What is logic? We know that certain laws of mathematics lead to properly functioning formulas.
In logic we know that certain procedures lead to valid arguments, and others to invalid. Respectively, we call the former logical in colloquial terms and the latter illogical.
Thus logic is the proper model for objective reasoning.
We know enough about logic to solve the most basic problems of life and even complicated problems of mathematics, physics and philosophy.
We know enough about logic to properly solve problems concerning human affairs. Because we can apply objective reasoning to human affairs, we need not make the decisions with respect to human affairs on whim, or value judgment.
There is no doubt that value judgment has something to do with human affairs, but it must not be pure value judgment. In other words, we can logically analyze our likes and dislikes, see if they need to be changed or acted out upon, and if so how we go about both. We need not just act out on our passions because we are far more rational than that.
I do not see the relevance of any of this to the notion that we can figure out some things with logic.
In order to know why exactly no human being has lived over 165 requires that we collect the factual information. This does nothing to vitiate the logical form in itself.
Logical form well executed leads to valid arguments.
Logical form loaded with factually accurate information leads to sound arguments. Logical form loaded with inaccurate information leads to unsound arguments.
Inaccurate information has little to do with invalidity, or only with unsoundness. Arguments that we deem to be sound today can be deemed unsound later, but this does nothing to tell us that logic is an unreliable method of investigation. For sound argument, it is only a matter of taking care of attributes external to reasoning in itself.
I either have a watch around my arm or I do not. I cannot both have it not and have it. What could be easier to prove?