Here is a principle I use all the time.
The likelihood of the conclusion of an argument being true is the product of the likelihoods of each statement used in reaching that conclusion being true.
When someone is making an argument to me I assume that each statement of their argument stands alone but the statements are linked in the order that the person has made them.
Each statement has a probability of being true and the probability of the conclusion being true depends on the product of the individual probabilities.
This sounds unobjectionable, but consider the implications.
1) An argument of 6 statements, each of which has a 90% chance of being true, has only a 53% chance of being true. You might as well have flipped a coin.
2) Any statement that has a lower probability of being true, reduces the probability of the whole argument being true. A single statement can invalidate the whole argument.
3) Absent absolute certainty in your statements, short arguments are more powerful.
Why is this useful?
In my ideal, every claim would be derived from some small set of axioms. This was the ideal of Euclid and Spinoza as well. This ideal is only achieved in very small areas of human thought, and we need rules for making decisions faster, or when the axiomatic basis is not so clear, or when we just need to earn a living or get dinner on the table. This is a reasonably formal rule for making those decisions.
There are many claims on our attention. It is worthwhile to concentrate fully on an idea or a proposal, but not every idea or proposal that will repay the attention. This is a way to eliminate a huge pile of junk.
The converse is more important. Your readers and listeners have many claims on their attention. If you make unsupported or weak claims in the process of building your argument, you will lose their attention.
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