Rules of replacement
1 / 23

Rules of Replacement - PowerPoint PPT Presentation

  • Uploaded on

Rules of Replacement. 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Rules of Replacement' - tasha-howard

An Image/Link below is provided (as is) to download presentation

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 - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript



A very elementary introduction

Rules of replacement1
Rules of Replacement

Demorgan’s Theorems

Some basic laws of logic
Some basic laws of logic

  • The law of non-contradiction

    A is not ~A

  • The law of identity


  • 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
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
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
Not all sentences are propositions

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

Sense and reference
Sense and Reference

  • Sense: The meaning of a statement

  • Reference: The state of affairs of the universe to which my utterance points.


  • What goes before. In an if, then statement the antecedent would be “if” portion.

    For example: If it rains then wear a jacket.


  • 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
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

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
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
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
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
A table for truth

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

Constructing truth tables
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
Rules of Inference

  • Modus Ponens

    P -> Q


    :. Q

  • Modus Tollens




Rules of inference 2
Rules of Inference #2

  • Hypothetical Syllogism



    .: P->R

  • Disjunctive Syllogism

    P v Q



Rules of inference1
Rules of Inference

  • Constructive Dilemma

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

    P v R

    :. Q v S

Destructive dilemma
Destructive Dilemma

(p->q) & (r->s)

~q v ~s

.: ~p v ~r

More rules of inference
More Rules of Inference


P & Q





.: P & Q

One last one
One last one



.: p v q