Logic

Inference and shit

An inference is the reasoning that connects the premise and the conclusion. So, in this example, an inference connects the two propositions "all roses are red" and "all flowers are roses." The inference (or connection) between the two premises is what allows us to conclude, "Therefore, all flowers are red." Even though it is clear to us that there are many flowers that are not red, the logic behind this argument is sound because the inferences we can make between the premises and conclusion is sound.

Aristotle is considered the father of logical theory (organon)

Aristotle is considered the father of logical theory. He believed that logic is the instrument or the organon (the Greek word that means "instrument" or "tool"), by which we come to know any type of knowledge. He thought that all of learning could be placed into three different categories—theoretical, practical, and productive. Logic underlies each of these categories and could be used as a tool to validate our knowledge. Aristotle sought to use logic to create arguments that represented the true nature of reality. Logic, being based upon rules and forms, is not subjective, so it could be used as a tool to reveal the way things really are, rather than just the way we see them. His proposed his logical theory in a compilation known as Organon. This work first sets out the basics of the rules of logic—an analysis of propositions and their fundamental relationships with each other. Then, Aristotle goes on to explain more complex forms of logic, such as syllogisms and dialectics. Organon is the core of logical theory, and it has been extremely influential in the realm of logic for the last 2,000 years. Only in the modern era has Aristotle's logic been challenged, and a new branch of logic (mathematical logic) created.

Deductive and Inductive Logic

In order to understand how logic works, it is important to understand the basic terminology used. In logic, the whole point is to determine whether an argument is true or false. Argument does not mean a fight between two people, but rather a group of propositions, or statements, which follow logically from one to the other. For example, "The man is not married; therefore, he is a bachelor," is a statement followed by a conclusion. Logic seeks to determine the reasoning behind arguments. In this case, we can use the statement and conclusion to logically prove that the argument "The man is not married; therefore, he is a bachelor" is true. Another important term is premise. A premise is the basis of an argument, and gives us reasons, grounds, or evidence to support our conclusion. For example, a premise could be "all roses are red." Another premise could be "all flowers are roses." The conclusion following the premises is a factual statement, which is supported by the premises and the way they relate to each other. For example, a conclusion to the two premises above would be: "Therefore, all flowers are red." As you can see, the premise does not always have to be true in order to have a logical argument.

Paradox

On the opposite spectrum of logical fallacies and invalid arguments are arguments that result in a completely impossible result, otherwise known as a paradox. Paradoxes are problematic because the logical reasoning behind the argument appears to be sound, and the argument contains apparently true premises, but the conclusion is still impossible. Some paradoxes are extremely complex, and some, upon close examination, can be revealed to actually contain fallacies. Paradoxes have been a matter of logical study ever since the invention of logical argument. Zeno was an ancient Greek philosopher who conceived of many paradoxes regarding time and motion. One of his paradoxes stated that an arrow could never move, because at any given moment in time, the arrow has to completely occupy the space where it exists. An arrow is always only where it is, and nowhere else. Therefore, it is stationary. If time is a series of moments and the arrow exists at all of those stationary moments, then it never moves. Nevertheless, we know that an arrow can move from one place to another after it has been fired. So, which is flawed, our version of reality, or the logic of the paradox?

The trolley experiment

One famous thought experiment is the Trolley Experiment: A madman has tied five people to a trolley track, and an out-of-control trolley car is about to run them over. You can save the five people by pulling a lever and switching the trolley to a different track, but the killer has tied a person to that track as well. What do you do, pull the lever and choose to kill the one person or let the trolley run its course and let the madman kill the other five? Although it sounds like a crazy problem, the philosophical questions here run deep, and examining the many possible answers to the Trolley Experiment can help us learn more about the nature of philosophy.

Philosophical puzzles and thought excercises

One of the ways philosophers have been able to delve deeply into the complex world of paradoxes, logical arguments, and theories, is through thought experiments. Unlike the field of science, which is based on experiments with actual physical objects, philosophers perform their experiments based on thoughts and reasoned theory. Thought experiments are mental concepts or hypotheses, sometimes like riddles, that are used to illuminate the issues surrounding a philosophical issue. Some thought experiments are designed to prove a philosopher's point. Others are designed to refute another philosopher's argument.

Syllogism

The term for an argument with two prepositional statements and a conclusion is a syllogism. Although there are many different types of syllogisms, the classic form is with two propositions considered together, which state the relationship between multiple classes of things, and then come to a conclusion regarding those classes of things, depending on the type of information presented in the argument. In the previous example about Socrates being mortal, there were three classes of things: men, mortals, and Socrates. If we say that Socrates is represented by the letter A, men are represented by the letter B, and mortals by the letter C, then we can restate the syllogism in this form: • All A are B. • All B are C. • Therefore, all A are C. This is an example of a logically sound argument, meaning that the logical reasoning behind the argument is correct. A logically sound argument with true premises is called valid. However, even though an argument may be logically sound, it can still lead to a conclusion that we know to be false. Here is an example: • All roses are red. • I have a rose. • Therefore, my rose is red. However, you may reasonably ask "what if my rose is actually orange?" In this case, we see that even though the logical reasoning is sound; it is based on a premise that is not true, making the argument invalid.

Types of philosophies of logic

There are many different types of philosophies of logic, such as mathematical logic, symbolic logic, deductive logic, and inductive logic. Each uses a different method in order to examine the reasoning behind an argument and to determine whether a conclusion is valid. All types of logic must be free of emotion and based on reason to ensure that the conclusions derived from an argument are valid. Many forms of logic have complex sets of rules that must be followed in order to ensure that the reasoning of the argument is correct, rather than based on opinion or emotion. Because of its lack of subjectivity, logic is a valuable tool that is used in all fields of thought, not just philosophy. Lawyers, businesspersons, politicians, mathematicians, and scientists all use logic to form strong arguments.

Fallacy False cause- Assumes that just because A comes before B, A caused B. Although A and B have a type of relationship, it does not necessarily mean one caused another Slippery Slope- Assumes that when A happens, Z will ultimately happen. Slippery slope fallacy is wrong because it takes the arguiment away from the present and places conjectures on the issue. Bandwagon- Assumes a premise must be correct simply because may think the same thing. This causes a problem because the mass's opinion is rarely based on facts. Appeal to authority- Similar to bandwagon fallacy. Assumes just because an authority figure says something is true, then it must be true. Black or white- Assumes that there are only two sides or answers to a question. There may be multiple sides, however.

Example -I wake up every morning, the sun rises each morning, so I must be the reason the sun rises each morning. -We have to stop the increase in tuition each semester. Before we know it, tuition will be $30, 000 for each semester. -All my friends think sugar is healthy for me, so it must be true. -They mayor says the current US trade policy is increasing the unemployment and he is an expert on trade policies, so it must be true. -You either finish your hw right now or never go to the movies again.

Examples

Explanation: From the first premise, "all flowers are trees," we can deduce that "some trees are flowers." From both premises ("all flowers are trees" and "no fruit is a tree"), we can also deduce that "no fruit is a flower."

Paradoxes (cont.)

Paradoxes are other examples of thought experiments, which are specifically aimed at determining the logic behind a seeming impossibility, or the fallacies within its reasoning. Some paradoxes are surprisingly simple, and pretty fun to think about. Consider this paradox: Statement A: Statement B is true. Statement B: Statement A is false. If Statement A is false, then it would mean that Statement B is also false, because Statement A says that Statement B is true. But, if Statement B is false, then it would follow that Statement A is true, because Statement B says that Statement A is false. So, which is it? If Statement A is true, then it means that Statement A is also false, and the same thing for Statement B!! Consider also the following metaphysical paradox: If you gradually replace every single piece of your old car with a new piece, you will eventually have replaced your entire car with a new car. So, it is your old car, or is it a new car? At what point did it become a new car rather than your old car? Some philosophical thought experiments, like the Trolley Experiment, can help us understand the nature of morality and ethics, and help guide our moral actions and decisions. Other philosophical thought experiments, like the paradoxes we just read about, serve to amuse and entertain, as well as train our thinking and illuminate our reality a little bit. These philosophical thought experiments are a great way to have fun with philosophy. Brain teasers, logical paradoxes, and metaphysical dilemmas all help to open our eyes to the world around us, and how everything works together. Rather than merely reading about stuffy old Greek men in a long-forgotten past, these types of philosophical thought experiments can be translated to our everyday life, shaking up the ways we see things and waking up our brains. Thought experiments help reminds us that philosophy is an activity.

Logical Fallacies and paradoxes

When an argument fails, resulting in an invalid conclusion, it is usually due to some sort of faulty reasoning within the argument, such as a false premise. These false, or invalid, arguments are often due to fallacies. A fallacy is a flaw in an argument, which ultimately causes the argument to be false. When an argument turns out to be invalid, a close examination can reveal the fallacy that was its downfall. This close examination of logical reasoning—discovering fallacies, and then making a more sound argument—is one way in which modern politicians and lawyers (and in Plato's time, Sophists), create strong arguments against their opponents and for their own causes. Plato's Republic has many examples of Socrates asking persons within the Republic about their opinions regarding a matter, and then through close examination determining that their reasoning is faulty (or contains fallacies). In this way, Socrates was a master of argument, because he could find the fallacious reasoning in a person's argument and in turn prove his own point, much like modern lawyers and politicians try to do today.

Deductive and Inductive (two main types of arguements)

here are two main types of arguments: deductive and inductive. A deductive argument is based on clear connections between premises, so that it is impossible for the premises to be true and the conclusion to be false. The conclusion follows necessarily from the premises. Here is an example: All men are mortal. Socrates was a man. Therefore, Socrates was mortal. In a deductive argument, if you accept that the premises are true (all men are mortal and Socrates was a man), then you must accept the truth of the conclusion (Socrates was a mortal). Inductive arguments function differently. They are also based on premises, which may or may not be considered factually correct. But instead of the conclusion necessarily following the premises, it is simply improbable that the conclusion would be false. Here's an example of an argument that uses inductive logic: Socrates was Greek. Most Greeks eat fish. Therefore, Socrates ate fish. In an inductive argument, it is possible for both premises to be true and the conclusion to be false (what if Socrates was allergic to fish and therefore never ate them?). Both types of arguments have their uses: deductive arguments are good at proving factual points, but inductive arguments are useful for exploring different possibilities.

Aristotles influence on logic

logic is the study of reasoning and how we come to know is an argument is right or wrong. Rather than worrying about the actual content of an argument, or premise (the basis of an argument), logic dissects the reasoning behind a premise and any resulting conclusions to make sure that the reasoning behind the thinking was valid (or correct).