Phil 10 Midterm 1 - Corrected

Validity

Any argument that is impossible for the conclusion to be true while all the premises are false

Sentence

Premise

The settings of the argument, usually the first few sentences

Conclusion

What derives from the premises; usually the last sentence of the argument

Argument

A series of premises that is followed by a conclusion

Necessary truth

There is no way for the sentences to be false

Necessary falsehood

There is no way for the sentences to be true

Contingent

Can be true in some instances and false in other instances

Grey area or middleground between necessary truth and necessary falsehood

Connectives

Disjunction

Negation

Biconditionals

"if and only if"

<-->

Parentheses

Used for two way connectives

Two way connectives

Any connective that is not negation

Disjunction

v, |

"...or..."

Negation

"Is not"

Note: be careful with negation as it is the absence of the original sentence, not the opposite!

Invalidity and validity

Properties of arguments

Truth and falsehood

Properties of sentences

Atomic sentences

Any sentence that does not have a smaller subsentence in it

Necessarily equivalent

Both of the sentences have the same true or false value

Sentence rules

Every atomic sentence is a sentence

If A is a sentence, then the negation of A is also a sentence

If both A and B are sentences using two way connectives on them will also result in sentences

Suppositional argument

Potentially true, create a fake scenario

Bracketing conventions

Do not put brackets around an atomic sentence

Do not put brackets around negation

Round and square brackets ("( )" and "[ ]") are interchangeable and can be both used

Relaxed bracketing convention

The outer brackets that are not a negation are optional

^, &, *

"or..."

Disjunction

v, |

"and..."

Conjunction

-->

"if... then..."

Conditional

<-->

"if and only if"

Biconditional

Main logical operator

1. If the first symbol outside the brackets is a negation, then that is the main logical operator

2. Otherwise, count parentheses with "(" being 1 and ")

being -1, when your count is exactly 1 the main operator aside from negation is the main logical operator

Scope

Subsentence of which the operator is the main logical operator