René Descartes famously divided the world into mind (the ideal realm of thoughts) and body (the material world). The physical world is a deterministic machine, but our ideas and thoughts can be free (undetermined) and can change things in the otherwise pre-determined material world (through the pineal gland in the brain, he thought).

Descartes wrote in 1644

The freedom of the will is self-evident.

There is freedom in our will, and that we have power in many cases or withhold our assent at will, is so evident that it must be counted among the first and most common notions that are innate in us.
(Principles of Philosophy, Part One, Section 41, trans. Haldane and Ross, 1911, p.235)

In his 1874 book Principles of Science, the great logician and economist William Stanley Jevons is unequivocal that scientists have a freedom to hypothesize. In a section entitled Freedom of Theorizing, he declares

It would be a complete error to suppose that the great discoverer is one who seizes at once unerringly upon the truth, or has any special method of divining it. In all probability the errors of the great mind far exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must almost of necessity be many times as numerous as those which prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record may remain of more than the hundredth part. There is nothing intrinsically absurd except that which proves contrary to logic and experience. The truest theories involve suppositions which are most inconceivable, and no limit can really be placed to the freedom of framing hypotheses.

(Principles of Science, Chapter XXVI, vol.II, p.221)

We know that William James read Jevons. In 1880, he credited Jevons with explaining the creativity of the genius as dependent on random hypotheses. James said,

"To Professor Jevons is due the great credit of having emphatically pointed out how the genius of discovery depends altogether on the number of these random notions and guesses which visit the investigator's mind. To be fertile in hypotheses is the first requisite, and to be willing to throw them away the moment experience contradicts them is the next."

("Great Men, Great Thoughts, and the Environment", Atlantic Monthly 46 (October 1880): p. 456)

But James said explictly that he learned to affirm his freedom as a starting point from the French philosopher Charles Renouvier. In an 1876 review of Renouvier's Essais de Critique Générale, James quoted Renouvier, "Let our liberty pronounce on its own real existence," and said

{Freedom] and necessity being alike indemonstrable by any quasi-material process, must be postulated if taken at all.

"I prefer to affirm my liberty and to it by means of my liberty. . . .My moral and practical certitude begins logically by the certitude of my freedom, just as practically my freedom has always had to intervene in the constitution of my speculative certitude."

"I think that yesterday was a crisis in my life. I finished the first part of Renouvier's second Essais and see no reason why his definition of free will — 'the sustaining of a thought because I choose to when I might have other thoughts' — need be the definition of an illusion. At any rate, I will assume for the present — until next year — that it is no illusion. My first act of free will shall be to believe in free will."

(The Thought and Character of William James (Boston, Little, Brown, 1936) vol.1, p.323)

The philosopher John Searle says:

The problem of free will is unusual among contemporary philosophical issues in that we are nowhere remotely near to having a solution. I can give you a pretty good account of consciousness, intentionality, speech acts and of the ontology of society but I do not know how to solve the problem of free will.

Well, why is that important? There are lots of problems we do not have solutions to. The special problem of free will is that we cannot get on with our lives without presupposing free will. Whenever we are in a decision-making situation, or indeed, in any situation that calls for voluntary action, we have to presuppose our own freedom.
(Freedom and Neurobiology, p.11)

The scientist Nicolas Gisin says:

I know that I enjoy free will much more than I know anything about physics. Hence, physics will never be able to convince me that free will is an illusion. Quite the contrary, any physical hypothesis incompatible with free will is falsified by the most profound experience I have about free will.

The scientist Antoine Suarez says:

Free Will is an axiom, like the Free Will Theorem of Conway and Kochen.

Conway and Kochen claim that if experimenters have free will, then so do the elementary particles (of which experimenters are made). This is the reverse of Arthur Stanley Eddington, who said that the freedom (quantum indeterminacy) of the elementary particles cracked opened a door for human freedom. Eddington said,

"The revolution of theory which has expelled determinism from present-day physics has therefore the important consequence that it is no longer necessary to suppose that human actions are competely predetermined. Although the door of human freedom is opened, it is not flung wide open; only a chink of daylight appears."
(New Pathways in Science, 1935, p.87)

American philosopher Henry Allison said,

"To take oneself as a rational agent is to assume that one's reason has a practical application or, equivalently, that one has a will. Moreover, one cannot assume this without already presupposing the idea of freedom, which is why one can act, or take oneself to act, only under this idea. It constitutes, as it were, the form of the thought of oneself as a rational agent."
("We Can Act Only under the Idea of Freedom," Proceedings of the American Philosophical Association, 71:2; pp.39-50)