I must not have been clear in my previous post: there is a difference between an objective confidence (such as from experimental measurements) and subjective confidence (such as my own personal confidence that something is correct). Objective confidences can be meaningfully quantified. Subjective confidences cannot.

For example, I am confident that special relativity is correct and that the speed of light is the unreachable-ceiling for the speed of matter with mass. A century's worth of observations and experiments support this. However, trying to quantify that subjective confidence is meaningless.

I don't believe the your notions of objective and subjective confidence really stand up too well. I think you'll find that the more you try to define the exact difference between them the more it will fade away. Perhaps it is a philosophical question. Similarly the only reason to look at measuring the length of a rope as 'objective' versus the combination of the many measurements that make up the supporting evidence for special relativity is because the former is subjectively (intuitively) simpler. .

However the main point is that probabilities are required for decision making. Whether you like it or not, any statement must be interpreted probabilistically to be incorporated into decision making. You need to multiply the probability by the risk/reward differential to have basis to work things out. You do this internally without realising it. 'What are the chances that this movie will be good versus the cost of going to see it'. Exaggerated statements can hurt people's decision making capabilities. That is why I oppose them.

You need to replace the Booleans in some of your mental constructs with fractions.

Let's say I measure a rope many times, and come up with a mean value and a 95% confidence interval for the length of the rope. That is, assuming my "experiment" is constructed correctly, I say that the true length of the rope lies within that range, with a 95% confidence. That's an objective confidence.

But in order to come up with that number, I had to assume my experiment was correct. I very well could have had a systematic error in the experiment such as misusing my ruler, accidentally holding the rope such as to artificially shorten it, or completely misunderstood the concept of length. My confidence that my experiment is correct is both independent of the confidence interval I reported, and not quantifiable.

What about measuring the speed of light? or measuring the distance from the earth to sun? Where do these fall in your neat divisions between subject and objective?

Is there a certain class of proposition that is too complicated to be called objectively true? Are all medical theories, for example, simply subjective and have no real meaning in terms of predicting likely future outcomes?

Any statement or theory that does not have predictive power is meaningless. Predictive implies probability. Probability implies odds. Put up or shut up up.