True Skepticism

Can a true skeptic know anything? What is truly knowable?

I will start. 

From an intellectual and from a gut perspective as much as it will allow I maintain one thing that is truly knowable:

I apparently exist.

Can a true skeptic know anything? What is truly knowable?

I think knowledge is reality modeling.

I imagine a spectrum of certainty regarding the accuracy of the various parts of one's model of reality.

At one end is 100% certainty and the only thing at that location is direct present experience. It is the only thing that cannot be doubted. As soon as you begin to move away from the present moment, and start remembering or abstracting or predicting, the certainty is <100%. 

At the far end is 0% certainty (which is not 100% certainty of the opposite).

Just like we've taken the EM spectrum and arbitrarily assigned names to different regions depending on the purpose (X-band, K-band, Ka-band, X-rays, gamma rays, UV, Visible, IR, etc.), we also arbitrarily assign names to different regions of the spectrum of certainty depending on our purpose.

To start with, we can divide the certainty spectrum in thirds and label the top segment "knowledge", the middle segment "belief", and the bottom section "doubt". There's always a portion of each in the other two - it is a spectrum.

In the top segment labeled "knowledge", our certainty in our model is high enough that we generally don't feel the need to put forward any further effort to validate the model.

In the middle segment labeled "belief", we would like further validation of the model, but are nevertheless sufficiently certain to consistently behave as if our model is accurate.

In the bottom segment labeled "doubt", we have encountered little to no reason to trust the accuracy of this portion of the model and so we have it marked for tentative deletion or revision.

IMO, a "true skeptic" is someone who realizes the boundaries marking off different segments of the certainty spectrum are entirely arbitrary and dependent upon the purpose or needs of the moment. A "true skeptic" is also aware of his own biases and the various contextual factors which cause him to push his model towards one end of the spectrum or the other.

When there is no practical immediate need to make a firm judgement and act as if a model is true or false, a "true skeptic" is comfortable with keeping his models in the middle of the spectrum and neither tossing them out nor trusting fully. When there is no practical need for judgment, a "true skeptic" is comfortable with raising the threshold of certainty required for knowledge all the way to 100%. In short, solipsism is the core philosophy of the true skeptic. So the "true skeptic" is fully aware that to have any abstract knowledge at all requires a degree of belief.

Nicely put, Tar.

Tar,

In your model what do we do with stuff like:

2+2=4.

Seems true onto itself.

It depends upon what the numbers and symbols precisely represent as to whether it is true or not.  If they represent nothing then they are meaningless.

It does seem that mathematics has an internal logic and consistency that is hard to deny. But so does Moby Dick, I suppose.

Tar,

In your model what do we do with stuff like:

2+2=4.

Seems true onto itself.

It is true by definition. It is like saying: "if we decide to break a thing up in this particular way, then it is broken up in this particular way, and we're going to label the parts that we've just created through differentiation: this and that."

Differentiation and identification is something we choose to do, so it is always contingent on the "if" statement. There is no reason we must break reality up in a particular way. But if we are going to break up reality into pieces and stitch it back together with labels attached, it is most useful to us if we are consistent in the way we break things up and label them. And the things that are most useful eventually get called "true". 

So the "truth" of abstractions are evaluated on internal consistency.

So 2+2=4 is certainly true if and only if we are internally consistent in the way we label our abstractions.
2 gallons + 2 liters does not equal 4 cubic feet.

By adding inconsistent units, the statement is no longer internally consistent. When units are not given, it is assumed that the units are consistent and therefore the statement is internally consistent.

I could say,
2 gallon containers plus 2 liter containers equals 4 cubic feet containers.
And now I can choose to judge the truthfulness of this statement on the consistent units or the inconsistent units. If my purpose is to break reality up into quantities of containers regardless of volume, then this statement is internally consistent. If my purpose is to break up reality in consistent volumetric quantities, then it is false.

It does seem that mathematics has an internal logic and consistency that is hard to deny. But so does Moby Dick, I suppose.

I'd vote for pure mathematics as the thing you can be surest of, in the sense that the whole structure follows provided the axioms are assumed.

And I don't believe something like number theory depends on the physical world at all. Fermat's Last Theorem would mean just the same thing to beings of pure spirit as it does to us.

I'm fairly certain that if I jump out of a 40-story window I will soon be dead.

~~ Paul