Dr Newton Smith
@11 on 13 Oct 99
can see the validity of the argument without understanidng the content � logic is about form, not content
logic = study of valid arguments, whose validty arises from form not content
can do logic without dictionary
if the premises are true, the conclusion must be true
can use symbols, cos is not content-dependent
systematic description of the pathways of valid argument
F: icabod fails prelims
D: icabod will be sent down
if F then D
F
:. D
P: The weather is cold
Q: The weather is wet
P and Q
\ P
! P or Q
! \ P
argument = premises + conclusion
use sentences (of English)
premises <> sentences
premises = statements [propositions]
statement = �what is meant, said or conveyed by a sentence.�
e.g. il pleut
it is raining
caesar stabbed brutus
brutus was stabbed by caesar
same sentence sometimes �/span> 2 statements �
not all sentences �/span> statements/propositions � only indicative sentences
property of a statement
any statement either has or lacks it
true or false
one = true, other = false
study of arguments
validity
defined conditionally
if the premises are true
the conclusion must be true
false premises � false conclusion
it is possible for premises to be true but conclusions to be false
e.g. A = a smart Balliol student, B = a smart Balliol student
\ all Balliol students = smart
if = any possible circumstances in which the premises are true, the conclusion is true
validity is truth-preserving
representing explicitly procedures followed implicitly � explains your capacity systematically
linguistics
system of rules: sentences vs non-sentences
aim:
system of rules
represent explicityly
mathematical model
computer program
premises can support but not entail
= inductive, not deductive arguments
consistency of belief
belief��� = mental state (not relevant to Hodges logic � varies over time and with different people)
�������������� = content = proposition
only interested in the content of the belief, which forms a proposition/statement
consistency of set of statements = when there is a possible circumstance in which all are true
but: consistency � truth
validity
form not content
definition (if premises = true �/span> conclusion = true
test
counter-example set {B or O, no-O, not-B} = inconsistent
formed from premises of the argument + the negation of conclusion
argument = valid just in case its CES is inconsistent
CES is inconsistent
{B or O, not-O, not-B}
no way that it can all be true
B or O�������� true
not-O���������� true
not-B���������� false
so B is true
and the argument is valid
an argument = valid if and only if its counter-example set is inconsistent
an argument is valid exactly when its CES is inconsistent
Hodges (with the CES set thing) and the traditionalists are doing the same thing
sometimes have to interpret rather than take sentences literally
contradictions: reinterpret to enforce ambiguity