https://en.wikipedia.org/wiki/Radical_skepticism
I am thinking that simple statement such as "I am", "I think" are all beliefs that are also knowledge and conditional statements such as "This dog does exist in this world if the world is real" are also knowledge since they are true even if proven to be an illusion.
A good question.
Every machine is fallible, including the human brain; this means that when the human brain comes up with any conclusion, there is always the possibility it made an error and came to the wrong conclusion. Even if the brain in question is your own. Computers can make occasional errors in calculation due to manufacturing defects, cosmic ray impacts, hard disk drive failure, software bugs, or even quantum tunneling (the latter with extremely low, but nonzero probability, and the fact it is nonzero is all that matters to the point). That means that when a computer tells you the result of any calculation, you cannot rationally trust it 100%. Perhaps you can trust it very close to 100%, but never exactly 100%.
The human brain is a piece of hardware subject to many of the same kinds of faults that affect computers. Humans are known to make calculation errors at a much higher rate than computers do. Therefore, we should not say we "know" something, unless by that we mean that we believe it with high confidence. Knowledge is a kind of belief, not something fundamentally different from belief. Everything is in doubt.
"Even that?"
Yes. It's a consequence of the physical basis of your brain.
Note that, if everything is uncertain, the degree of uncertainty is also uncertain. If you calculate a 99.999999% chance that you're right about X, you can't trust that calculation perfectly. Maybe you made an arithmetic error and really the chance of being right about X is only 30%!
As a practical matter, almost everyone is more confident of their own views than is objectively warranted. People, probably including you and me, would be more rational if they were less certain. Doubting your views is the only way to change them, and changing your views is the only way to become more right over time. Of course, it is not guaranteed that change is for the better; doubt also the change. But because like most people you likely have a bias towards overconfidence in your established views, it is necessary to put more effort into doubting your own views than doubting the change.
I've sometimes seen a strange reaction to the fact that all knowledge is uncertain. Some people associate uncertainty with the notion that truth is subjective, or that because we can never certainly reach absolute truth, it doesn't matter to us. This is like saying that because maps are sometimes printed with mistakes, mountains don't exist or don't matter to us. It's a complete non sequitur. It is entirely possible to both believe that a mountain exists because it's shown on the map, and that the mountain might not exist because the map might be misprinted. Not only is it possible, it's the most reasonable perspective. One believes in objective reality at the same time as one acknowledges that all of one's beliefs may be mistaken.
One ancient counterexample for radical skepticism is just ask such a skeptic whether he or she accepts the skeptic's own knowledge that "one should reject any knowledge". If the skeptic accepts then he or she contradicts own POV literally, if one rejects then one rejects one's own POV directly. Either result seems logically awkward for the radical skeptic.
Some modern radical skeptics use Brain in a vat (BIV) to argue that technology can be so perfect that one can never know if one is real or just a "disembodied" brain in vat, thus knowledge is impossible:
The simplest use of brain-in-a-vat scenarios is as an argument for philosophical skepticism and solipsism. A simple version of this runs as follows: Since the brain in a vat gives and receives exactly the same impulses as it would if it were in a skull, and since these are its only way of interacting with its environment, then it is not possible to tell, from the perspective of that brain, whether it is in a skull or a vat. Yet in the first case, most of the person's beliefs may be true (if they believe, say, that they are walking down the street, or eating ice-cream); in the latter case, their beliefs are false. Since the argument says one cannot know whether one is a brain in a vat, then one cannot know whether most of one's beliefs might be completely false. Since, in principle, it is impossible to rule out oneself being a brain in a vat, there cannot be good grounds for believing any of the things one believes...
Please note that any asserted knowledge like "I have a hand" could be leveraged by a radical skeptic as an argument for radical skepticism holding the view that one cannot know she is a BIV or not since technology may be prefect enough not to be able to distinguish any more. How? First the skeptic will claim we all agree with a self-evident principle of epistemic closure:
Epistemic closure is a property of some belief systems. It is the principle that if a subject S knows a (proposition) p, and S knows that p entails q, then S can thereby come to know q.
Since the proposition you have a hand entails the proposition you are not a BIV, once you know you have a hand, then you must also know you are not a BIV. But this is a contradiction with the undisputable fact that one can never know if one is BIV or not as introduced context above. So you cannot claim you know you have a hand...
Then how to construct a counterexample for this hopeless situation? Some philosophers like Robert Nozick proposed we have to abandon above "self-evident" principle of epistemic closure and change the philosophical JTB definition of knowledge. If you adopt this approach, then by external experimental confirmation of the existence of our hands then we can somehow confidently claim we have some certain real knowledge if common probabilistic types of knowledge doesn't qualify per your standard...
A realist and recovering ex-engineer weighs in.
The process of living one's life and (metaphorically) getting from A to B constitutes the solution of a never-ending series of problems. Engineer are trained to solve certain classes of problems in the physical world and with the passage of time and experience, they eventually get good at it and are able to pay bills, buy houses, support families and so on.
This process is imperfect, meaning you make mistakes and must recover from them and with luck converge on the truth through an iterative process which is built on the accumulation of facts and data.
As such there is no place for radical skepticism in this paradigm. Passenger planes, cars, houses, computers, bridges, freeways, MRI machines, sewage treatment plants and so on are not invented nor are they built by radical skeptics.
In this sense, therefore, radical skepticism is amply refuted by the ability of humans to solve problems, which has furnished us with the world we currently live in.
It is an imperfect world to be sure, but as a very recent cancer survivor I owe my current existence to MRI and CT machines and the people who know how to use them to solve problems.
There's two types of knowledge: Knowledge from looking at the universe, and created knowledge.
To be skeptical of created knowledge makes much less sense than knowledge derived from observation.
An example of created knowledge is the author of a story: How does he know where the hero has hidden secret widget? Because he decided.
Another example might be where you live: How do you know you live at 123 Acme Street? Because you decided to live there. I guess this latter combines observed knowledge that a house existed there in the first place, and an agent put a contract under your nose. But still there is a decision point there.
I guess it is possible to doubt your own decisions, but that route insanity lies, and is a common theme in psychological horror, such as Shutter Island.
Is there any counterexample given against radical skepticism?
Here is my humble opinion: radical skepticism has no practical value. The level of confidence someone needs before acting rises or falls with the importance or lack of importance of the decision under consideration. If there is a life-altering decision to be made, then nearly 100% certainty might be called for. For a lot of day-to-day decisions, it is often sufficient to accept what is true randomly.
But what if you don’t know the level of confidence that is justified by the data, or even whether the data itself is accurate? The answer is that you do what you can. It could be anything: run an experiment, check the newspaper.
But the answer to the basic philosophical question, while interesting, does not affect daily life.
What is radical skepticism?
According to the above analysis, B. Russell's point is demonstrated:
Skepticism, while logically impeccable, is psychologically impossible, and there is an element of frivolous insincerity in any philosophy which pretends to accept it.
In the sense of the above analysis, it is no wonder the archetypal depiction of the skeptic philosopher is sitting down, doing absolutely nothing (if "doing absolutely nothing" could really be depicted), while, in contrast, a philosopher like Aristotle was always walking.
