Week 3: PHIL 120 / Chapter 9 Section 1,2,3 (AND, NOT, XOR, IF)
1) Simple and Complex Propositions logic. Lotsa stuffs!
- A form of sentence can be presented in other similar forms (example
- 2 kinds of propositions: conditional and conjunction
- Complex Propositions: combine simple propositions with connectives
- Simple Propositions:
- Negations: a proposition that denies another proposition
Possible form of negations: original case is ‘g’. Negations are as follow: ~g / g is
not the case / Not g
Other forms of words that represent negation: no, never, can’t, nothing, nowhere,
- Double Negations: can be equivalently presented as X = ~~X or X = Not Not X.
Double negations act to make the sentence positive.
- Conjunctions: read pg 206
- Do exercise pg 206: 1-a)d), 2-b)f)
2) understand Disjunctions and Conditionals (or)
- the Exclusive Disjunctions: when statements of both X and Y can’t
significance be both true which means, you can have either one but not both. *I
think this is represented by XOR whereas it the option
between either..or is made explicit and YOU CAN’T HAVE BOTH
- Inclusive Conditionals (If X, then Y): the other forms that exist; X Y, if X,
Have to be careful with some statements as the antecedents could be combined.
E.g: If (X & Y), then Z
See example pg 210 and read the notes in the block
- Do exercise pg 211: 1- a)d)g), 2—b)f)i)l) 3) Translation (10 Rules to Obey)
#1 Use lowercase letters to represent simple propositions
- Let the simple proposition appears as a POSITIVE statement
#2 Use brackets to avoid ambiguity
- Example: If a, then b or c. this can be interpreted as follow: if a, then (b or c) / (if a,
then b) or c. Both imply different meanings.
#3 Do not confuse indicator words with connectives
- Words like because and therefore are logical indicators that are used to identify
argument and premises
- So, they can’t be represented with symbols << can only be used by connectives
#4 Distinguish ‘if’ and ‘only if’
- The phrase that follow ‘if’ is called antecedent. E.g: If [the t-shirt is blue]
- The phrase that follow ‘only if’ is the consequent. Only if [you’re done with your
- ‘only if’ also denotes that the condition is necessary but not sufficient for the premise.
Meaning, there could be additional premises exist.
#5 Treat biconditionals as conjunctios with conditional conjuncts
- Ordinary condition: the implication goes one way; the antecedent implies the
- Biconditional condition: the implication goes 2 ways; the antecedent implies the
consequent and the consequent implies the antecedent
- The case where ‘if and only if’ applies – order doesn’t matter
#6 Treat ‘unless’ statements as conditionals
#7 Translate sentences that express the same proposition in the same way #8 Translate logical connectors literally if you can
#9 Ignore variations that do not affect the validity of an argument
#10 Check your translation by translating back to ordinary English
- Do exercise pg 216. 1—e)i)j)l)q), 2—a)b)e)f), 3—f), 4—e)g)
Supervised Lab 3
- Lots about deductively valid arguments – read / figuring out how to know when