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Take three principles: The Principle of Sufficient Reason: Every fact can be explained in terms of some other facts. Call those other facts the suffic
by justinpombrio 10y ago
Take three principles:
The Principle of Sufficient Reason:
Every fact can be explained in terms of some other facts.
Call those other facts the sufficient reasons for said fact.
The Principle of Non-Cyclic Reasoning:
No fact is ever explained in terms of itself. That is,
if you repeatedly take the "sufficient reasons" for a fact,
you never get back to the original fact.
The Principle of No Infinite Regress:
There is no infinite chain of (distinct) sufficient reasons.
That is, there is no infinite sequence F1, F2, F3, ... such
that "F2 is one of the sufficient reasons for F1", "F3 is one
of the sufficient reasons for F2", etc.
You can't have all three: every directed graph whose nodes are facts and whose edges are "is one of the sufficient reasons for" either has (i) a dead-end, or (ii) a cycle, or (iii) an infinite chain.
For those who believe the PSR: which do you give up? Are you ok with cycles, or with infinite regress?
- westoncb 10y agoI think your claim is true for a single moment in time, but if you look at the Principle of Sufficient Reason as only talking about the potential for facts to be explained in terms of other facts ("Every fact can be explained in terms of some other facts")—then I think dead ends at single points in time are fine.
- justinpombrio 10y agoAnd the graph of all potential facts? Which does that have: dead ends, cycles, or infinite chains?
- westoncb 10y agoWell, that's one way you can approach it: look at the graph of potential facts instead—but what I was considering was an interpretation of the Principle of Sufficient Reason where dead ends are fine at a single point in time, which adds another dimension to the graph and leaves freedom for not having dead ends, cycles, or infinite chains (as long as 'dead end' is interpreted as a node not only without outgoing edges, but which cannot develop any at any future time).
- colanderman 10y agoYou're implicitly assuming the law of the excluded middle. Depending on the logical foundation, a fact chain could exist which is seemingly infinite, but for which no finite proof exists that it violates any of the three laws.
- Chris2048 10y agoThere have to be logical axioms, on how to even represent, interpret or progress facts (all meaning, including interpretation of above paragraphs depend someone one these). These axioms might for the basis of all others, they cannot be explained though, they are inherent. Why can only one thing be True, for example (single objective reality). What does 'one' mean in this context? etcetcetc