You know (a lot) less than you think. Or perhaps you know (a lot) more than most Philosophers.
The World as You Know It
Is knowledge possible?
This is a very difficult question, which has a tendency to get bogged down in the definition of knowledge. My approach will be slightly different. Most philosophers who say we know things do so to defend our 'knowledge' of the world as it is commonly understood. I will outline what we mean by this world and why knowledge of it is impossible.
Then I will outline the problems with the skeptical position. I won't give a rigorous response, but will highlight some of its assumptions and shortcomings.
Things, People and Science
We think there are things and people in the world. We think there are rules which govern how the things behave, and this allows us to understand them. Even if our rules aren't perfect, they are good enough to make accurate predictions and understand the world.
This is most clearly seen in Science, where we view there as being a set of rules which govern things, and we can discover these through experiments. Yet even without Science a similar framework is used.
For instance, a tribe which has never encountered Science as we know it might have an understanding of the world based on several things. They have an understanding of rules which govern nature: they aren't surprised when something falls if they drop it. They might have a religion which explains non-observable things, such as what happens after death.
We use 'mental' objects, reasoning, to create explanations. This governs most our understanding of the world on a practical level. We create a set of explanations which do not contradict our observations, and may be able to make predictions. In doing so we think there is some causal chain, or 'way things are' which we capture in our reasoning.
If someone is hit by lightning, we think they are unlucky. To explain why, you use ideas of probability and chance which you think captures the situation.
The first test
The first test of whether we know something is the alternative explanation test. This basically is whether other explanations are compatible with the way things are. If this is the case then you do not know your explanation is the case.
Science and its failings
Science fails this test. Consider the following thought experiment.
Someone lives in a box. Whenever they touch a button, the wall turns green briefly and food appears in the room.
In this experiment you are in the privileged position of knowing the rules which govern the world. Imagine that after several million years of a society living in such a box. Using Scientific reasoning would dictate that when they touch the button there is a causal link between pressing the button and the wall changing colour and food appearing. Yet you can see that the programme changes so that after 5 million years the wall changes colour to blue and no food appears.
Thus we can see that, in the position of knowing all the rules, a Scientific methodology might not find the truth. We would have to prove that the rules were somehow necessarily as we think they are. Yet our current method doesn't do that, it merely observes.
And if Greek metaphysicians teaches us anything, it's that humans' abstract reasoning about what necessarily is the case is not very good. (See link below and listen to a few of the podcasts). In their abstract reasoning the presocratics concluded everything from change being illusory to everything being made out of water.
Society and People
More worryingly, our understanding of people and society fails this test. Matrix-style hypothesis or the possibility that other people are just mindless robots who act like humans are hard (impossible?) to disprove. This is because we assume others are like us because we think they act like us, but we do not directly experience their minds. (on the last point you might think that is an incorrect assumption of Western Philosophy, in which case there might be a response to this type of skepticism)
First test in action (an example)
Many modern counters to skepticism emphasise how certain thoughts would be impossible without other people and the world existing.
In this case, we can see that there are many ways these conditions exist. Perhaps everyone else did exist, but unbeknownst to you your brain was lifted into a 'vat' and hooked upto a computer simulating the world while you were asleep. You would still have the mental faculties learned by being around other people, but you would no longer be acting in the world.
Knowledge in General
For most things we care about, there seem to be alternative explanations. In proving something is necessarily true we face a further problem.
The Second Test
To prove something is necessarily true, we want to know our reasoning is correct. Yet to check our reasoning is correct requires thought and argument which, again, might be wrong. I know that I have been wrong on many occasions when I think I have been right.
To prove our reasoning is correct, we would then need to prove our reasoning that our reasoning is correct is correct. (and so on). Otherwise we would face the other possible explanation that our argument is wrong and we merely think it's correct. This is especially true as it appears we accept something as true only if we cannot find a flaw in the reasoning. In this case, the flaw may just be too complicated for us to see.
In fact, this is the basis of an article I wrote titled Does Mathematics Provide Truth? (link below)
The Final Test(?)
Finally we face the problem that our thoughts are all muddled. We refer to concepts and we aren't entirely sure what we are referring to all the time. This is why Philosophers spend so much time debating what knowledge is.
We aren't entirely sure what constitutes a proof, and we find it difficult to decipher our own emotions. Consider the statement we do not directly experience others' consciousness. A scientifically minded person might agree instinctively, yet it is not clear whether or not it is true.
We are not sure what makes something consciousness, or makes something necessary. Perhaps a robot which acts like a human in every way does necessarily imply a consciousness - after all our consciousness in the scientific approach is no more than the result of physical processes with certain computations and actions.
Some Philosophers emphasise how language isn't 'built' for Philosophy, and many Philosophical questions are essentially meaningless. Yet a question being meaningless doesn't mean the statement it is about is true. The question 'do others exist' may be meaningless. That doesn't tell us anything about the 'others' we want to know about, just a limit on what we can express in the language we use.
Under such circumstances, how could you have knowledge? Nearly everything you could use can be questioned. As so many ways of thinking can be questioned, it is hard to see how you could respond to these issues - if all ways of thinking can be doubted, then you cannot approach the skeptical problem as you would be using a method of proof which was itself in doubt.
In short, you are left with ambiguity, not answers.
The Way Forward
Here I will highlight some potential flaws and weaknesses in the skeptical way of thinking.
A large part of skeptical thinking relies on thought experiments and alternatives. Yet these haven't been justified.
For instance, consider the deterministic world where the light flashes blue then green (and nothing else happens). The question 'what if it flashed orange' is partly meaningless - it couldn't have flashed orange. It flashing orange was merely an image your head could construct, not a possible state of affairs.
These are when an argument's own conclusions undermine the argument. In the skeptical case it typically boils down to use of concepts and alternatives which may not exist if the skeptic is correct. The brain in a vat argument is a case in point, and I wrote about this a while ago. (If I re-wrote the article, the title should be 'the brain in a vat hypothesis is an inconsistent belief' as the current title implies it is wrong)
In general, skeptical arguments undermine truth claims. Yet skeptical arguments are truth claims, specifically ones about lack of knowledge. The 'second test' is an example - using that argument I undermine my claim that the 'second test' itself is a valid argument! This is because, if I argue that you need to prove my reasoning for an argument is correct, and also do so for my reasoning that the reasoning is correct, and so on ad infinitum, then I need to do likewise for my claim that you need to do this. If I can do it here, then my claim that constructing a truth claim is impossible is undermined.
These don't help us prove anything per se, but undermine the adequacy of skepticism as a Philosophical position to hold.
The traditional skeptical position requires a large number of assumptions.
It is not immediately apparent that we don't experience others' consciousness directly. Arguments against this are mostly based on a scientific and reductionist view of the world which skeptical arguments destroy anyway.
It is not clear either that arguments are non-verifiable, nor that we don't have more knowledge than we think as a starting point for Philosophising. It may be that Philosophy just confuses us, because we lack a conscious explanation and reason for some knowledge, and experience in other areas makes us demand explanations and reasons for everything. Even if you require an explanation for some things, that doesn't imply you need an explanation for others. Perhaps it is valid to expect a reason for someone's political opinions, but is it necessary for their favourite colour? How about for my choice of an owl as the cover picture? (Short aside - can you justify using reason to make decisions and form opinions? Can you avoid this argument being circular?)
P.S. The reductionist + Scientific approach (i.e. humans no more than their brains, world entirely explained by natural laws) might be helpful in the future. If we are no more than our brains, then theoretically it would be possible to 'interact' directly with someone else's consciousness, even if the technology doesn't exist yet.
Our understanding of consciousness is very shallow.
We often draw a distinction between actions and consciousness. Yet the skeptical position assumes that robots emulating people's actions wouldn't have consciousness - why not? This is an arbitrary assumption. Perhaps the act of carrying out those behaviours gives rise to consciousness. For someone who already thinks we are no more than the neurons interacting in our brain, is there a substantial difference between that and machines carrying out human like actions as a result of some programme? Is there a substantial difference between that and the interaction of any objects based on a programme (such as the laws of nature).
Problem 5 - A Very Human One
There is something very unsatisfactory about the skeptical position, and I doubt any human will ever accept it. We find ourselves in the world as moral agents, and how to live the 'good life' is the problem of Philosophy.
Nietzsche persuaded me of the former point after several years of skepticism.
'The eagerness and subtlety, I should even say craftiness, with which the problem of "the real and the apparent world" is dealt with at present throughout Europe, furnishes food for thought and attention; and he who hears only a "Will to Truth" in the background, and nothing else, cannot certainly boast of the sharpest ears. In rare and isolated cases, it may really have happened that such a Will to Truth—a certain extravagant and adventurous pluck, a metaphysician's ambition of the forlorn hope—has participated therein: that which in the end always prefers a handful of "certainty" to a whole cartload of beautiful possibilities; there may even be puritanical fanatics of conscience, who prefer to put their last trust in a sure nothing, rather than in an uncertain something. But that is Nihilism, and the sign of a despairing, mortally wearied soul, notwithstanding the courageous bearing such a virtue may display.' - Friedrich Nietzsche, Beyond Good and Evil
The author of this article is 'The Sociable Solipsist' who studies at Cambridge University. His favourite pastimes include Mathematics, Philosophy and writing flattering bios about himself in the third person.