time travel the bootstrapping paradox ii

The diary paradox 1. The diary has exactly n entries in it when it is handed to Jane in Jane writes an entry in the diary before handing it to Peter in If (1) and (2), then the diary has exactly n+1 entries in it when it is handed to Peter in [So] The diary has exactly n+1 entries in it when it is handed to Peter in Peter writes an entry in the diary before handing it to Jane in If (4) and (5), then the diary has exactly n+2 entries in it when it is handed to Jane in If the diary has exactly n+2 entries in it when it is handed to Jane in 1999, then it does not have exactly n entries in it when it is handed to Jane in [So] The diary has exactly n entries in it when it is handed to Jane in 1999 and it does not have exactly n entries in it when it is handed to Jane in 1999.

argument 1 1. The time of Jane’s writing (Tjw) is later than the time of Jane’s receiving (Tjr). 2. If (1), then the entry that was created at Tjw cannot be in the diary at Tjr. 3. [So] The entry cannot be in the diary at Tjr (i.e., Jane’s entry cannot be in the diary when she receives it).

argument 1a 1. The time of Jane’s writing (Tjw) is later in external time than the time of Jane’s receiving (Tjr). 2. If (1), then the entry that was created at Tjw cannot be in the diary at Tjr. 3. [So] The entry cannot be in the diary at Tjr (i.e., Jane’s entry cannot be in the diary when she receives it).

argument 1b 1. The time of Jane’s writing (Tjw) is later in the diary’s personal time than the time of Jane’s receiving (Tjr). 2. If (1), then the entry that was created at Tjw cannot be in the diary at Tjr. 3. [So] The entry cannot be in the diary at Tjr (i.e., Jane’s entry cannot be in the diary when she receives it).

argument 2 1. If Jane’s entry is in the diary when she receives it (at Tjr), then it will be in the diary right up until the time of Jane’s writing (Tjw). 2. If the entry is in the diary right up until the time of Jane’s writing, then she won’t be able to write it (at Tjw). 3. Jane will be able to write the entry (at Tjw). 4. [So] Jane’s entry isn’t in the diary when she receives it (at Tjr).

argument 2 Creation 1: In order for someone S to create something X at some time T, there must be some time T* such that (i) T* is earlier (in external time) than T, (ii) X does not exist at T*, and (iii) X does not exist at any time between T* and T. Creation 2: In order form someone S to create something X at some time T, S must do something that causes X to exist at time T.