NYC COLLEGE OF TECHNOLOGY Intro to Philosophy PHIL 2101 Prof. Carlo Alvaro

LOGIC

LOGIC DEFINITION, AND MORE

Logic is the Study of the principles and concepts of good reasoning.

This implies that there is a distinction between good and bad reasoning.

Also, logicians, people who study logic, are not interested in HOW people reason, those are psychologists. Logicians are interested in the principles of reasoning.

THE THREE LAWS OF THOUGHT

Early Logicians defined logic as the science of the laws of thought and that there are three basic laws we must obey to think correctly:

1. The principle of identity: Whatever is, is! (A=A)

2. The principle of non-contradiction: Nothing can both be and not be. ( [A and A])

3. The principle of excluded middle: Everything must either be or not be. (A or A)

History of Logic

Aristotle (384-322 B.C.E.) invented logic. He used letters for terms, he created syllogistic logic, which studies arguments like these

All humans are mortal. = All H are M.

All Greeks are humans. = All G are H.

Therefore All Greeks are mortal. = All G re M.

This argument is valid because of its structure. So any argument with the same structure is valid.

Aristotle studied the logic of possibility and necessity.

Stoics continued Aristotles work and in the Medieval Period many thinkers developed ways to teach Aristotles system of logic. During the Enlightenment many philosophers would just agree that nothing significant was invented in logic after Aristotle. Leibniz (1646-1716), however, anticipated modern logic, proposing a concept of symbolic language, but his work was published after George Boole (1815-1864).

In 1879, Gottlob Frege (1848-1925) invented modern logic. He created more ways to express logic through symbols and operators. His project was to show that arithmetic is reducible to logic. Some sets, such as the set of all teacups, or of all cats are not members of themselves. The set of all teacups is not a teacup and the set of all cats is not a cat. Other sets, such as the set of all non-teacups, or the set of all abstract objects are members of themselves because the set of all non-teacups is a non-teacup and the set of all abstract objects is an abstract object. Now, consider the set of all sets that are not members of themselves R. If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Freges life work was destroyed! This is known as the Russells Paradox. Russell and Whitehead developed a system that fixed this problem.

These new developments propelled logic forward to new territories that Aristotle would be impressed. Systems like truth tables were invented. Modern Logic was important in the development of computers. Also the most important aspect of logic is modal logic dealing with necessary and possible.

The distinction between analytic and synthetic judgments, and by that between a priori and a posteriori knowledge.

Analytic and Synthetic Judgments

Any sentence has a Subject and a Predicate.

A simple subject/predicate sentence can be either universal, all bachelors are unmarried, or particular, this chalk is white is Analytic if and only if the predicate concept is contained in the subject concept.

To analyze something is to determine how it is constructed out of its constituent parts. An analysis of a concept is like a definition of the concept. For example, we might discover that something fits the concept bachelor if and only if it is an unmarried male person. In this case we can say that the concept bachelor contains such concept as being unmarried. So a judgment is analytic if analysis of the subject-concept reveals that it contains the predicate-concept.

A judgment is synthetic if and only if it is not analytic. Or, a judgment is synthetic just when the predicate concept is not contained in the subject concept. For example, all bachelors are tall, the Sun will rise tomorrow, or the children are playing in the playground, are synthetic judgments.

A Priori and A Posteriori Knowledge:

Consider these two statements:

1. All bachelors are unmarried.

2. Some bachelors are happy.

While we know both to be true, how we know differs.

A judgment is knowable a priori if and only if it can be justified independently of experience. A judgment is a posteriori if it cannot be known without recourse to experience. Arguably, the truths of mathematics (2 + 2 = 4) and logic (if George will go only if John will go, and George will go, then John will go) are a priori. We do not need empirical evidence in order to know that they are true.

Most judgments of particular fact, however, are a posteriori. I cannot know that a particular room is more than 10 wide without some sort of experience, for example the experience of measuring the room with a tape measure.

Analytic

Synthetic

A Priori

X

?

A Posteriori

X

Can we have synthetic a priori knowledge?

Immanuel Kant says yes.

Consider, for example, our knowledge that 7+5=12 and that the interior angles of any triangle add up to a straight line. These (and similar) truths of mathematics and geometry are synthetic judgments: the concept the sum of the interior angles is not contained in the concept of a triangle. Yet, clearly, such truths are known a priori, since they apply with strict and universal necessity to all of the objects of our experience, without having been derived from that experience itself.

Quine

In 1951, Willard Quine argued that the analyticsynthetic distinction is untenable. The argument at bottom is that there are no analytic truths, but all truths involve an empirical aspect.

Quine argues:

Analytic propositions propositions grounded in meanings, independent of matters of fact.

Synthetic propositions propositions grounded in fact.

The notion of an analytic proposition requires a notion of synonymy, but establishing synonymy inevitably leads to matters of fact synthetic propositions.

What is knowledge? What is Truth?

Religion: many have justified belief in claiming knowledge of the existence of a god. Others, in a similar way, have sound justification to claim that there isnt any god.

Then to what extent is it possible for a given subject or entity to be known?

One view is the objection that there is very little or no knowledge at allskepticism.

Before Galileo, earth was known to be at the center of the universe. Today we know betterbut do we? What puts us in a better position? If knowledge is linked with truth, what is the best instrument with which to acquire truth? Is it science? Is it religion?

Traditional Theory of knowledge: Many epistemologists hold the Justified True Belief (JTB) account of knowledge: the claim that knowledge can be conceptually analyzed as justified true belief.

A subject S knows that a proposition P is true if and only if:

1. P is true

2. S believes that P is true, and

3. S is justified in believing that P is true

Is Justified True Belief (JTB) knowledge? Consider these 3 scenarios:

I. Your roommate is watching TV in the kitchen. Youre in the bathroom preparing for work. You need to know the time and so you get out of the bathroom and see the time as it appears on the lower right corner of the TV set, which reads 2:15 P.M. Youre late for work. You get dressed quickly and zoom out. Now what you dont know is that your friend was playing a tape. It just so happened that the time in the video precisely coincided with the real time. Now, do you know the time?

1. It is true that the time is 2:15.

2. You believe that the time is 2:15, and,

3. You are justified in believing that the time is 2:15.

LOGIC THE SCIENCE OF ARGUMENTS

Different sciences, like biology, mathematics, etc. study their respective subject matters. Logic studies arguments. Arguments are the subject matter of logic.

In logic, an argument is a piece of reasoning used to show or express or prove a point; that point, whatever it may be, is supported by sub-points, which are statements.

For example:

All humans are mortal. My logic prof. is human.

Therefore, my logic prof. is mortal.

This is a classic example of an argument. A point is expressednamely, that logic prof. is mortal. This is called conclusion. The conclusion is supported by certain statements, All humans are mortal and my logic prof. is human.

ARGUMENT DEFINITION: An argument is a group of premises (at least one premise) in support of a conclusion.

OR

A group of statements, one of which is claimed to follow from the others.

PREMISE DEFINITION: A premise is a statement capable of being true or false. Fetch me a bagel! is not a premise. Joe is my dog. is a premise.

CONCLUSION DEFINITION: A conclusion is also a statement capable of being true or false; in addition, it is the main point of the argument, that is, the statement that is claimed to follow from other premises (statements).

How to understand/recognize an argument

To understand an argument you must first pick out the conclusion. To pick out the conclusion ask yourself, Whats the main point? What does the speaker want to persuade me to believe?

Also you can spot the conclusion as it is often preceded by certain clue words: Therefore, thus, it must be deduced that, so, consequently

On the other hand, premises often begin with these words: Since, because, for, given that

ARGUMENT