Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do)? Descartes used 'I think' as this fixed point where the skepticism abates, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy?
Descartes was the modern founder of what is called foundationalism about knowledge, the idea that we must find a secure self-evident ground from which all the rest of our knowledge can be justified. Many classical philosophers (e.g. Plato, Kant, Frege, Husserl) shared this belief, and some continue to share it. The alternative, they believe, is universal scepticism. But it was severely shaken in the 20th century, and an alternative conception of knowledge and justification emerged.
For balance, let me give you the view of one of its founders, a prominent mathematician and the father of philosophical pragmatism Peirce. According to him, we do not question our beliefs until we are called to question them, doubt must be motivated, not a "paper doubt". But we do not thereby take any beliefs as secure either. All knowledge is fallible, but "there is a world of difference between fallible knowledge and no knowledge". We act on it as we must, which puts it to the test, and discard those parts of it that do not pass the test. Here is Peirce's critique of Descartes' cogito, and his advice on doubt:
"Descartes thought this "très-clair"; but it is a fundamental mistake to suppose that an idea which stands isolated can be otherwise than perfectly blind. He professes to doubt the testimony of his memory; and in that case all that is left is a vague indescribable idea. There is no warrant for putting it into the first person singular. "I think" begs the question. "There is an idea: therefore, I am," it may be contended represents a compulsion of thought; but it is not a rational compulsion. There is nothing clear in it. Here is a man who utterly disbelieves and almost denies the dicta of memory. He notices an idea, and then he thinks he exists. The ego of which he thinks is nothing but a holder together of ideas. But if memory lies there may be only one idea. If that one idea suggests a holder-together of ideas, how it can do so is a mystery. [CP 4.71]
"We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. Hence this initial skepticism will be a mere self-deception, and not real doubt; and no one who follows the Cartesian method will ever be satisfied until he has formally recovered all those beliefs which in form he has given up... A person may, it is true, in the course of his studies, find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it, and not on account of the Cartesian maxim. Let us not pretend to doubt in philosophy what we do not doubt in our hearts." [CP 5.265]
Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do). Descartes used 'I think' as this fixed point, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy?
Your first sentence ought to end with a question mark since it is a question.
You don't keep questioning until nothing is left. You also don't pick any fixed point on which to stand.
Tearing down all your knowledge until nothing is left makes no sense since a lot of your knowledge is okay. You can walk down the street without killing yourself so there is no reason to think you ought to ditch your knowledge about walking.
A fixed point doesn't make any sense since you can't explain which fixed point you take. If you're going to try to build all of your knowledge on some fixed point you have to pick it arbitrarily. Any non-arbitrary way of picking it would require knowledge, which is what you're supposed to get from the starting point.
There is no need for a starting point. The way you actually understand and create knowledge is to look for problems with your existing knowledge, propose ideas that might solve the problems and criticise the proposals until only one is left and it has no known problems. This is rational in the sense that it will allow you to fix problems.
Any notion of rationality that involves justification (showing ideas are true or probably true) will suffer from the dilemma of questioning forever or irrationally picking a fixed point. So all theories involving justification are irrational.
The person who originally understood this was Karl Popper, see 'Realism and the Aim of Science', Chapter I and 'On the sources of knowledge and of ignorance' in 'Conjectures and Refutations'.
Also, Popper often took the position that hypothesis formulation was an evolutionary process involving some sort of internal trial and error of hypotheses. See Popper's contribution to Radnitzky and Bartley volume on 'Evolutionary Epistemology'. Popper's point about the origin of a theory was that it didn't much matter where an idea came from if it stood up to criticism.
Yes, we should question everything. Just not all at once. That, according to a central strand in modern philosophy, for which Descartes himself has been a guiding example. Descartes's so called fixed point was a point that he reached through the questioning process. It's not as if he decided on a fixed point before he started questioning. On the contrary, he first embarked on an unlimited (*) process of questioning. Neither did Descartes assume in advance that he will in fact find such a fixed point.
I shall proceed by setting aside all that in which the least doubt could be supposed to exist, just as if I had discovered that it was absolutely false; and I shall ever follow in this road until I have met with something which is certain, or at least, if I can do nothing else, until I have learned for certain that there is nothing in the world that is certain. (Descartes, Meditations II)
In general, a fixed fixed point, like the one that Descartes believed he found, is not necessary. But provisional fixed points are necessary, in the questioning process. The questions themselves have pre-suppositions, so you cannot ask and doubt everything at the same time (that is, in fact, how Descartes arrived at his "fixed point"). But you can e.g. rely on A and question B, and later rely on B and question A.
For ... knowledge, like its sophisticated extension, science, is rational, not because it has a foundation, but because it is a self-correcting enterprise, which can put any claim in jeopardy, though not all at once. (Wilfrid Sellars, Empiricism and the Philosophy of Mind)
(*) Note that Descartes's questioning was limited to theoretical matters. He carefully separated those from practical matters.
For I am assured that there can be neither peril nor error in this course, and that I cannot at present yield too much to distrust, since I am not considering the question of action, but only of knowledge. (Descartes, Meditations I)
Descartes formulated, in fact, a small "moral code", which he pledged to hold, regardless of the turn of his skeptical questioning.
And finally, as it is not sufficient, before commencing to rebuild the house which we inhabit, to pull it down and provide materials and an architect (or to act in this capacity ourselves, and make a careful drawing of its design), unless we have also provided ourselves with some other house where we can be comfortably lodged during the time of rebuilding, so in order that I should not remain irresolute in my actions while reason obliged me to be so in my judgments, and that I might not omit to carry on my life as happily as I could, I formed for myself a code of morals for the time being which did not consist of more than three or four maxims, which maxims I should like to enumerate to you. (Descartes, Essay on Method)
I believe the last statement is at the heart of the question. Most people I know care less about the history of how ideas formed and the major contributors of the idea (Kant, Descartes, etc in this case). So I will cut to the chase and not talk about history of philosophy:
But what is a rational way to find one, if any? How is this question addressed in modern philosophy?
The answer is Yes.
To list a few:
Evidentialism or some form of it such as Pragmatic Evidentialism is my go to. Evidentialism in a nut shell requires evidence for all claims. Pragmatic Evidentialism deals with the infinite regress by requiring evidence to a reasonable level based on the size of the claim, etc.. I belive this is the newest of the ones I am listing here. https://www.youtube.com/watch?v=14JavH4Rk7k
Objectivism comes from Ayn Rand who has a different take on reality based Epistemology. https://www.youtube.com/watch?v=hlJD0i_WwdQ
Materialism is notion that all that exists is matter and its movements and modifications. This one is the grand father of objectivism and evidentialism.
Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do).
This leads to Solipsism aka. how do you not know we are brains in a jar. From a pragmatic perspective this epistemology is unproductive since it doesn't get us anywhere. Some philosophers still regress to this state today. Although taking the questioning back this far is 'ok' as a thought experiment, living with this notion as being correct or using it as a defense against a claim or argument is intellectually dishonest since if they believe they are a brain in a jar they should not be participating in the discussion at all. Solipsism can be debunked as begging the question or being unfalsifible depending on the specific variation and the opponents epistemology.
Philosophy must stand within the sphere of reason, which can only be bound by the empirical, which is best represented by the scientific method (no capital letters).
For an a-priori theory to be complete, without any further possible doubt, it cannot deviate from the empirical. Word and evidence must agree.
Evidence that 'energy can neither be created nor destroyed, it can only change forms', that the local spacetime is flat to within the margin of error, special relativity, general relativity, more recently relational quantum mechanics. Tarski's undefinability theorem.
That neither Being nor Essence are observed within our empirical world, that both Being and Essence cannot even be formally expressed within our philosophical world, points to the doctorine of non-self. The 'root of all things' is found empty.