So, why am I unable to know what is false? Why am I unable to know that 1+1=3 is false?

We are always mistaken with the truth. Unfortuneately the truth is ineffable. I've explained before, so I'll explain briefly:

The truth requires that a 'tree' is equivalent to a tree in reality.
So we can say that the truth infers that 'tree'=tree.
Of course 'tree' is a word, and is absolutely not the tree, in this case the truth is a deviant, or in other words a lie. the truth cant be a lie so the truth is ineffable.

That was my point - that we might be mistaken, whatever it is we think to be true.

.

But we can elaborate. We can acknowledge that 'tree' is a convenience for easily referring to members of a category and then proceed further to elaborate our meaning. We can refer to 'that tree' or 'this tree.' we can refer to big trees and small trees, healthy trees and orange trees. I can tell a story about the tree I fell from when I was young. Or the trees I pass on the way to work. We can say a forest is an area where trees are more present than other plants.

Human thoughts exploit abstractions, and generalizations such as these. That is actually an advantage in both language and thought. In order to know perfect truth we would have to dispense with categories entirely. That just isn't feasible. We would have to walk around with a copy of the entire universe in our heads.

We have many deficiencies as truth seekers, but our mental function is actually amazingly good at dealing with in exact information, and getting to a good result regardless. Good thing too, because we never have perfect information.

I prefer to judge truth in a utilitarian sense. If a structure of thought is useful I keep it, if not I look for one that works better.

Because your intuitive, knowledgable mind is not a figment of mathematics or language, it might be a figment of physical properties which can be ascertained with maths or language, yet any observations (expressed in maths/language) will be restricted by the linear charicature that both are founded in. When you 'know' that pain is felt when x is done you are not strictly speaking aware of a linguistic principle, instead you are aware of an instinctive arrangement of emotional properties, properties which are fluid and metamorphic unlike language.

But, again, just because we cannot know that we know, it does not follow that we never know.

If I say "It is true that my dog is sitting next to me" we can say there is something absolutely true - whether or not my dog is sitting next to me. There is also what is true to the best of my knowledge - that my dog seems to be sitting next to me. There is also what is true to the best of your knowledge...

But how on earth does any of the above show that when we point to a tree, and state, "that's a tree" that we are not right? Not at all, that I can see.

truth is useful (if that is what you mean by "utilitarian", although I really don't know what you do mean by it)

Well, of course we always might be mistaken. But that does not mean, of course, that we might always be mistaken. Human beings are fallible. But that, of course, does not mean we are, in fact, mistaken whenever be believe some proposition. For, after all, if we might be mistaken, we might also be correct. All that means is that when we claim to know, we cannot (in at least one sense of those words) know that we know, or (again in one sense of that word) be certain. But, again, just because we cannot know that we know, it does not follow that we never know.

the truth being ineffable

You are arguing with someone else "tree" is a category that includes actual trees. So "that's a tree" means "the object to which I gesture is illustrative of the category 'tree'' " The word is not specific, and certainly lacks detail. The word invokes certain connotations and denies others. If I point to a tree and say "That is my new desk" I'm a crazy person, even though I could render the tree into a desk. But the desk is in the tree in some sense.

Language is a blade, it selects which aspects of the world are important, at the moment in order to clarify human needs, such as utility or purpose. We choose our words, to cut away the irrelevant aspects of objects under discussion. Words are not the thing. Words indicate aspects of the thing. If words were things I'd be a truly wealthy man, as I have too many words and not nearly enough things.



In the real world, where most of my interest and problems lie, the True is often unavailable to me.

What I have instead are beliefs which are true to some degree. For example I know that objects fall at 9.8m/s^2, which is an untrue fact.

It is useful even thought it is untrue, because it is sort of true, it is semi-true, it is pseudo-true, it is almost true, it carries elements of truth, it is very very nearly almost true, but despite being all these things it is a lie because it is not TRUE. It's truth comes from it's utility in a very deep sense.

This doesn't apply to items of concern, such as capitols of countries, because such things have no true existence beyond their own definitions. The capitol of X is Y, ONLY because someone says so. Cities are not real, they are imaginary boundaries that humans agree on only.

To repeat, there are things which only exist by definition your arguments apply well to them. Then there are things that exist in the universe, these things are not so easy to capture. Language does not necessarily distinguish between these but we can, and should.

Why do you think that sometimes when the cat is on the mat you do not know that it is true? Don't you know it is true that Quito is the capital of Ecuador? I do. That does not mean, of course, that I am certain that it is, beyond the possibility of error. There are some conventional truths. Cities are such. Another conventional truth would be that Barry Bonds hit a home run. That is true only within the context of the game and the rules of baseball. But it is a fact that Barry Bonds has hit many home runs. That is a social fact, but a fact, nevertheless.

As I said, I don't doubt trivial facts, nor conventional truths, I simply maintain an awareness of our limitations. To not do so is to invite error more so than the alternative, which would be to accept blindly all ideas which appear plausible to me at the moment as truths. I don't trust plausibility, it's lead me down a lot of dead ends.

So I acknowledge shades of truth, various levels to which ideas may be non-identical to reality, what ever you want to call it. This doesn't get in the way of my operating in the world, and helps me ferret out the things I don't know.

I also don't trust my own apparatus to think properly without keeping an eye on it, largely because of my flirtations with neuroscience, and my study of psychology, computer science, and the history of ideas. You shouldn't fully trust your equipment either. The brain is an amazing device but we are using it for purposes for which it was not designed.

Another aspect is personal taste. For me, the most important truths are the ones I don't know, and the stranger I find them the better. Once I believe that I understand a particular aspect of reality it no longer interests me all that much. I like my truth raw and messy, I want to feel it's blood drip down my chin as I tear it into bite sized swallows of epistemic candy.

I don't know what you have in mind by a trivial fact. Is the fact that Quito is the capital of Ecuador trivial? Why? What would be an example of a non- trivial (important) fact? By a " fact" I, of course, mean a "truth". And I am not clear what you mean by "shades of truth" either. I think that to say France is shaped like a hexagon is true. But that there are more accurate ways of describing the shape of France. Perhaps that is the sort of thing you mean by "shades of truth".

I would suppose that you mean that the most important truths are the ones you did not know until you discovered them, since I don't see how you would find a truth important until you discovered it. But do you really mean what you say.

Surely some truths you do know are more important than some of the truths you do not know. You know that you were born, for instance, and I cannot believe you don't think that more important than whatever the truth is about who will be vice-president in 15 years, which you do not know.

That would qualify. As would any understanding that is approximate. Metaphorical understanding is another major category. Most scientific knowledge would apply (I know you don't like this use of the word but that's what we call it.) Other pragmatic truths would as well.

The question is often enough to show that there is a truth to be found. It's the question and the process that motivates me. It's like a bloodhound, who follows the scent because someone placed it in front of him, the hound doesn't care what the scent is, and even less what the scent came from he just likes to chase scents.

Your example is strange to me, but yes of course there are some truths that I know (or in your terms beliefs I am confident are true.) The importance of information fluctuates with my goals, but of course some information is useful.
-----

People usually don't have trouble with things like "is the cat is on the mat?" or not. These are things we accept based on our direct experience. "where is the cat?" we ask, then we look around and see, we say "Oh there's the cat, she's on the mat."

The question "why is the cat on the mat" is more difficult as we have limited access to information that is relevant. We can't know the cat's mind directly so even if we are right we can't fully confirm our assertion.

Non-trivial truths require understanding of mechanisms, for example various elements of cellular function, or the physics of everyday objects. These understandings are not about where something is or what they are called, so much as they are about how things behave.

------------
My doubts about the validity experience don't really apply to the simplest of facts, or rather they do to some degree but as a practical mater it's useless to worry constantly about every little thing.

I agree that people are never (or at least rarely ever) in possession of perfect information (whatever that comes to). Therefore (and for other reasons too) "to err is human". But that is, of course, a commonplace. Are you saying anything more than that?

Socrates, in Plato's Apology famously announced that all he knew was that he knew nothing. But, when it was pointed out to him that, after all, he did know that he was a male, and not a female; and that he was a citizen of Athens, and many other things of that kind, he amended his declaration to say that he knew nothing of "importance". And, I imagine that Socrates meant by that he did know truths that he could learn about through his senses, but that he did not know any philosophical truths such as the nature of courage or the nature of justice which, according to Plato, were not accessible to the senses, but rather to the "intellect" (what was called, "Nous"). I think it is this view (perhaps) which you are getting at.