This question stems from an ongoing discussion I was having with @Bumble (link for anyone interested).

There are certain arguments that seem on the face of it very strong. For example, simply seeing my neighbor every day for 10,000 straight days may be used as a strong enough premise to conclude that I will see my neighbor tomorrow. On the other hand, “Charlie is a woman. Some women like poetry. Therefore, Charlie likes poetry.” may be seen as a weak argument. Yet in either case, the conclusion does not automatically follow from the premises.

The closest thing I can find that may objectify this process is the notion of logical probability. As quoted from the article,

Indeed, the logical interpretation, in its various guises, seeks to encapsulate in full generality the degree of support or confirmation that a piece of evidence e confers upon a given hypothesis h, which we may write as c(h,e)

After some responses to the logical interpretation, the article then introduces an evidential interpretation:

It may not be a matter of logic that the sun will probably rise tomorrow, given our evidence, yet there still seems to be an objective sense in which it probably will, given our evidence. In a crime investigation, there may be a fact of the matter of how strongly the available evidence supports the guilt of various suspects. This does not seem to be a matter of logic—nor of physics, nor of what anyone happens to think, nor of how the facts in the actual world turn out. It seems to be a matter, rather, of evidential probabilities.

But this notion is hotly contested as written in this snippet:

However, some authors are skeptical that there are such things as evidential probabilities—e.g. Joyce (2004). He also argues that there is more than one sense in which evidence tells for or against a hypothesis. Bacon (2014) allows that there are such things as evidential probabilities, but he argues that various puzzling results follow from Williamson’s account of them, in virtue of its identifying evidence with knowledge. Moreover, one may resist demands for an operational definition of evidential probabilities, while seeking some further understanding of them in terms of other theoretical concepts. For example, perhaps P(h∣e) is the subjective probability that a perfectly rational agent with evidence e would assign to h? Williamson argues against this proposal; Eder (2023) defends it, and she offers several ways of interpreting evidential probabilities in terms of ideal subjective probabilities. If some such way is tenable, evidential probabilities would presumably enjoy whatever applicability that such subjective probabilities have. This brings us to our next interpretation of probability.

The article then moves on to the notion of subjective probability but that itself is hotly contested in the remainder of that article.

This then begs the question: how does one objectively analyze the strength/weakness of an argument, or what it even means for an argument to be strong or weak? In the case of a deductive argument, we can at least seem to know with certainty whether it is valid or invalid.