On Necessity and Possibility

By Dennis J. Darland

June 5, 2007

Revised December 19, 2007

Copyright © 2007 Dennis J. Darland

On Identity


Simple identity statements, if true, are necessary. From the prior example Cicero = Tully, and Necessarily(Cicero = Tully).  But ‘Cicero’ ~= ‘Tully’. So ~Necessarily(Belief-R(Tom,’a=b’,’=’,’Cicero’,’Tully’,now). But Someone else can see of Tom

Tom believes Cicero = Cicero now so also

·         Belief_r(Tom,now,,’=’,’Cicero’,’Cicero’)

·         Symbol_1r(Tom,now,”=”,=)

·         Symbol_0r(Tom,now,’Cicero’,Cicero)

·         Symbol_0r(Tom,now,’Tully’,Tully)

But since Cicero = Tully (even though Tom doesn’t know it)


So it follows Tom believes Cicero = Tully now.

But still ~belief_r(Tom,now,’=’,’Cicero’,Tully’).

Because of Tom’s ignorance.

The important thing here is that ~(Symbol_0r(S,t,x,a) & Symbol_0r(S,t,y,a) => belief_0r(S,t,’=’,x,y)), i.e. S may have different symbols for the same thing without realizing it.

I would think necessity of a proposition would just be that the proposition was a theorem of logic.

On Essences

There are no essences. All necessary truths are purely logical.  Necessarily Cicero = Tully, but this says the same as Necessarily Tully = Tully. So is implied by (x)Necessarily x = x. Tom just doesn’t know it is such a case. Likewise denounced(Tully,Catiline) is not necessary, but it is necessary that (supposing Tully is the only person to do so) that the x, such that denounced(x,Catiline), denounced Catiline. But this is not a property of Tully, it is because of the logical form of the proposition. Perhaps I should add that even though Tully = the x such that denounced(x,Catiline), this will not be necessary, which can be seen by Russell’s definition of ‘the’ in this context.

On Possibility
Possibility is just not necessarily not.

On a prioi and a posteriori

I do not see how there can be any knowledge without experience.  There may be concepts that seem to apply to all possible experience, but we still learn them through some particular experiences.(e.g. numbers).  That the concepts are useful still depends on very general facts of nature; imagine these facts different and different concepts can also be imagined.  I think this distinction of little importance.

On analytic vs. synthetic

There are relationships between concepts which seem to be just conceptual.  E.g. that unmarried men are bachelors.  And others which are not. E.g. that gold is a yellow metal.  But what about “Whales are mammals”? Our concepts can change with experience.  This distinction has some use, but I do not think it very important.  Most analytic knowledge would be eliminated by going to a minimum volcabulary, but not all, as a spot is red seems to imply that it is not green. Is this analytic or synthetic? 


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