Argument For using "if ....then".

Let p = 2 < 3       Let q = Venus is a planet

(i) if 2<3 then Venus is a planet -- (if p then q)-- is treated as true.

(ii) if 2>3 then Venus is a planet -- (if p then q) -- also true.

(iii) if 2>3 then Venus is not a planet -- (if p then q) -- also true. but.....

(iv) if 2<3 then Venus is a Star -- (if p then q) -- is treated as false.

Material implication ( => ) does not conform exactly to the English form we use, that is , "if ..... then" or "implies".  Nevertheless, when we translate the Material Implication (=>) to the English statement "if....then" or "implies" within the logic statement nothing of importance is lost, which means that nothing of the argument in which the implication is used, is lost when it is translated to the English form. the argument is still valid.If we construct a Truth Table for p --> q (if.....then) we can see the results of both p and q.

From the Truth Table we can see that for statement (i) "if 2<3 then Venus is a planet which have the values of T and T so nothing is lost. 

Argument Against using "if....then"

There are Paradoxes when we use Material Implication which can be seen from the truth table, ( 1 ) when the Antecedent is FALSE the resultant or condition is TRUE and ( 2 ) when the Consequent is true the resultant is TRUE especially where p=F and q=T. These statements seem wrong when viewed grammatically but they are not contradictory, but because of these facts "if ......then" and "implies" seem to be "counter intuitive".  What we are looking for is a TRUTH functional type of IMPLICATION i.e. the connective between the Antecedent (p) and the Consequent (q) so that we can look at the Truth values alone and not the content of the Antecedent and the Consequent. If we think like this the content of the Antecedent and the Consequent is not applicable this in turn could mean that they are unrelated to each other.  For example:- (p) if.. we change the car oil  then.. we sometimes change the filter.  In sentence form we find a cross reference from p to q and from q to p but it may be impossible to paraphrase to remove the cross reference.

Alternative

Rather than look for alternatives in English form e.g. implies, is possible that, necessity, etc. I think we should look to an alternative for the LOGIC propositional form P --> q and the one with identical truth properties is the propositional form ¬P v q . which has the exact same truth table characteristics as shown in the truth table for P--> q. (Not P or q).

p	q	P => q	¬P v q
T	T	T	T
T	F	F	F
F	T	T	T
F	F	T	T

* Due to the facts above some Logicians have developed what they call "Relevance Logic" where the Antecedent and the Consequent must be in some way related. Entailment is used instead of Implication to describe the connective, but this has its own problems, Entailment cannot be treated as Truth Functional.  

*Paradoxes of Material Implication... www.earlham.edu/~peters/courses/log/mat-imp.htm

               ....................LOGIC COURSEWORK QUESTION...............

                ------------COUNTERFACTUAL OR SUBJUNCTIVE CONDITIONALS---------


           1. "If I were Tony Blair = P"
         "I would not be a socialist= q"

With regards to the English form this statement, I feel , would be false
because "if I were Tony Blair " then I would do say and think exactly
what he does because I would be him! so I have to treat this argument as 
hypothetical (subjunctive). Therefore the argument is invalid and
inconsistant.
Counterfactual or Subjunctive conditionals state that if it were the
case that P (I were Tony Blair) which I'm not then q (I would not be
a socialist) being hypothetical, are ideal for thought experiments
but do not lead to a definitive conclusion. 

If we try to represent Counterfactual Conditionals using the Material
Implication symbol --> we find it totally unsuitable for the reason
that any Material Implication with a false antecedent is classed as
true. When P is false then P --> q and P --> not q are both true,
it does not matter what q represents.

P "if I were Tony Blair" is in fact (making an assumption) replacing
a fact and therefore is a contradiction and the only way that I can 
see to return a true Truth Function is to negate both P and q.
not(p --> q)  not P V not q.
 p --> q is inconsistant because q is in direct opposition to P and invalid.
 
Take the example  P1 " if I stand beside wet paint and"
..................P2 " there is wet paint on my hands"
then..............C  "I touched the wet paint" 

This example can thought of as sound but it can never be logically
valid because P2 can happen without P1 which in turn means that 
P1 + P2 can be true when the conclusion C is FALSE and this is the 
contradiction to LOGICAL VALIDITY.  

Then if we represent the MI (-->) with "it is possible that" that is:-

P "if I were Tony Blair" `it is possible that` q "I would not be a socialist"
we can see because the argument is hypothetical (subjunctive) and the
connective is uncertain and forms a cross reference between P and q which 
cannot be removed.

If I were not Tony Blair "it is possible that"....... is exactly the same as
If I were Tony Blair....."it is possible that"

then because it does not matter what q represents we can have 

P "it is possible that" q or 
P "it is possible that" not q  which in all cases are assumptive by their 
very nature therefore the answers are not definite and can be possibly
right or possibly wrong in other words it is impossible to assign a 
Truth Table to Subjunctive or Hypothetical arguments of this kind.   
     

           ----------------------------Strict Implication---------------------------------

If 2<3 then necessarily 2<3+1 is true precisely if it is true in every possible 
situation.
Necessity means true at all times! and the Logic of Necessity is called 
Modal Logic and is symbolised by a small square.

Necessity (*Modal Logic) views this present world, everything considered, as 
just one vast range of existing and real possibilities. Each other world is a,
written in stone, reality of individuals with their own relations and properties
which are complete and definite (with exact limits).
Each world to be considered is actual (existing and real) to itself. Our world
i.e. this present world we live in, to us is actual, other worlds are merely
possibilities.
With all this in mind our problem "if 2<3 then necessarily 2<3+1" can have what
is termed as a "negative back half" which means that it is possible that 2 is 
not less than three and 2 is not less than 3+1 which would make the argument
"if 2<3 then necessarily 2<3+1 a contingency (a chance occurrence) and not a
necessity, so here necessity does not guarantee truth and as seen in the 
previous Question on Material Implication, we should not treat sentences as
truth bearers.  

*Modal means:- of form or of node as opposed to substance. In logic:- involving
affirmation of, possibility, necessity, or contingency. (Oxford dictionary)

              Example of necessity where P-->q.

P is a sufficient condition of q when P's truth guarantees q's truth.
By contrast, q is a necessary condition of P when q's falsehood guarantees P's
falsehood. 
Necessary propositions must be thought of as the special limiting case were the
value always turns out to be true irrespective of the world or how the world
might be i.e. every possible world.
Therefore if it is not logically necessary it must be contingent (a chance 
occurence).

Contingent Propositions:- how the world is (which may or may not be true.)
Necessary Propositions:- can not be false.