"If it was so, it might be; and if it were so, it would be..." What does this mean?

I'm translating a book, which involves logic and quoted the sentence from Lewis Carroll's Through the Looking Glass: "If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic." The Carroll's book can be found here: http://sabian.org/looking_glass4.php

I cannot even make out a clue what this sentence means, let alone translating. It seems I never come across any modal verbs or tenses used like this.

I'm not 100% sure, but maybe it's the valid argument form called "Modus ponens". If one thing (A) is true, then the other thing (B) will also be true.

Put in a logical form:

If A, then B

A

therefore B

For example: If it's Monday today, Sarah has to go to work

It is Monday today

Therefore Sarah has to go to work

I think that kind of logic might be, what Carroll was trying to explain.

"If it was so, it might be and if it were so, it would be; but as it isn't, it ain't. That's logic."

Translation:

If it was A, it might be B, if it were A, it would be B, but it isn't A then it ain't B

But maybe the last part "but as it isn't, it ain't" is actually Modus Tollens:

If A, then B

Not B

Therefore not A

So the last part (but as it isn't, it ain't) might be translated to:

But it isnt B, then it ain't A

If the latter is true, then the logic explained is Modus Tollens instead of Modus Ponens

I hope I didn't confuse you, and that you're satisfied with the answer :)

"If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."

This is simply a literary play on words - One that uses the sort of confused and ambiguous logic that Carroll is well-known for. In it's most basic form it is a simple confusion of subjunctives inside an, 'Alpha AND Beta' format. The thought process is deliberately confused, runs in a circle, and comes to an unexpected end without reaching any sort of useful conclusion.

In order for the logical statement, 'alpha and beta' to be true both alpha and beta must be true. If either one is false then the import of the entire statement collapses. The contrapositive, 'alpha or beta' might be a viable alternative; but with confusion as his desired goal, Carroll knew better than to introduce an opposing conjunction.

One thing is certain: You cannot correctly use, 'if' and, 'was' in the same simple sentence, and remain grammatically correct. 'If' implies, 'were'; and that's a tough subjunctive structure to get around. (It can be done; but a highly descriptive context would be needed.)

Look at it this way: 'If it were so, it might be; and if it were so it would be; but as it isn't, it ain't.' 'That's logic.' If you change, 'was' to were, and recognize the fact that, 'alpha AND beta' (by the author's own admission) is a true statement, then, instead of relying upon logic, Carroll's compound assertion is actually referring to the preposterous development of an, otherwise, certain event.

However, with both, 'alpha and beta' being incorrect the entire statement is grammatical gobbledygook that fits in very well with the bizarre world of illogical impossibilities that Carroll so eloquently portrayed.