Thursday, February 28, 2013
Assert - to present some claim that may or may not be true
Argument - set of statements that are presented as true and that have a very important internal relation
Elements of an argument:
o Premises - statements which are intended to provide rational support or establish the truth
of a further statement
Conclusion - statement intended to rationally supported by set of premises
Essential Premises - premises that would remain if all irrelevancies are removed it will still be true
Propositions, sentences, claims - forms you could make an assertion in
Validity - structural property of arguments. A argument is valid just in case there is no way for the
conclusion to be false if all premises are true.
Soundness - is valid and have all true premises therefore it proves its conclusion.
Inference - act of reaching a conclusion on the basis of some premises.
Aristotle Laws of Thought:
Univocal - a term that has only one single meaning or interpretation
Law of Identity - for any proposition "P"; "P" if and only if "P"
Law of Non-Contradiction - not both "P" and not - "P"
Law of Excluded Middle - "P" or not - "P"
Classical Logic - all of the above
Intuitionistic Logic - system of logic that does not include Law of Excluded-Middle
Tolerates vagueness and fuzzy boundaries
But you cannot take a disproof of not - P as a proof P
Dialetheic - keeps the law of Excluded-Middle but gives up or restricts the Law of Non-Contradiction (ex
anything in the legal system)
Model Logics - includes notions like : belief, knowledge, obligation, possibility and temporality
Explanations - where we appeal to some facts in order to rationalize or make sense of some other facts
Causal Explanations - describing in part the prior conditions that caused some event
Pseudo-Explanation - providing some triviality or a mere label when an explanation is called for (one
word answers to not one word questions)
Modus Ponens - if "P" then "Q", "P" therefore "Q"
If it raining, then the ground is wet. It is raining, therefore the ground is wet.
Modus Tollens - if "P" then "Q", not "Q" therefore not "P"
If it raining, then the ground is wet. The ground is not wet, so it is not raining.
Conditional Reasoning - if "P" then "Q"
If it is raining then the ground is wet
Whenever something happens that is dependent to something else
Disjunctive Syllogism - all premises are conditional
Either foxes are mammals or rabbits are birds, rabbits are not birds, therefore foxes are mammals.
Hypothetical Syllogism - if P then Q, if Q then R, therefore if P then R
Method of Counter-Example - a way to prove an argument invalid by thinking of ways for all the
premises to be true while the conclusion is false The club president appoints the treasurer, the chair of the club appoints the vice-president
therefore the treasurer and the vice-president are appointed by different people, which is invalid
if the same person is both president and chair.
Simplification - "P" and "Q" therefore "P"
Conjunction - "P" + "Q" = "P" and "Q"
Addition - "P" therefore "P" or "Q"
My hair is brown, therefore my hair is brown or blonde.
If we already know that "P" is true, it guarantees that "P or Q" is true no matter what "Q" is
Constructive Dilemma - P or Q, if P then R, if Q then S, therefore R or S
If i am blonde or brunette, if i'm blonde then i'm 16, if i'm brunette i have a phone, therefore i'm
16 or i have a phone
Destructive Dilemma - if P then R, if Q then S, not R or not S, therefore not P or not Q
If i'm blonde then i'm 16, if i'm brunette i have a phone, i'm not 16 and i don't have a phone,
therefore i'm not blonde or brunette
Linked Arguments - premises tie together to support a single overall conclusion
List style, 1 2 therefore 3
Convergent Argument - whole bunch of premises that directly support conclusion and do not depend on
Sequential Arguments - premises establish intermediate conclusions which the service premises for
some further conclusion
Literacy is important life skill, if you go to university you must be literate, Joe goes to university,
therefore Joe is literate, therefore at least one person is literate, therefore one person has a skill
Truth Conditions - how things would have to be in order for statement to be true
Bivalent - only two possible truth values
Truth values - degree of truth
Contingent Truth - only truths that are only truth in some situations, but could have turned out
Necessary Truths - they would be true not matter how things may have turned out
Necessary Conditions - a condition that is true but not sufficient, cannot be flipped around
Being warm-blooded makes you a mammal, but a mammal does not make you warm-blooded
Conjunctive Statements/ Conjunction - contains two or more sub-statements that contain "and" or
"but", a conjunction is true if and only if both of its conjuncts are true
Disjunctive Statement - statement of the form "P" or "Q" and is true in case at least one of the "P" and
"Q" are true
Conditional Statements - statement of the form if "P" then "Q" is true unless "P" is true but "Q" is false
Antecedent - "IF"
Consequent - "THEN"
Types of Conditionals:
Indicative Conditionals - if "P" then "Q"
Subjunctive Conditionals - if it were to be the case that "P" then it would be the case that "Q"