Let's start with your general question:
Does a pattern constitute evidence, logic or both?
In order to avoid the begging the question
fallacy, you should add "or neither" as well :)
A pattern could often be considered evidence, and the strength of the evidence depends on the details as well as what the pattern is being considered evidence for. To use your examples,
1) A "pattern" of physical characteristics to classify organisms sounds a bit like we are shoehorning the word "pattern" in here. It doesn't quite fit the definition. We are referring more to common characteristics.
2) The media releasing stories on weekends they want to "cover up." Be careful not to overreach
here. By this, I mean if what you perceive as an "embarrassing story" is run on the weekend, all we can conclude at this point is that what you perceive as an "embarrassing story" is run on the weekend, not that a "cover up" has occurred. Not yet. But here is where the patterns come in...
First, we need to make sure we have a reliable metric for what we consider an "embarrassing story." Then, we need to avoid the confirmation bias
and make sure we have a good understanding of how often these embarrassing stories are run during the week versus on weekends. It might be the case that "embarrassing stories" are more for weekends (puff pieces) due to more important news during the week. In other words, a pattern such as this would be evidence for good publishing practice rather than anything nefarious. No doubt there are media sources with political bias, so for example, if MSNBC consistently (pattern) runs dirt about Trump during the week and Fox News holds those stories for the weekend, we can reasonably conclude (evidence) that we are witnessing bias (not really a "cover up"), but we cannot be sure whose bias at this point (likely a bit of both parties). Perhaps if one did have a media source that they felt was neutral, this can be a 3rd data point to see where the bias is.
As for logic, in the informal sense, extracting evidence from patterns is a logical process, as is knowing the that we have a tendency to see patterns where there are none (some much more than others - this is usually referred to as a pattern-seeking bias or Apophenia
). In a sense, "patterns" occur all the time in randomness (e.g., if you roll a die a 1000 times, it is a statistical certainty that you will get a long string of the same numbers). The real power of logic and reason is knowing when inferring meaning or agency behind the pattern is justified.
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