- 118 Views
- Uploaded on
- Presentation posted in: General

Rules of Replacement

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Logic

A very elementary introduction

Rules of Replacement

Demorgan’s Theorems

Some basic laws of logic

- The law of non-contradiction
A is not ~A

- The law of identity
A=A

- The law of excluded middle
statements that have a truth value are either possibly true or possibly false not half true or half false

Types of Logic

- Symbolic Logic
- Modal Logic
- Propositional Logic
- Propositional logic is also called propositional calculus is it includes the following A) consonants, sentential connectives such as if,then,and B) existing rules of inference

What is a proposition?

- A proposition is a statement of thought that is expressed in language. [Can be any human language] This statement has a truth value.
- For example: Boiling water is hot. This is either true or false.

Not all sentences are propositions

- Sentences such as: Go outside and play ball have no truth value.

Sense and Reference

- Sense: The meaning of a statement
- Reference: The state of affairs of the universe to which my utterance points.

Antecedents

- What goes before. In an if, then statement the antecedent would be “if” portion.
For example: If it rains then wear a jacket.

Consequent

- What follows after. The consequent is the then portion. Using our last example If it rains then wear a jacket
Jacket here is the consequent.

Soundness vs. Validity

- Valid arguments contain true premises therefore the conclusion that follows must also be true. It is possible for an argument to be factually untrue but logically valid.
- Soundness on the other hand refers to a valid argument that contains factually true premises.

Truth Functional connectives

Truth functional connectives link propositions together. For example V or vel stands for “or” the dot . Stands for “and” these truth functional connective link together logical statements.

Causation and Logical relations

- Logical relations do not account for contingencies. For example if we were to look at the causal relationship between my throwing a rock and it breaking a window we would have to examine the force of my throw, the thickness of the window, the distance, the thickness of the rock, the timing of my throw, the arm I am using, etc.

Deductive Nomological account

- The logician Carl Hempel argued that for every antecedent cause x, the consequent y must by necessity happen.

Implication or Material Equivalence

P implies Q is always true except when the antecedent [P] is true and the consequent is false

A table for truth

- Truth tables are logical diagrams so that every possible truth value can be examined.

Constructing truth tables

- 2 times the number of variables gives us the possible number of truths. 2(n)
For example p v q contains two variable p and q so for this truth table we would construct it like this:

p q p v q

t t t

t f t

f t t

f f f

Rules of Inference

- Modus Ponens
P -> Q

P

:. Q

- Modus Tollens
P->Q

~Q

.:~P

Rules of Inference #2

- Hypothetical Syllogism
P->Q

Q->R

.: P->R

- Disjunctive Syllogism
P v Q

~P

.:Q

Rules of Inference

- Constructive Dilemma
(P->Q) & (R->S)

P v R

:. Q v S