The most basic feature of Galileo's method is that we must rely on data and evidence. We cannot judge without evidence and facts. We must first take notice of data before we can judge. Science should not be based on a priori principles, meaning that science should not be based on principles that we have before we actually get evidence. Science should be done in an a posteriori manner, meaning that science should be based on evidence and experience. In short, sciences should be empirical. Also, a scientist should not just cherry-pick evidence that already confirms the beliefs that she or he holds. Recalcitrant evidence, or evidence that seems to go against one's presuppositions, is the most important evidence. Scientists should not be concerned with confirming presuppositions but they should want to explore all of the evidence and let the data itself determine the progress of the sciences.
Once we have the data, scientists should provide a causal account. For example, we can explain the movement of billiard balls by explaining how forces are transferred between two entities when they come in contact with one another. The scientist aims to identify necessary and universal links that explain the relationship between causes and effects. A ball moves because it is hit by a cue or by another ball. If this is truly a discovery of cause and effect, then it must be the case that in general, all balls will move when hit by a cue or another ball. Scientific principles thus seek to provide general truths that apply to a broad class of events and occurrences. The power of such principles is that we can use them to predict the motion of, for example, billiard balls or constellations in the sky. Because sciences identify universal truths, they can predict the future.
Causal accounts should be represented in mathematical form. Effects should be calculated from causes. If we formulate causal principles in mathematical form, then we can deduce certain effects. For example, if we know that f = ma, and we know the mass and acceleration of a certain object, then we can calculate the force of that object. Not only can the sciences predict, but they do so with mathematical certainty. Galileo thought that humans can have perfect knowledge of mathematical truths. Indeed, he thought that our perfect knowledge of mathematical truths was comparable to God's knowledge of mathematical truths.
One example of this method in Galileo's work is his discussion of the surface of the moon. Aristotle, for example, thought that the moon was made of ether, or an unchanging substance. The moon was popularly thought to have a smooth, glassy surface that was unchanging. Galileo, using a telescope, saw that the moon's surface was actually rough and included many features. This was evidence that directly contradicted Aristotelian physics. Dr. Bencivenga notes that Galileo's knowledge of techniques used in perspective painting may have allowed him to correctly "read" the combinations of color and shadows on the moon as evidence of mountains and other features. To show that the moon had a rough surface, the characters in the dialogue show how the rough surface of a wall reflects light in a more uniform way than a mirror does. With a mirror, light is reflected in a very directed way. With a rough wall, light is reflected in many directions, creating a more uniform appearance of light. Rough and irregular surfaces have many different angles off of which light can be reflected. This means that no matter the angle from which one is viewing the surface, light will be equally reflected. On a smooth surface, in contrast, light is only reflected at one certain angle. Here we see how Galileo 1) used empirical evidence to 2) challenge presuppositions and then 3) theorized about how the evidence can be explained.
Another point that Galileo made about the moon is that the light that comes from the moon is actually a reflection off of the earth.
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