On Kripke
By Dennis J. Darland
July 2, 2007
Revised December 19, 2007
Copyright © 2007 Dennis J. Darland
We will take the following as primitive for my discussion
person_slice(event,t) it the event (Whitehead’s actual_occasion) which is a member of a person at time t.(actually there would be a set of events for some duration, but I think these technicalities can be ignored for the purposes here.)
same_person(event1,event2) relation between two person_slices belonging to the same person.
Person = class of events such that they are all person_slices related by same_person.
Person_id(event) = person with event as a member
f(p) = Person(p) & ($e)Person_id(e) & e e p & f(e)
p1968 = won 1968 presidential election.
Nixon(p) = was called ‘Nixon’
Consider “The person who won the 1968 presidential election won the 1968 election.”
This can be analyzed:
1) ($p) ((x)(p1968(p) ó p1968(x) ) & p1968(p)
2) Or (Ep) ((x)(p1968(p) ó p1968(x) ) & p1968(p)
3) But p1968(p) = Person(p) & ($e) Person_id(e) & p1968(e).
4) Or p1968(p) = Person(p) & (Ee) Person_id(e) & p1968(e).
5) So 1 is ($p)((x)((Person(p) & ($e) Person_id(e) e e p & p1968(e) ) ó Person(x) & ($y) Person_id(y) & y e x p1968(y) ) & p1968(p)
6) Or (Ep)((x)((Person(p) & (Ee) Person_id(e) e e p & p1968(e) ) ó Person(x) & (Ey) Person_id(y) & y e x p1968(y) ) & p1968(p)
7) I suggest the analysis should be instead
8) ($p)($z)(z e p & p1968(z) & (x) (p1968(x) ó x e p) & p1968(z)
9) Or (Ep)(Ez)(z e p & p1968(z) & (x) (p1968(x) ó x e p) & p1968(z)
10) Also
11) Nixon won the 1968 election would be.
12) ($p)($z)(x)(z e p & Nixon(z) ó x e p) & p1968(z)
13) Or (Ep)(Ez)(x)(z e p & Nixon(z) ó x e p) & p1968(z
14) Thus the proposition presumes the meaningfulness of ‘same_person’.
15) It would seem that when fully analyzed a propositions about a person-slice at one time would relate in any necessary way with another time-slice of the same person at another time. But we presume there is such a relationship when we use a name.
16) E.g.
17) Symbol_0r(S,’Nixon’,Nixon,t) implies there is a person Nixon.
18) Thus when we speak of a person, such as Nixon, we imply there is a class of person slice, related by ‘same_person’, which there is an application ot the word ‘Nixon’ to refer to.
19) The state (psychological) of the person with a belief_r containing a sub-experience, that the person takes to be referring to Nixon, could exist even if Nixon did not.
20) Thus, with my definition the ‘belief’ would not exist – even though the ‘belief_r’ would.
21) For different people, the class of person-slices (or facts about them), for Nixon (or whoever) would (at least almost always) vary.
22) Different people know Nixon differently.
23) But they agree there was a person, which (at least much of) what they collectively believe to be true of, applies.
24) This is what using the name must entail, which is necessarily vague.
25) If we want to be more precise, we can replace names with definite descriptions.
26) This, however, is not
mere analysis – the meanings are not exactly the same.
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