the regress problem

In Posterior Analytics I.2, Aristotle considers two challenges to the possibility of science.

1. One party (dubbed the “agnostics” by Jonathan Barnes) began with the following two premises:

– Whatever is scientifically known must be demonstrated.
– The premises of a demonstration must be scientifically known.

They then argued that demonstration is impossible with the following dilemma:

– If the premises of a demonstration are scientifically known, then they must be demonstrated.

– The premises from which each premise are demonstrated must be scientifically known.

– Either this process continues forever, creating an infinite regress of premises, or it comes to a stop at some point.

– If it continues forever, then there are no first premises from which the subsequent ones are demonstrated, and so nothing is demonstrated.

– On the other hand, if it comes to a stop at some point, then the premises at which it comes to a stop are undemonstrated and therefore not scientifically known; consequently, neither are any of the others deduced from them.

Therefore, nothing can be demonstrated.

2. A second group accepted the agnostics’ view that scientific knowledge comes only from demonstration but rejected their conclusion by rejecting the dilemma.

Instead, they maintained:

Demonstration “in a circle” is possible, so that it is possible for all premises also to be conclusions and therefore demonstrated.

Aristotle does not give us much information about how circular demonstration was supposed to work, but the most plausible interpretation would be supposing that at least for some set of fundamental principles, each principle could be deduced from the others.

(Some modern interpreters have compared this position to a coherence theory of knowledge.)

However their position worked, the circular demonstrators claimed to have a third alternative avoiding the agnostics’ dilemma, since circular demonstration gives us a regress that is both unending (in the sense that we never reach premises at which it comes to a stop) and finite (because it works its way round the finite circle of premises).

3. Aristotle’s Solution: “It Eventually Comes to a Stop”

Aristotle rejects circular demonstration as an incoherent notion on the grounds that the premises of any demonstration must be prior (in an appropriate sense) to the conclusion, whereas a circular demonstration would make the same premises both prior and posterior to one another (and indeed every premise prior and posterior to itself).

He agrees with the agnostics’ analysis of the regress problem:

– the only plausible options are that it continues indefinitely or that it “comes to a stop” at some point.

However, he thinks both the agnostics and the circular demosntrators are wrong in maintaining that scientific knowledge is only possible by demonstration from premises scientifically known:

– instead, he claims, there is another form of knowledge possible for the first premises, and this provides the starting points for demonstrations.

To solve this problem, Aristotle needs to do something quite specific.

It will not be enough for him to establish that we can have knowledge of some propositions without demonstrating them:

– unless it is in turn possible to deduce all the other propositions of a science from them, we shall not have solved the regress problem.

Moreover (and obviously), it is no solution to this problem for Aristotle simply to assert that we have knowledge without demonstration of some appropriate starting points.

He does indeed say that it is his position that we have such knowledge (An. Post. I.2,), but he owes us an account of why that should be so.

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

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