I was wondering if there are any Gettier-style counterexamples or deeper objections to either of Goldman's reliabilist (1979) or causal (1967) theories of knowledge?
Thanks in advance!
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Emil, welcome to PSE
While Goldman's reliabilism can handle the original Gettier cases, other Gettier cases can be devised for which it appears not to work.
... consider Goldman's (1986) "relevant alternatives" version of reliabilism. It requires not only that a belief be produced by a reliable process (he refers to process reliability as "global reliability") but also that there be "local" or proposition-specific reliability (Goldman 1986, pp. 44-45). For Goldman, this latter amounts to a capacity to distinguish situations in which one's belief is true from relevant alternatives in which the belief is false. ... Relevant alternatives theory ... solves the original Gettier cases: with respect to the Ford case there is a relevant alternative to Smith's belief, that is compatible with his evidence—the situation in which Jones does not own a Ford, and Brown is not in Barcelona (Goldman 1986, pp. 54-55). With respect to the other coins case, the relevant alternative that falsifies knowledge attributions to Smith is that he himself has ten coins in his pocket and will get the job. ...
However, there are also Gettier cases that arise for this form of reliabilism. For example, in good lighting conditions, I see what appears to be a sheep in a nearby field, and form the belief that there is a sheep in the field. It is in fact a wolf dressed in sheep's clothing that is stalking a sheep elsewhere in the field (the sheep is obscured from my view), and if the sheep were not there, then neither would be the wolf. My belief that there is a sheep in the field is true, it is produced by the generally reliable process of vision (or, perhaps, vision with respect to medium sized physical objects good lighting conditions from fairly close range), and the relevant alternatives here are presumably those where I am looking not at the disguised wolf, but at the sheep (Since the wolf would not be there if the sheep were not, there are no relevant alternatives in which I see the disguised wolf when the sheep is not in the field). Given the presence of the sheep, I am extremely reliable with respect to the proposition that there is a sheep in the field. My belief thus satisfies the requirements imposed by the relevant alternatives view—but it is not knowledge.
(Mark McEvoy, 'Causal tracking reliabilism and the Gettier problem', Synthese, Vol. 191, No. 17 (November 2014), pp. 4115-4130: 4117-8; A. Goldman, Epistemology and cognition, Cambridge, MA: Harvard University Press, 1986.)
Gettier problems are a consequence of the intersection of the "true" of Justified True Belief criteria for knowledge, with indirect realism -- where because we do not directly access the world, we have to infer its circumstances. We can be wrong about those circumstances, and thus have what we think are justified beliefs which are not true. Gettier also noticed that we can have true beliefs which are based on invalid justifications.
This is all a problem for someone who holds that one's beliefs must be "true" in an absolute sense to be knowledge. But reliablism explicitly rejects that criteria for "truth" and instead adopts a pragmatic and probabilistic meaning. This insulates reliablism against Gettier problems, although it does not insulate it against Great Deceiver or Long Dream skepticism.
Here is the SEP discussion of reliablism: https://plato.stanford.edu/entries/reliabilism/ There are 5 objections noted in section 3, and one (objection 2) is a Grand Deceiver, and one (objection 3) is a Gettier-type-problem. Note however, that objection 3 does not depend on a truth or logic issue with reliablism, but instead on the objector's dogmatic rejection of clairvoyance despite it having been demonstrated to be reliable.
Goldman's reliablism is not at risk from Gettier problems.