Propositional Logic Symposia - [6] – Complex and Partial Truth Tables

[de_budding]

I like you art work, it's been coming along nicely and thank you very much for the time and effort you have put into these posts. Most helpful and now I get it
Dan.

[Arjen]

Originally Posted by de_budding

God I really need to figuer out what the difference is between the two (reality/actuality) >.<

So feel free to give me a hard time

Perhaps a new topic would be appropriate?

[de_budding]

Ok, what sub forum would be best suited?
And how are the questions...

What is actuality?
What is reality?
How do actuality and reality differ?

Dan.

[Arjen]

Take your pick..

[Holiday20310401]

Originally Posted by Arjen

Such a table cannot be constructed because it would be a table used for the creators personal opinions of the usage of such words.


I'll not give you a hard time on actuality and reality....

Anyway, the popular use of logic contains the understanding that correct reasoning has no bearing on reality; only on an actuality.

I'm sorry but I have to disagree with you here, but that is probably because we do not have the same definitions of actuality and reality in our heads, because I struggle to entertain myself with your version when mine just makes so much more sense. Perhaps you could start a thread to clarify, Arjen.


Also Vide, I don't quite understand step 8 at the very beginning. When we dealt with connectives it was all with two variables, not 1. So vT = T and vF = F, because single variables will always imply themselves?

And are partial tables mandatory?

[VideCorSpoon]

Step 8 is the culmination of the entire truth table. Steps 1 – 6 were obviously just a set up for the entire problem. In other words, we had to get the truth values that we worked out in steps 4 into the main problem area so that we can work out the connectives. Once you reach 7, step 7 and 8 have to be done simultaneously. Let me explain. Looking at the conjunction and disjunction, we can see we have to determine which is in fact the main connective, or simply, the primary column we are going to be able to judge the truth table upon. The bracket version of PEMDAS in symposia 5 we examined tells us that the conjunction is the first to be solved, then the disjunction. Now with the conjunction, we compare the opposing variables to the connective A and B. Once we get the column for the connective, we completely forget about the truth values in those opposing columns of the conjunction and then do the disjunction. To do the disjunction, we compare the conjunction column and the B column, the two opposing columns. Solve and your done!

As to your points about a single variable, that’s a really good observation. I suppose you could say that single variables always imply themselves. Perhaps we could think of it as a statement rather than an argument. Good point!

As to partial truth tables being mandatory, no they are not necessary, but they are useful. Remember that if you have more than a few variables, you will have one heck f a long truth probability matrix to sort out. The partial truth tables do away with that.

As to your comment on reality and actuality…. I agree with you. Philosophically, it is a relative notion. Descartes, etc. all held different beliefs in accepted perspectives. Good point.