I will begin with an examination of the achievement problem. Roughly, the achievement problem may be put as follows: C-externalist thought experiments seem to demonstrate that given an appropriate difference in the external world, there will be a difference in thought content, without this difference being reflected in any inner detectable manner. This seems to imply that one cannot tell, without consulting the external world, which of two thoughts one is entertaining, and hence one cannot be said to know what it is one believes or thinks. The intuition underlying a priori incompatibilism is typically illustrated via an appeal to Boghossian-style slow-switch scenarios.
Slow-switch Sue :
Imagine a subject, Sue, who was born and spent most of her life on Earth, where the word ‘tiger’ refers to the creature of the family and genus felidae panthera. However, at some point in the past Sue was secretly transported to Twin-Earth where there are no felidae panthera but only pligers, animals which are visually indistinguishable from felidae panthera but are of a different evolutionary heritage, family and genus. Moreover, Sue is ignorant of the relevant biological facts that distinguish tigers from pligers. Sue is at the zoo, looking at a familiar large striped mammal, and thinks a thought which she expresses with the utterance, ‘that tiger has stripes’. According to the C-externalist, whereas Sue formerly entertained tiger-thoughts, she is currently entertaining a pliger-thought. However, according to the incompatiblist, Sue would fail to notice the change in her environment or her thought contents. If we were to ask Sue whether her thoughts have changed in content after they have in fact done so, she would most likely say they have not. Sue could only know that her thought contents have changed by learning additional empirical facts about her environment. Thus, the incompatibilist concludes that Sue cannot distinguish a priori between the actual situation in which she thinks ‘that tiger has stripes’ and the alternative situation in which she lacks this thought. Thus, Sue’s actual belief that she thinks ‘that tiger has stripes’ fails to constitute an instance of a priori knowledge.
We may unpack the intuition illicited by the Slow-switch Sue example via the following reductio:
(S1) Sue knows, without consulting her environment, that she is entertaining the thought that tiger has stripes.The central intuition on which the above reductio hangs is (S6). I see no reason to question this intuition. To wit, it may be agreed on all sides that a subject can only ascertain that she is in a pliger world by consulting her environment. In my next post, I will limn a compatibilist reply that involves the rejection of (S4).
(S2) Sue knows, without consulting her environment, that C-externalism is true.
(S3) Given (S2), the thought Sue is now entertaining—the tiger-thought—is a different thought than the thought ‘that pliger has stripes’ (the thought she would have in a pliger-world).
(S4) Given (S1), Sue is in a position to know, without consulting her environment, that she is not thinking the thought ‘that pliger has stripes’.
(S5) Given (S1)-(S4), Sue is in a position to know, without consulting her environment, that she is not in a pliger world.
(S6) Intuitively, neither Sue nor anyone else can know that she is in a pliger world without consulting her environment.
(S7) Therefore, if C-externalism is true, Sue does not know, without consulting her environment, that she is entertaining the thought, ‘that tiger has stripes’.