So do you think there is any objective way to determine whether there is such a thing as synchronicity?
Yes. But first it is important to understand that the way in which you and others talk about finding synchronicity is the way in which it cannot be found. You are taking patterns that are formed by the way we think, and stating that these patterns correspond to synchronicity. However, synchronicity is not necessary for the formation of these patterns - they can form in the absence of any underlying order - so their presence cannot be taken as a marker for the presence of synchronicity. It may be that some of these patterns are due to synchronicity, but
unless you have a way to distinguish a pattern created from the way that we think from a pattern created by synchronicity, we cannot use those patterns to discover synchronicity. We need something different.
An analogy would be the discovery of effective medicine. For the longest time, we attempted to discover effective medicine by using the pattern of trying things until we felt subjectively better. An effective medicine was whatever we took just before we felt subjectively better. However, this pattern can be created for anything - even stuff that is completely ineffective. And so it happened that almost everything we considered effective was actually completely ineffective. And more importantly,
those few medicines which were actually having an effect were completely indistinguishable from those which weren't. It wasn't until we developed a different means of discovery - measuring changes in disease rather than changes in symptoms, removing the effect of timing on the application of treatments - that we vastly increased our discovery of effective medicine.
Until you shed the practice of using patterns created by cognitive bias as markers of patterns created by synchronicity, no progress can be made in this area.
Linda