Philosophy 382
Bradford Skow

	
						Handout on the Epistemology of Geometry
			


Some Definitions:


	S knows that P a priori =df. S's knowledge that P is not based on any 
	observational evidence.


	S knows that P a posteriori =df. S knows that P and it is not the case that 
	S knows that P a priori.
	
	
	
An argument that we cannot know which geometry is true a priori:


	1.	If there is more than one possible geometry, then we cannot 
		know which geometry is true a priori.
		
	2.	There is more than one possible geometry.
	
	3.	Therefore, we cannot know which geometry is true a priori.
	
	


An argument that we cannot know which geometry is true:


1.	Our evidence is compatible with both G+P and G*+P*.

2.	If our evidence is compatible with both G+P and G*+P*, then our 
	evidence does not favor G+P over G*+P*.
	
3.	If our evidence does not favor G+P over G*+P*, then we cannot know that 
	G+P is true.
	
4.	Therefore, we cannot know that G+P is true.




Three views about when some evidence favors one hypothesis over another:


	The Initial View:
		
		If E is compatible with both H1 and H2, then E does not favor H1 over 
		H2.
						

	Methodological Conservatism:

		If our evidence is compatible with H1 and H2, and H1 deviates from our 
		previous theory less than H2, then our evidence favors H1 over H2.
		
	
	The "Simplicity" Theory:
	
		If our evidence is compatible with H1 and H2, and H1 is simpler than H2, 
		then our evidence favors H1 over H2.
	
	

	Definition:
	
		H1 is simpler than H2 =df. H1 can be written down with fewer words
		than H2.