Philosophy 382
Bradford Skow

	
						Handout on Locality
						
						

Definition:

	D1.	C is a direct cause of E =df. C causes E, and there is no
		event X (different frm C and E) such that C causes X and X causes E.
		
		
Preliminary definitions of "spatial locality" and "temporal locality":

		
	D2. Spatial Locality =df. There is no gap in space between E and any of its
		direct causes.
	
	D3. Temporal Locality =df. There is no gap in time between E and any of its
		direct causes.
		
		

A fact about the structure of time and space:

	Between any two times there is another time. Between any two points of space 
	there is another point of space.
	
	

An argument that D3 is an incorrect definition:


	This argument is based on a scenario in which an event has no direct
	causes. We discussed the scenario in class.


	1.	If D3 is a correct definition of "temporal locality", then temporal 
		locality is true in the scenario.
	
	2.	Temporal locality is not true in the scenario.
	
	3.	Therefore, D3 is not a correct definition.
	
	
	

Final definitions of "spatial locality" and "temporal locality":

	
	D4.	Temporal locality =df. For any event E, if C is a cause of E, then
		for any amount of time t (no matter how small), EITHER
		
		(i) C is a direct cause of E and the temporal gap between C and E is 
			less than t, 
		
		OR
		
		there is an event X such that 
		
		(i) C is a cause of X
		(ii) X is a cause of E
		(iii) the temporal gap between X and E is less than t.
		
		
		
	D5. Spatial locality =df. For any event E, if C is a cause of E, then
		for any distance d (no matter how small), EITHER
		
		(i) C is a direct cause of E and the spatial gap between C and E is
			d,
		
		OR
		
		there is an event X such that 
		
		(i) C is a cause of X
		(ii) X is a cause of E
		(iii) the spatial gap between X and E is less than d.
		
		


The Contingency Principle:

	If C is a cause of E, the it is possible that C occur but E does not.