Logos Formal Logic

Deductive Logic – the process of reasoning where a certain conclusion is reached from following a set of general or universal premises/statements. Premise – a statement used as a proof or observation in an argument Conclusion – the end point or result of the premises stated in an argument

Validity – a deductive argument is valid if it has a form that would make it impossible for the premises to be true and the conclusion false. Validity is a matter of the form or structure of an argument, as opposed to the content of the argument. If an argument is valid, then any other argument with the same logical structure will also be valid, regardless of its content. Keep in mind that an argument can be valid even if its premises are not actually true.

Soundness – an argument that is both valid and factually correct is sound; if argument has the correct form and the premises are actually true in reality, the argument is sound.

Syllogism – the simplest form of a valid deductive argument, containing three things: a major premise a minor premise and a conclusion, which follows logically from the major and the minor premises. The major premise is a general principle. The minor premise is a specific statement. Logically, the conclusion follows from applying the major to the minor premise.

The common form of a syllogism is: If all P are Q (major premise) And A is P (minor premise) Then A is Q (conclusion)

For example, this is the classic syllogism given by Aristotle:   If all humans (P) are mortal (Q) (major premise) And all Greeks (A) are humans (P) (minor premise) Then all Greeks (A) are mortal (Q) (conclusion)

Another example: Men die. (general principle) Socrates is a man. (specific statement) Socrates will die. (application of general principle to specific statement)

Fallacy – an error in logic based on the form of the argument. Example: If A happens then B happens. B happens. Therefore, A happens. If A happens then B happens but that does not mean that B ONLY FOLLOWS A. B might actually happen for a number of reasons, A simply being one of them. Therefore, B happening without A is possible and simply the presence of B is not enough to assume A.

Tautology – a valid argument that is seen as so obvious that it did not need to be stated. A logical tautology is very different from a rhetorical tautology. It's a statement that will evaluate as true regardless of the truth values of the components of the sentence. For example, in logic "or" is non exclusive, which means that if we say "A or B", the statement "A or B" would be true if A is true, if B is true, or if both are true. The only way "A or B" can be false is if both A and B are false. From this we can construct an example of a logical tautology. We can say "A or not A", and it will be always be true regardless of whether A is true or not. This is the case because whenever A is false, not A is true, so at least one of the two will always be true. A real world example of a logical tautology would be "the car is moving or it is not moving" or "the door is locked or it is not locked" or "the girl is pregnant or she is not pregnant."

Tautology in writing A major nuclear disaster could have occurred . . . . . . who died of a fatal dose of heroin . . . equalized the game to a 2-2 draw . . . kept it from his friends that he was a secret drinker

Inductive Logic the process of reasoning in which: a) the premises of an argument support the conclusion, but do not guarantee it b) the conclusion contains information that is not contained in the premises.

Inductive arguments use premises that often take specific examples and observations from the world in front of the person, and are used to make larger generalizations about the world unseen by the person.

Example: (premise 1). My dog Barky has four legs. (premise 2) Example: (premise 1) My dog Barky has four legs. (premise 2) All of Barky’s dog friends have four legs. (conclusion) All dogs have four legs.   Both of the premises give information that is seen by the person speaking (his own dog and other dogs he has seen), but the conclusion gives information about “all dogs” even though the speaker has not seen all dogs. The premises support the conclusion and make it logical, but the conclusion could still be wrong. For example, what if a dog has a birth defect and only three legs? Is that creature no longer a “dog”? Or what if a new species of dogs is found in the Amazon that has a fifth leg for hanging from tree branches to find food?

There are four common types of inductive arguments: Generalization Statistical Syllogism Analogy Simple Induction

Generalization: starts with a specific observation and makes an assumption about the world. My cat Fuzzy likes to eat fish. Jennifer’s cat Scratchy likes to eat fish. All cats like to eat fish. Most of the kids I know like candy. Most kids like candy.

Statistical Syllogism: starts with an assumption about the world and makes an assumption about something specific. Most cats like to eat fish. Felix is a cat. Felix likes to eat fish. Few dogs lack fleas. Spot is a dog. Spot has fleas.

Analogy: Drawing a conclusion from comparing two or more similar things. Jorge and Alex have similar talents and work equally hard. Jorge did well on the test. Alex did well on the test.

Simple Induction: Drawing a conclusion about a member of a group from observations about the rest of the group. All of the cats I’ve known like to eat fish. My new cat will like to eat fish. Most students dislike tests. Betsy is a student. Betsy dislikes tests.

DO: Deductive - 1) Write 5 syllogisms, indicating each premise and the conclusion. 2) Using the fallacy example, write 1 fallacies.   Inductive – 1) Write one examples of each of the four common types of inductive arguments (Generalization, Statistical Syllogism, Analogy, Simple Induction), labeling premises and conclusions.