I also think that synchronicity occurs at all levels in the world (including human relationships), but I don't think synchronicity can be used to prove anything since there is no effective means to study this phenomena. It is very subjective - based on what we find meaningful, but there is no means to predict when a synchronous event will occur (at least none that I am aware of).
***As for the circular reasoning in Smolin's hypothesis- it seems to me that both math and physics are inherently circular, being self-consistent.***
Perhaps we have different definitions of what circular reasoning is. My view of circular reasoning is if you assume as a premise the conclusion you wish to reach. For example, black holes cause universes (premise) which leads to fine-tuned universes that can cause black holes (conclusion). Circulus in demonstrando.
Mathematics does not fit this description. Math starts with simple axioms (e.g., there is an empty set that contains no set) and makes proofs that are altogether unexpected (e.g., Gödel's second incompleteness theorem).
***My point however is that one can propose a natural mechanism for antropicity that could be an alternative for intellectual design.***
Absolutely. Every feature of the world can be described as a product of contingency or a product of necessity (or combination of the two). The question is what kind of baggage does each carry. We could describe all the events in the world as the result of a infinite collection of random event universes. Our universe may be the one that appears more ordered up until now, but it may quickly become totally random in the next second (i.e., an infinite collection of random universes imposes no real law that keeps the atoms and molecules together - they just happened to be in this state up until now). The reason we don't accept this view is because philosophically it seems to be a much less likely to be true ontology.
This is why the anthropic principle is as much a philosophical concern as it is a scientific concern. It is very important to review the options and make reasonable philosophical distinctions as to what is the more reasonable perspective.
Warm regards, Harv