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# 1.14 Logic

Scientists must make several important assumptions to do their work. These assumptions sound reasonable but they are hard to prove once and for all. For instance, we assume that causality holds true in the universe. In other words, we believe that all events have causes. This sounds very reasonable. The behavior of the universe would be capricious if causality did not exist — imagine objects moving for no reason or time flowing backward! Scientists also assume that the laws of nature that we measure on Earth hold everywhere in the universe. Since we have not traveled beyond the solar system, this is a major assumption. Although unproven, these assumptions are crucial to the scientific method. They form a backdrop against which we can interpret the observational evidence of astronomy. They also lead us down the path of logical inquiry, while our ancestors were often content not to seek causes at all, or to believe in supernatural causes.

Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC; the alabaster mantle is a modern addition. Click here for original source URL.

Scientists assume that logic leads to valid conclusions about the natural world. The basis of every scientific argument is logic. By combining their ideas and observations logically, scientists can draw conclusions and create secure knowledge. The scientific method uses two forms of logical proof that were originally developed by philosophers. One of these methods is deduction. A deductive argument starts with statements or premises and then draws a conclusion for a particular case. For example, by combining the premises that "The Sun is larger than the Earth" and "The Earth is larger than the Moon," we can deduce that "The Sun must be larger than the Moon." The rules of deductive logic were first devised by the Greek philosopher Aristotle nearly 2500 years ago.

In deductive reasoning, if the initial premises are correct, the conclusion must be correct. However, a deductive argument is like a piece of machinery that blindly gives an output for a given set of inputs. If the premises are wrong, the conclusion will be wrong. We have to be careful about premises as well as conclusions. For example, if we start with the premise that "Pigs have wings," we could waste a lot of time trying to investigate why a particular pig does not have wings. The deductive method is valuable only if we demand evidence to back up our premises. Aristotle and his teacher Plato argued a lot about this. Plato held that we could understand the natural world by pure thought, while Aristotle believed that understanding and knowledge had to based on observations as well as logic.

Many branches of mathematics like arithmetic and algebra are deductive. They can be used to illustrate one great advantage and one great disadvantage of this type of logic. The advantage is that, with accurate premises, deduction yields certain conclusions. Following the premises of basic arithmetic, we can say that "2 + 2 = 4." This is not just true occasionally, or true every day except Thursdays; it is always true. The disadvantage of deductive logic is that the conclusion of a deductive argument contains no more information than is contained in the premises. If we say that 2x3 + 7 = 61, where x is unknown, we can follow the rules of algebra to deduce that x = 3. The solution to a complicated algebra problem may seem like a wonderful discovery, but it contains no more information than the original equations. Pure deduction has the serious limitation for science that it cannot create new knowledge.

Induction is another logical tool of the scientific method. An inductive argument starts with specific observations (not broad premises) and then infers a general conclusion that is widely applicable. For example, an inductive argument might start with the observation "Not one of the 100 pigs I have seen has wings." Generalizing from this observation, we could hypothesize that no pigs anywhere have wings. Of course, we might be wrong; a mutant pig somewhere might have wings. But the conclusion seems very reliable. After looking at a hundred white swans, it would be tempting to conclude that all swans are white. In this case the conclusion not reliable because black swans do exist, though you might not know it unless you visited Australia.

Portrait of Isaac Newton. Click here for original source URL.

We pay a price with inductive arguments, however: the conclusion of an inductive argument is never absolutely guaranteed. In practice, careful use of induction can lead to very good hypotheses. Three hundred years ago Isaac Newton jumped from the observation that "Every planetary orbit so far tested fits the Universal Law of Gravity" to the inductive conclusion that "All astronomical orbits follow this Law of Gravity." So far as we know, his conclusion is correct (although minor but important corrections have been made to allow for the relativity effects discovered by Albert Einstein). The power of induction is that it allows us to generalize an argument and reach very broad conclusions. Scientists took the evidence that the planets follow Newtonian orbits and made a hypothesis that these orbits apply far beyond the Solar System.

Good inductive arguments can be very reliable, but they also can be flawed if the data are too limited. For example, what about the observation that "All people examined so far are right-handed," leading to the inductive conclusion that "All people are right-handed?" Obviously, whoever conducted that piece of science did not have a large enough sample of people. Black and white swans provide another example. You can understand why science is such a data-hungry enterprise: we need large data sets to be sure our inductive logic is reliable. As attractive as it would be, no logical system has been devised that yields certainty and creates new knowledge. Scientists use both deduction and induction in their work.

Photograph of the Milky Way in the night sky over Black Rock Desert, Nevada taken on 7/22/2007. It is a 54 second exposure taken with a tripod mounted Cannon EOS 5D digital camera with a 16mm lens, wide open at f2.8 and ISO800. The Milky Way is our home. Can we assume that the Milky Way is typical of all galaxies. Click here for original source URL.

Let's look at an astronomical example of induction. There is evidence to support the statement that "Most of the mass of the Milky Way galaxy is invisible dark matter." If we then hypothesize that "The Milky Way is typical of all stellar systems," then we could conclude that "Most of the mass of the universe is dark matter." It is a bold conclusion, but it raises several questions. How good is the evidence for dark matter in the Milky Way? Is the Milky Way really typical of all galaxies? Is there evidence for dark matter in any galaxies other than the Milky Way?

Another example of induction relates to the possibility of life on Mars. We know that life has formed at least once in the Solar System — on Earth. The jury is still out on the evidence from Mars. If we hypothesize that "Most stars form planetary systems as a natural byproduct of their formation," we might conclude that "Given the large number of stars, life in the universe is common." Notice the danger — we are generalizing a conclusion on the likelihood of life throughout the universe based on only one example. How sure are we that planets have actually formed around other stars? If they have, how many are suitable sites for life? What about evidence for life itself? Perhaps a planet can be Earth-like and habitable without ever developing life. As long as we use logical arguments and insist on evidence at every step, the scientific method can lead us to the answers.