Theli

This shows that one should be carefull when using the "truth-word" descibing a positive claim.
Personally, I very seldom use the word "truth" or "fact" when describing an objective positive claim.
"Most likely based on obervations/logic" seems much more honest to me.

Clutch

Theli, agreed.

Tron, also agreed. That's why most logicians and philosophers reject the 'KK' principle (Kp --> KKp). Just because you know doesn't mean you know you know.

John Page

Clutch:

Can you clarify what you think p represents in the above. Is it a proposition, an existential body or thing, an item of knowledge or maybe something else?

Cheers, John

Clutch

It is normally understood as a schematic letter ranging over propositions, written in the way I've given it. But you might think of it instead as a universally bound variable.

John Page

Assuming extentionality over things that are not known seems dubious.

So, aside from adequate and definitions of truth and knowledge , I would re-phrase the princople as "If propositions can be proven to be true then we know the truth of those propositions", which is more like "If p then p".

The analysis you provide seems to create the illusion that propositional logic can maintain that propositions can be both true and false at the same time. In addition to my prior comments, I think the distribution creates the impression that the same p can be both known and unknown at the same time. This may be true in the universale case of all "knowers" (whose views may be different), but for a single "knower" either you know it or you don't.

Of course, a single human mind brain can be considered a separate parts. In this sense the knowability paradox may actually exist in our minds (parts or which know p and other parts which don't). So, if you consider a group of knowers, which could be societies, individual humans or parts of the brain it is inevitable (and I daresay demonstrable) that the truth varies. So much for extentionality, I suggest that a complete understanding of paradox would have to employ clearer definitions of truth and knowledge.

Cheers, John

Keith Russell

Greetings:

Doesn't this depend utterly on our definition of God?

God is not only usually defined as omniscient, but also as the 'Creator'.

Just because some being far off in the distant future might come to 'know everything', doesn't mean that this being is 'God', the Creator, who loves us, and whom we should worship, and to whom all our present religions refer as 'God'.

Keith.

Clutch

Keith, yes that's a powerful objection to seeing Plantinga's claim as demonstrative of Christianity.

Of course, there's a long tradition of this fallacy, going back to Aquinas's dreadful "And this everyone knows to be God."