Science cannot be defined in only one way; it is a kind of inquiry that never finds complete description. Thinking and verifying one's thought have always been a part of the human experience; we have always observed, found patterns, argued and systematized, but science puts these things into a specific order and demands a certain kind of verification for its assertions. It is thus a natural ability to order that comprises science, and it is not foreign to any people, though it emerges gradually over long periods. Saying that there was no science here or there – then or later – is misleading, but because neither our particular ordering, nor method, was present in the ancient world, we must say that science did not exist in antiquity. Still, it existed in pieces. The root of the word is scio, a Latin verb meaning “to know.” Modern science is an attempt at knowledge of a given subject through reason and verification, relying on probabilities. It attempts to reason about the likelihood of a given event or process. In knowing the probabilities of things, science allows humans to control their environment and manipulate specific processes in that endeavor. Science has many geneses: political, social, economic, geographic, ethnographic and intellectual, but as Bernard Pullman points out science cannot flourish without free expression, a willingness to consider different theories, openness toward debate and tolerance from public authorities.[i] It is a body of theoretical knowledge that employs technology in the solution of problems and the current belief about the nature of reality. It is a rigorous and precise attempt to attain and understand an assumed objective reality, and as such it filters out speculation, conjecture and imagined beliefs in favor of empirical verification of hypotheses. Its reach extends to almost every human endeavor: physics, medicine, politics, economics et alia. Science has made the human family master of nearly all of the earth and because it did not exist in its complete form in antiquity, it is necessary to provide a tentative definition, one that will allow us to see in some measure and how ancient inquiry survives in contemporary scientific analysis. This text focuses specifically on physics, and so our definition must center around physical change, a central unifying principle and a system that explains how that principle functions in the universe.

Science is a manner of understanding the behavior of nature, using deductive reasoning in the form of logic or mathematics to establish hypotheses. It empirically verifies these hypotheses through a process of experimentation, which involves understanding the interactions of things in material reality – other belief systems notwithstanding. Here is a tentative, general definition of science that is useful for understanding the continuity between ancient and modern methods for understanding. G.E.R. Lloyd claimed [ii] that science is “certain investigations that are continuous with what is normally included in our term science [which were] initiated in ancient Greece”, yet while valuable and accurate, Lloyd’s perspective leads to R.K. French’s suggestion [iii] that “to see science in antiquity we need to have a definition of science so broad as to be meaningless.” Our tentative definition is needed in order to begin discussion and to refrain from meaninglessness. It is not complete, but it allows a discussion about what may be called "ancient science.”

On the one hand, science is an intellectual inquiry into a particular subject-matter and on the other, it is the empirical or experiential verification of that continued inquiry. One part cannot be science without the other. Physics comes to mind when one uses the word “science”, perhaps because we have inherited Aristotle’s prejudice that knowledge of physics is knowledge of everything.[iv] Our aim is to discuss science on a fundamental level, so a discussion focusing on the thought process of science will reveal some measure of how ancient inquiry was a continuous investigation without the definition being meaningless. The thinking in science and its manner of verification in its most fundamental form are then our topics, and in order to understand the epistemology of science, we must understand some significant part of logic. Along the way, we will be able to discuss some of the empirical dimensions of ancient investigation.

Deduction and Induction

Logic is the engine of reason and science is only as strong as its reasoning. Reasoning involves the drawing of inferences. The connections that exist between accepted facts or postulates provide a new assertion. These new assertions proceed from what one does know to what one did not know: inferences. One calls such connections logic and the stronger the connection the more potent the reasoning; the more potent the reasoning, the truer the inference. There are two significant kinds of logic that are part of a rigorous system of thought used to investigate nature. These are deduction and induction.[v] The ancients understood these terms differently than we do, naturally, and it is valuable to point out the general differences between the ancient and the modern conceptions of logic in order to bring into sharper relief how ancient thought founds modern science. In the ancient view, deduction is a thought process that proceeds from universals to particulars. One begins with a universal conceptual thought, perhaps an abstraction, and proceeds to comprehend a subject on the basis of characteristics that define the whole of a category. What is consistent, what is cohesive and what follows thus from generalities are primary concerns of the ancient notion of deduction. Ancient induction proceeds from the particular to the universal. One begins with an observation or a sense that some members of a category possess specific characteristics and then one proceeds to understand universals through perhaps comparison. A syllogism is a set of assertions about the world that together allow for a “bearing in” or inference from statements that are accepted as true to a previously unrealized assertion.

Example one:

• All cats are quadrupeds. Assertion

• All lions are cats. Assertion

• Therefore, all lions are quadrupeds. Inference

If the connections are strong and real, the inference is said to be true. If the connection is faulty or non-existent, then it is said to be false. Because it is true that all cats are quadrupeds and all lions are cats, it is true that all lions are quadrupeds. Here is a possible connection between thoughts, entities, or happenstances that possesses an internal consistency. It speaks of universals in the sense that it expresses the whole of a category of things. All members of the set of lions are quadrupeds if they fit into the class of cats, which in turn is a subset of quadrupeds. There is inherent in this simple syllogism a mathematical dimension in the sense that it makes an assertion about sets of things. Ancients did make distinctions between what they perceived as universals in particular manifestations of things – what we may call abstraction – and the particular things themselves. The particular things exist in the realm of becoming; they come into being and proceed to grow to fruition and decrease, then perish. They have no permanence in the sense that they change. In seeking fixed and absolute aspects of reality, ancients generally sought permanent categories of things perceived in the world. The expression of a connection between particulars is a different form of assertion.

• Some humans are owners of sports cars. Assertion

• Some owners of sports cars are safe drivers. Assertion

There is no conclusion here because the connection made between particular statements is not strong enough to generate a strong inference (more below). These assertions talk of only a portion of a class of things: at least one member of a category. In the first sentence at least one member of the class of humans is a member of the class of safe drivers, and the same with owners of sports cars and safe drivers in the second sentence. So, when making assertions of this kind, one makes statements about only parts of whole categories of things. In particular and universal statements such as these, there are subject terms and predicate terms, indicated by the “S” and the “P” in the examples below.

• All S are P.

• Some S are P.

These are the subject and the predicate of the given statement. There are also middle terms, indicated by the “M” in the examples below.

• All M are S.

• Some P are M.

The middle term is the category that is common to both the other terms when a logical connection can be made. So, in example one “cats” is the middle term. It has something in common with both “lions” and “quadrupeds.” This commonality is what allows one to draw an inference. Two statements of categories together coupled with a conclusion comprise a syllogism. A syllogism draws an inference when it makes a connection, and that connection thus allows a conclusion. “All lions are quadrupeds” is the inference made through the connection and thus it is the conclusion. In Aristotelian, syllogistic logic there are four types of assertions whose elements possibly have a connection. An “A” statement asserts that one whole subject set is a subset of the predicate set:

• All S are P.
• An “E” statement asserts that one whole subject set is excluded from a predicate set (and vice versa).
• No S are P.
• An “I” statement asserts that one part (at least one) of a subject set is a subset of the predicate set.
• Some S are P.
• An “O” statement asserts that one part (at least one) of a subject set is excluded from the predicate set.
• Some S are not P.

The first two sentences are universal; they assert something about all of at least one set of things. The third and fourth sentences are particular; they assert something about at least one of a set of things. The majority of ancient thinkers looked for first principles or fundamental first elements that would allow them to explain change and continuity in processes encountered in physical happenstances. They believed they needed to find a permanent aspect of reality that was the foundation for impermanence. They thus sought what was fixed and lasting and attempted to base their arguments on permanence even as some ancient thinkers embraced change as a fixed element. In other words, they sought universals. A and E statements were the kinds of assertions, then, that they wished to employ in their reasoning.

Induction as understood by ancients operates from the other direction. One proceeds to make the same kinds of connections, but from particulars to universals. I and O statements are inductive statements, asserting something about at least one member of a set of things and asserting something about particular manifestations (this specific cat). The connections made between parts of sets by their nature cannot be as reliable as those made about all of the members of a certain set. An assertion about all of one set and all of another set encompasses all possibilities, and so is obviously a much more reliable connection. Again, the above example.

• All cats are quadrupeds.

• All lions are cats.

• Therefore, all lions are quadrupeds.

There is certainty in the statement “All lions are quadrupeds” because the sentences above it assert something about all of a given category. If we alter these statements and make them particular, they have a very different meaning.

• Some cats are quadrupeds.

• Some lions are cats.

There is no universal, and therefore reliable, connection between these statements because they make assertions about only some of a given category; we do not even know how many of a given category possess the characteristics asserted. If some cats are quadrupeds and some lions are cats, then the lions that are quadrupeds may not be the same cats; all of them may be or only some. We have no way of drawing a firm inference about the “some” in either sentence. Ancient thinkers generally sought the certainty that comes from the strong connection of a universal. In fact, many ancients perceived particulars as unreliable because they thought of them as unstable. One can see how dissatisfying it would have been for ancient thinkers to discover rules about logical connections only to find that logic cannot find the very universals it was meant to discover. Centuries of investigation passed before scientists disposed of the attempt to find universals in favor of probabilities.

Deduction and Induction in Modern Science

The modern view of logic and its limitations is different. When an argument has a good form and the connections it makes seem real and verifiable in terms of their relation to one another, we call the argument valid. So, that we have made a firm connection between lions and quadrupeds in the above example is that argument's validity. There is a conceptual connection between the different categories. When, however, an argument possesses not merely good form and connection but also has as its premises verifiable, true elements of the world (like facts or accepted conditions of existence), then one calls it sound. So, that lions who are cats exist in the world and that cats are actually quadrupeds along with the connections between them makes the argument sound. As one may imagine, an argument can be valid and unsound. But an argument cannot be sound and not valid because the connections as well as true statements need to exist for an argument to be sound. So, the following argument is valid.

• All paper towels are men with socks.

• All unicorns are paper towels.

• Thus, all unicorns are men with socks.

The statements do not need to be true, but the connections between the stated categories need to exist. If the form of the argument is good and if the connection is present, then the argument is valid. Additionally, one must accept the conclusion. If it has good form it is valid, even if it is nonsensical. Our initial example argument is sound.

• All cats are quadrupeds.

• All lions are cats.

• Therefore, all lions are quadrupeds.

There are such things as cats in the world and cats are actually quadrupeds. Also, there are such things as lions and lions are actually cats. Because the categories make a strong connection, the argument is valid; because the statements are true and because the argument is valid, the argument is sound.

Deduction in the modern sense means that if we accept the premises of the argument, then the conclusion will not only naturally follow, but we must accept the conclusion. The certainty of a very strong connection is deductive, given its assumptions. Mathematics is a good example of deductive reasoning. It presents clear and certain conclusions from commonly accepted constants, or the most certain calculations possible. Modern deductive reasoning is not necessarily in harmony with its subject. In other words, the internal consistency of a deductive argument may compel someone to accept the conclusion, but the assertions used in the argument may have little to do with reality. If one creates a perfectly cohesive mathematical thesis, it may be valid, but have little to do with how things interact in material reality. Scientists verify their arguments through an empirical means, which is, of course, the experiment.

Induction for moderns is the discovery of connections, but they are considerably weaker than those made by deduction, and modern induction is not concerned with particulars in the same way that ancient induction concerns itself with particulars. A modern inductive argument asserts something about the probability of some conclusion to be true. Obviously, there are different degrees of probability. So, an inductive argument in the modern sense is one that will make a kind of prediction about an event. Given the facts that we possess about the earth and its relation to the sun we can predict with a great amount of certainty that the sun will rise in the east and set in the west tomorrow. So, it is an argument that asserts a specific occurrence will take place with a great deal of probability, given certain circumstances, but not that the occurrence must take place. There is a predictability to the argument, but not absolute certainty. Thus, the probability. One sees this kind of argument when one reads the prediction for the weather. There is a certain percentage chance that rain will fall, for instance. The percentage is the probability of rain, induced by the circumstances that are taking place at a given time. So, if there are dark clouds in the sky and one hears thunder, one can make a relatively certain induction that rain will fall. Inductive arguments guide modern scientific investigation because the scientific search for universals has ended, or it has at least paused. We will return to the particulars of logic and Aristotelian logic rules later, but now it is necessary that we understand what part of this manner of thinking we are investigating. Other kinds of logic exist besides the syllogism. Propositional logic is similar to syllogistic logic, but it is a form of logic in which the fundamental components are whole statements or assertions. Propositional logic is the combining of two or more sentences, or propositions, in order to find more complicated assertions of truth. Propositional logic, then, operates in the same manner as syllogistic logic, but with more assertions. In fact, all logic operates on the same level in one sense. All of logic attempts to make connections based on the truth and falsity of certain statements, the categories that they represent and the connections or relationship between them. Symbolic logic is a development of propositional logic, but with different sigla. It replaces purely linguistic statements with symbolic ones and is comprised of a given set of proven connections that lead to more complex connections. Predicate logic makes use of the same symbols as symbolic logic, but accounts for the complete sets and partial sets that one sees in syllogistic logic. Mathematics is only a short step away from these kinds of logic in that it is in part a quantification of similar assertions. We will cover only a few of these kinds of logic, but we want to keep in mind that logic is not monolithic. There is a great similarity between kinds of logic, but they have different forms. The most fundamental aspect of logic is, again, that it makes connections, or in some cases disconnections, between things. Every kind of logic performs that function.

Induction as a Part of Scientific Method

We are examining the engine of science, its logical apparatus, in order to learn about ancient contributions made to the current scientific method. We are interested in the history of science, but merely stating at what conclusion a particular thinker arrived is hardly satisfying when we want to comprehend science as a way of determining truth and a way of discovering “laws” of the natural world. The awareness and manipulation of natural processes have allowed humans to possess great control over their environment and given us the modern age, as well as the virtual age. Humans have even journeyed outside the planet because of the thought that drives science. We want to keep the distinction between deduction and induction in mind as we examine systems of thought that have contributed to an overall scientific method employed today. We will come to some understanding of how much and in what way each element of thinking survives in current scientific method.

How, then, precisely does the thought of science operate and how does it demonstrate what it asserts is actually true about the world are fundamental questions for us. One part of science looks for the causes of things, so we need to have some way of understanding causes.[vi] There are three definitions of cause that apply for us. There are necessary conditions, sufficient conditions and sufficient and necessary conditions. Necessary conditions are conditions needed for something to happen, but in some cases in themselves are not enough to make something occur. Water is necessary to produce life, but it is hardly sufficient. If it were, we would have been able to create new forms of life at will, even in the ancient world. Water is a necessary cause for life. A sufficient condition is a condition, or cause, that itself is enough to make something happen. The chopping off of someone's head is a sufficient cause of death, but other methods prove efficacious. Shooting, stabbing or strangling a person will result in their death if done in a specific way. A necessary and sufficient condition is a condition that will in itself produce the desired effect, and nothing more than it is necessary. The acceleration of a body is caused by the action of some force upon it.[vii] Nothing more or less is needed for acceleration to come about.

If X is a sufficient condition for Y, then if X occurs then Y occurs. Beheading is our example. If someone beheads another person, that person will die. Additionally, if X is a necessary condition for Y, then if Y occurs X occurs, but not necessarily the other way around. So, if I am driving my car, my car's engine must be running, but simply because my car's engine is running does not mean that I am driving my car. Similarly, the absence of X is a sufficient condition for the absence of Y, if and only if Y is a sufficient condition for X. So, if there is no acceleration of my car, then there must be no force, its engine, acting upon it.

In a similar fashion, the absence of X is a necessary condition for the absence of Y if and only if Y is a necessary condition for X. If my car's engine is not running, then it must be that it has not been started, because starting a car is needed for its engine to be running. Lastly, X is not a sufficient condition for Y if X occurs without Y. If it so happens that I started my car and it is not moving, then starting my car is not a sufficient condition for it to move. And, X is not a necessary condition for Y if Y occurs without X. It is necessary, but not sufficient. If I started my car without wearing my hat, then wearing my hat is not needed for starting my car.

We talk about these conditions because they will be necessary for understanding how the reasoning process works in evaluating causes of things. Remember that for our purposes there are two realms in which science works. The one is more theoretical, and it involves making abstract arguments about things in the world. We use statements, propositions, axioms, mathematics and the like to make these arguments. They may apply to material reality and they may not. The other is more empirical, and it involves verifying those valid but perhaps not sound arguments upon circumstances in the world. When we experiment upon something, we find out if our seemingly logical standpoint really speaks to some objective truth about how things operate. So, now we need to understand what methods there are for verifying our reasoning. We will cover five methods for demonstrating causal connections.[viii] These are basic ways our reasoning may be involved in making scientific inferences.

The Direct Method of Agreement demonstrates the relationship between an effect and a necessary condition. One looks for a single element that is present in many occurrences where the effect sought is also present. The one element that is present when the effect is present is thought to be the cause. An example:

• Seven individuals came down with explosive diarrhea while eating in the

• same restaurant. They all ate different food, but used Momma's Sweet

• Red-Hot sauce. The hot sauce was the only commonality.

• Food scientists concluded that the ailment came about because of the hot sauce.

The following table shows how the conclusion came about. The occurrences are the individuals who ate at the same restaurant. The possible necessary conditions indicate the possible foods eaten. An asterisk shows the presence of something and the dash absence. The condition that is present in all of the occurrences is the condition taken to be the cause of the malady.[ix]