Mark James Wooding
Education • Comedy • Writing
Some days I post something here. Sometimes I Post Raisin Bran. Some days I Kellogg's. I never know in advance.
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January 06, 2022
Moving Forward: An Introduction to Formal Logic, Lecture 2

Notes from Lecture 2:

Logic is the study of rational argumentation.

Rational: that which we have grounds to believe is likely true.

Argument: a set of sentences in which one sentence, called the conclusion, is said to follow from the other sentences, said to be the premises. There can only be one conclusion, but any number of premises.

More than one conclusion, more than one argument; no conclusion, no argument.

There are indicator words that help determine if there is a conclusion, and help determine what any premises are.

Examples (non-exhaustive) of indicator words: because, therefore, so, thus, ergo.

In instances where there are no indicator words, you can try inserting your own indicator words. The lecturer's preferred indicator-words to insert are "therefore", and "because". If the word "therefore" can be inserted without changing the meaning of the sentence, the conclusion is the statement immediately after that. When you can insert the word "because", what precedes it is probably a conclusion, and what follows is a premise.

Sometimes premises are assumed to be obvious, and they are implied rather than stated. An enthymeme is an argument with a suppressed premise.

The steps in determining whether a set of sentences is an argument are:

1. Determine if a group of sentences contains a conclusion.
2. If so, does it include any premises, either stated or implied.
3. If so, it is an argument.

There are two types of arguments: deductive, and inductive

In a deductive argument, the conclusion is no broader than its premises. An example: All men are mortal. Socrates is a man. Socrates is mortal.

The premise "All men are mortal" is wide in scope. The conclusion, "Socrates is mortal", is narrower in scope than one of the premises, therefore it is a deductive argument.

Inductive arguments have a conclusion that is broader than either of its premises. Such as: The sun has risen every day. The sun will rise every day in the future.

The future days are not included in a premise.

In a deductive argument with true premises and a logically valid conclusion, the certainty of that conclusion is 100%.

[If a deductive argument has a premise that is only probable, then the certainty of that conclusion will be less than 100%.]

For an inductive argument, the certainty is less than 100%.

If an inductive argument can be restated as a deductive argument, then the degree of certainty increases. [However, the degree of certainty will always depend on the degree of certainty of the premises.]

There are two other important properties of an argument: Validity, and well-groundedness

An argument is valid if the conclusion follows from the premises.

An argument is well-grounded if all of its premises are true.

Both properties are necessary for a sound argument.

Formal logic looks at the structure of an argument.

Informal logic considers the well-groundedness of an argument.

[Personally, in regard to the argument about Socrates being mortal, one of the premises, "All men are mortal", cannot be proven. Some men are still living, others may be born in the future, and their mortality cannot be established.

Also, we can't be 100% certain that Socrates died. According to reports from the time, Socrates appeared to have died, so he was probably mortal. Whether the cup that was alleged to have hemlock actually contained a sleeping potion, and his friends spirited his body away to another location and left the shroud-wrapped corpse of another man in his place, isn't something we can know. We can only say, based on the reports, he appears to have died. It is highly improbable that he is still living, but it isn't certain.]

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