has these properties, and the nature of the thing that can be known in this way. What you need is what is captured in a definition like: “A triangle is a closed plane figure with three straight sides.” That tells you what a triangle is, and not merely certain properties of triangles or facts about them. Similarly, to say that physical laws make natural phenomena intelligible, or that they are stated in mathematical terms, or that we infer them from observed regularities, or that we can derive predictions from them, only tells us about certain properties of laws or facts about them. It does not tell us what a physical law is, does not tell us the nature of the thing of which these various claims are true.
Continued below.
