# propositions p and q

Discussion in 'Language Notes' started by naqshbandijamaati, Nov 7, 2008.

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1. ### naqshbandijamaatiVeteran

The reason that sometimes form can break down is that if we look carefully some of our Ps and Qs are not, formally, propositions at all; this is often the case with arguments people use about God etc.

a proposition as you know is formally 'a statement that can clearly be classified as true or false'. e.g. 3=1+6 is a propostion since it is clearly false whereas 'God exists' is NOT as it cannot be clearly identified as T or F without further info, logically speaking.

2. ### naqshbandijamaatiVeteran

i think the second argument is justified because it is equivalent in form to
~P v Q by definition of P---------> Q.

in other words
P--> Q
Q
I - P is invalid

is something i can accept.

3. in sentential logic, validity concerns itself with form not content. also we are not dealing with bi-conditionals but just conditionals alone. so the following two forms is what the discussion is about.

p --> q,

p

I- q is valid.
-------

p --> q

q

I- p

is inavlid.

this is the issue. so what do you say about where antecedent is justified from consequent as above in the second formulation?

4. ### naqshbandijamaatiVeteran

thus we see that logically such arguments hold no water....

5. ### naqshbandijamaatiVeteran

example:

if Ala Hazrat has said the Earth is stationary then the Earth must be stationary.

P = Ala Hazrat said the Earth is stationary.
Q = The Earth is stationary

We need (see above) to find the truth value of not P or Q [~P or Q] to analyse this so.

P is true (T), therefore not P is false and Q is false therefore we have a False and a False which is False. Therefore this argument is invalid. (A disjunction i.e. 2 propostions linked by "or" is true if either P or Q is true but if both are false it is false).

6. ### naqshbandijamaatiVeteran

ah...formal propositional logic...i teach it in one of my maths courses:

P ---> Q = if P then Q which, mathematically, has the same truth value (T or F) as
the disjunction "Not P or Q" [in symbols ~P v Q] which means it is true (i.e. a valid argument) if either proposition ~P is true (ie. P is false) OR if Q is true...where P and Q are propositions.

It is much easier to use P and Q with symbols actually to analyse a validity of an argument...

The mathematical equivalent of the logical argument "if and only if" or "equivalent to" is mathematically equivalent to the truth value given by [~P v Q] ^ [~Q v P] i.e .it is only valid if the proposition 'if P then Q' AND (^) its converse (if Q then P) are BOTH
true...

Last edited: Nov 7, 2008

7. there are three kinds of evidences: demonstrative, dialectical and rhetorical.
the first is about 'forms' hence our logical forms to make a point. the first form is an example of formal validity and second form is an example of invalid form in logic. prove to me that the second form is valid with reference to logic. please stick to rhetoricals. that was merely to test whether we can have a reductionist discussion but hazrat proved otherwise and instead would like to do lenghthy khitaabs.

thee first statements is reformatted for clarity thus:
1. if p, then q.
2. p.
3. therefore q.

-----------------------
second:
1. if p, then q.
2. q.
3. therefore not-p
illustrates what? if we have to prove q is not-p, why show any dependency at all? we common folk cannot easily grasp symbols; so let us use words.
1. if i have money (p) then i am rich (q)
2. i am rich (q)
3. therefore i do not have money (not-p).
erm...

Last edited: Nov 6, 2008