Johann said:
Godel, right?
Yep. He crops up everywhere.
I will say you are wrong here, and I won't even say perhaps; good dictionaries do define all their terms. I do get your point though.
I'm not a mathematician so won't make my own argument, but here's what I meant expressed by someone more competent.
"…since every word in a dictionary is defined in terms of another word… The only way to avoid circular reasoning in a finite language would be to include some undefined terms in the dictionary. Today we must realize that mathematical systems too, must include undefined terms, and seek to include the minimum number necessary for the system to make sense."
Leonard Mlodinow
‘Euclid’s Window’ (144)
In other words, either we use undefined terms or end up with a tautology.
I think you are arguing that reason is not enough to understand or describe the world, with which I may agree. My point was simply that reason is always striving for circularity, for having all concepts defined in terms of each other.
I agree with you here. We strive for circularity but we cannot achieve it, as Russell and Whitehead found. Have you read "Goedel, Escher, Bach" by any chance?
What is impossible about self-reference? Many people suspect reality is self-referential at some level.
I also suspect it, and would argue that this is why we cannot understand it by reason alone. Reality can be entirely self-referential, (thus the principle of 'nonduality' in mysticism, the use of 'Tao' as an undefined term and so forth) but reasoning about reality cannot be since it becomes tautological and ceases to refer beyond itself to that reality. Strictly formal reasoning, as usually defined, inevitably ends up going around in a circle to end up face to face with its starting assumptions, not able to derive them from within the system without turning the system into a tautology. This doesn't matter too much in our everyday affairs but it is a real problem when we reason about reality itself via metaphysics, ontology and so forth.
I don't think we are actually disagreeing. But a statement like "reasoning is circular, but the circle cannot be completed" is a bit puzzling, don't you think? Doesn't it imply reason is invalid, since it cannot fulfill its purpose?
I agree that we're probably just coming at the same conclusion from different angles. But I don't see why that comment should be puzzling. We know from mathematicians that formal 'Boolean' reasoning has limits. When we reason about reality we find that as our system of formal reasoning nears completion contradictions and paradoxes arise, caused by self-reference in the system.
In this way, when we reason about reality, we always find ourselves bumping into barriers to knowledge, divine mysteries, explanatory gaps, ignoramibuses, contradictions and paradoxes, most often in the form of undecidable metaphysical questions. So I'd say yes, in this sense reason is 'invalid', or inadequate to its task. One only needs to examine the literature of consciousness studies, quantum mechanics or quantum cosmology, where researchers have to get down to the nitty-gritty concerning reality, to see the truth of this. The 'hard' problem of the mind/brain relationship is IMO a paradigm example of the inadequacy of reason by itself as a means of grasping the truth about reality. Perhaps the inability of analytical philosophers to decide metaphysical questions is the most obvious evidence of the circularity/self-reference problem.