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## Logic

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Logic

A: Capital punishment is immoral.

B: No it isn’t!

A: Yes it is!

B: Well, what do you know about it?

A: I know more about it then you do!

B: Oh yeah? You’re an idiot!

Basic Terms

Logic: the study of how to reason well.

Argument: an attempt to show that something is true by providing evidence…the connection by which the conclusion is said “to follow” from the premise is called inference…

2 types of arguments: deductive and inductive reasoning

Deductive: reasons from the whole to the part…universal to the particular

Inductive: reasons from the part to the whole…particular to the universal

Syllogism: the most traditional and most common form of a deductive argument consisting of 2 premises and a concluding statement…Greek meaning propositions considered together…a valid argument form…there are 2 different types of syllogisms that we will look at…

The categorical syllogism: A complete sentence, with one subject and one predicate, that is either valid or invalid (needs reasoning).

The conditional syllogism: an argument that involves a precursor and a consequent signalled by the words “if…then”

Validity: Valid thinking is thinking in conformity with the rules. If the premises are true and the reasoning is valid, then the conclusion will be valid out of a force of necessity.

Non-sequitur: (it does not follow). This means that the conclusion cannot be deduced with certitude from the given premises. An invalid argument.

The Subject: that about which something is said.

All giraffes are animals. (giraffes = subject)

The Predicate: that which is said about something.

All giraffes are animals. (animals = predicate)

The copula: connects together or separates the S and the P. This term can hidden in the premise but can always be inserted back in to separate the S and P.

All giraffes are animals. (is/is not)

All monkeys climb. (hidden copula)

All monkeys areanimals that climb.

First, we look at categorical syllogism…then we will move on to conditional or hypothetical syllogisms next week…

For Example:

It is immoral to kill people.

Capital punishment is the killing of persons.

Therefore, capital punishment is immoral.

What is the subject?

What is the predicate?

The four Standard Propositional Codes for premises and concluding statements.

These codes come from the Latin words "Affirmo" and "Nego".

Affirmo: I affirm. Note the A and the I

Nego: I deny. Note the E and the O

A - universal affirmative: All S is P

I - particular affirmative: Some S is P

O - particular negative: Some S is not P.

E - universal negative: No S is P.

The parts of a categorical syllogism:

a. The two premises.

All A is B (first premise)Some B is C (second premise)Therefore, Some C is A

b. The Conclusion.

In the above syllogism, Therefore, Some C is A

The major term: this term is always the P (predicate) of the conclusion. In the example directly above, A is the major term.

The minor term: this term is always the S (subject) of the conclusion. In the example directly above, C is the minor term.

The middle term: this term is never in the conclusion but appears twice in the premises. (The function of the middle term is to connect together or keep apart the S and P in the conclusion).

Distribution: This is a very important term in logic. A distributed term covers 100% of the things referred to by the term.

An undistributed term covers less than 100% of the things referred to by the term (few, many, almost all).

For instance, All men are mortal. - and - Some men are Italian.

In this statement, "men" is distributed; for it covers 100% of the things referred by the term "men".

“Mortal” is undistributed. Why?

Because women can be mortal.

In Some men are Italian, "men" is undistributed; for the term covers less than 100% of the things referred to by the term "men".

“Italian” in undistributed. Why?

Because women can Italian as well.

Universal Affirmative statements (A statements): the subject is distributed, the predicate is undistributed.

Universal Negative statements (E statements): both the subject and the predicate are distributed.

Particular Affirmative statements (I statements): neither subject nor predicate is distributed (both are undistributed).

Particular Negative statements (O statements): the predicate alone is distributed.

E = No S is P

I = Some S is P

O = Some S is not P

Note the following (bold and underline = distributed)…the terms that are not underlined is undistributed…

Rules of Syllogistic (categorical) reasoning.

- In a valid categorical syllogism, the middle term must be distributed at least once.
- In a valid categorical syllogism, any term which is distributed in the conclusion must also be distributed in the premises.
- A syllogism must have three and only three terms.

Rules of Syllogistic (categorical) reasoningcontinued

- From two negative premises, no conclusion can be drawn.
- If a premise is particular, the conclusion must be particular.
- If a premise is negative, the conclusion must be negative.

- From two negative premises, no conclusion can be drawn.
- No dogs are cows
- No cows are pigs
- Therefore, no dogs are pigs.

- If a premise is particular, the conclusion must be particular.
- Some Italians are from Calabria.
- All Italians love spaghetti
- Therefore, all those from Calabria love spaghetti.

In a valid categorical syllogism, the middle term must be distributed at least once.

- All Germans love beer
- All Irishmen love beer
- Therefore, all Irishmen are Germans.

- In a valid categorical syllogism, any term which is distributed in the conclusion must also be distributed in the premises.
- All principals know about administrative problems
- No secretary is a principal.
- Therefore, no secretary knows about administrative problems

A syllogism must have three and only three terms.

- All Canadians like hockey.
- All Italians like soccer.
- Therefore, some Canadians like soccer.

If a premise is particular, the conclusion must be particular.

Some men are AmericanAll Americans love apple pieTherefore, all men love apple pie.

Again, if a premise is particular, the conclusion must be particular.

- Some men are Canadian.
- All Canadians love hockey.
- Therefore, all men love hockey.

- If a premise is negative, the conclusion must be negative.
- Some Canadians are not hockey players.
- Some hockey players are professionals
- Therefore, some professionals are Canadian.

Steps to Takein order to determine the validity of a syllogism

1. Circle your middle term.

2. Determine what kind of statement is the first premise (I.e., A statement, E statement, etc.)

3. Determine what kind of statement is the second premise. (I.e., A statement, E statement, etc.)

4. Determine what kind of statement is the conclusion. (I.e., A statement, E statement, etc.)

5. Place a “d” above all your distributed terms

6. Check to see if your middle term is distributed at least once. If it is, move on to #7.

7. Check your major and minor terms in the conclusion. If one of them is distributed, see if that term is distributed in the premises.

8. Check to see if any other rule is violated. If not, you have a valid syllogism.

A note on deductive logic…

Watson and Holmes are out on a camping trip. In the middle of the night Holmes wakes up Watson and asks, “Watson, look up into the sky and tell me what you see.”

“I see millions of stars, Holmes.” says Watson.

“…and what do you conclude from that, Watson” says Holmes.

Watson thinks for a moment. “Well” he says to Holmes.

“…Astronomically, it tells me that there are millions of galaxies an potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is about a quarter past three. Meteorologically, I suspect that we will have a beautiful day tomorrow. Theologically, I see that God is all powerful, and we are small and insignificant. Uh, what does it tell you Holmes?”

Holmes replies…“Someone has stolen our tent, Watson”

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