Here are classical statements of compatibilism:
"By LIBERTY, is understood, according to the proper signification of the word, the absence of external impediments: which impediments, may oft take away part of a man's power to do what he would; but cannot hinder him from using the power left him, according as his judgment, and reason shall dictate to him."
(Hobbes, Thomas. Leviathan. 1651. Pt. I: Ch. XIV; §2)
"LIBERTY, or FREEDOM, signifieth (properly) the absence of opposition; (by opposition, I mean external impediments of motion;) and may be applied no less to irrational, and inanimate creatures, than to rational."
(Hobbes, Thomas. Leviathan. 1651. Pt. II: Ch. XXI; §1)
"[A] FREEMAN, is he, that in those things, which by his strength and wit he is able to do, is not hindered to do what he has a will to."
…
"[F]rom the use of the word free-will, no liberty can be inferred of the will, desire, or
inclination, but the liberty of the man; which consisteth in this, that he finds no stop, in doing what he has the will, desire, or inclination to do."
(Hobbes, Thomas. Leviathan. 1651. Pt. II: Ch. XXI; §2)
"[L]iberty is the absence of all the impediments to action that are not contained in the nature and intrinsical quality of the agent."
(Hobbes, Thomas. "Of Liberty and Necessity." 1654. Reprinted in: D. D. Raphael, British Moralists 1650–1800, Vol. 1: Hobbes–Gay. Oxford: Clarendon Press, 1969. p. 67)
"[A] free agent is he that can do if he will, and forbear if he will; and that liberty is the absence of external impediments. "
(Hobbes, Thomas. "Of Liberty and Necessity." 1654. Reprinted in: D. D. Raphael, British Moralists 1650–1800, Vol. 1: Hobbes–Gay. Oxford: Clarendon Press, 1969. p. 68)
"Liberty…is the power a man has to do or forbear doing any particular action, according as its doing or forbearance has the actual preference in the mind, which is the same thing as to say, according as he himself wills it."
(Locke, John. An Essay concerning Human Understanding. 1690. Bk. II: Ch. XXI; §15.)
"By liberty, then, we can only mean a power of acting or not acting, according to the determinations of the will; that is, if we choose to remain at rest, we may; if we choose to move, we also may. Now this hypothetical liberty is universally allowed to belong to every one, who is not a prisoner and in chains. Here then is no subject of dispute."
(Hume, David. An Enquiry concerning Human Understanding. 1748. Sect. VIII: Pt. I; §23)
"[C]ompatibilists argue that to be free, as we ordinarily understand it, is (1) to have the power or ability to do what we want or desire to do, which in turn entails (2) an absence of constraints or impediments (such as physical restraints, coercion, and compulsion) preventing us from doing what we want. Let us call a view that defines freedom in terms of 1 and 2 'classical compatibilism'. Most traditional compatibilists, such as Hobbes, Hume, and Mill, were classical compatibilists in this sense."
(Kane, Robert. A Contemporary Introduction to Free Will. New York: Oxford University Press, 2005. p. 13)
Compatibilism trivializes the free-will problem, since we know we have compatibilist free will, in the sense that we can sometimes do what we choose/desire/intend/want to do without there being any external impediment or coercion.
The nontrivial and really interesting question is whether we also have
libertarian free will, in the sense that we can perform actions or form decisions or intentions to action which are
neither causally predetermined nor random.
According to libertarianism, given the total causal history of the world < time T, including agent A's total causal history < T, and A's deciding to do/doing X at T,
A could have decided/done otherwise at T. Libertarians believe that…
"[E]ach of us, when we act, is a prime mover unmoved. In doing what we do, we cause certain events to happen, and nothing—or no one—causes us to cause those events to happen."
(Chisholm, Roderick M. On Metaphysics. Minneapolis, MN: University of Minnesota Press, 1989. p. 12)
In his highly recommendable new book, Robert Sapolsky presents a compelling case for
hard incompatibilism, according to which the world is deterministic and there is no (libertarian) free will (and thus no moral responsibility either).
"[W]e are nothing more or less than the cumulative biological and environmental luck, over which we had no control, that has brought us to any moment."
(Sapolsky, Robert M. Determined: A Science of Life without Free Will. New York: Penguin, 2023. p. 4)
"What Do I Mean by Free Will?
People define free will differently. Many focus on agency, whether a person can control their actions, act with intent. Other definitions concern whether, when a behavior occurs, the person knows that there are alternatives available. Others are less concerned with what you do than with vetoing what you don’t want to do. Here’s my take.
Suppose that a man pulls the trigger of a gun. Mechanistically, the muscles in his index finger contracted because they were stimulated by a neuron having an action potential (i.e., being in a particularly excited state). That neuron in turn had its action potential because it was stimulated by the neuron just upstream. Which had its own action potential because of the next neuron upstream. And so on.
Here’s the challenge to a free willer: Find me the neuron that started this process in this man’s brain, the neuron that had an action potential for no reason, where no neuron spoke to it just before. Then show me that this neuron’s actions were not influenced by whether the man was tired, hungry, stressed, or in pain at the time. That nothing about this neuron’s function was altered by the sights, sounds, smells, and so on, experienced by the man in the previous minutes, nor by the levels of any hormones marinating his brain in the previous hours to days, nor whether he had experienced a life-changing event in recent months or years. And show me that this neuron’s supposedly freely willed functioning wasn’t affected by the man’s genes, or by the lifelong changes in regulation of those genes caused by experiences during his childhood. Nor by levels of hormones he was exposed to as a fetus, when that brain was being constructed. Nor by the centuries of history and ecology that shaped the invention of the culture in which he was raised. Show me a neuron being a causeless cause in this total sense. The prominent compatibilist philosopher Alfred Mele of Florida State University emphatically feels that requiring something like that of free will is setting the bar “absurdly high.” But this bar is neither absurd nor too high. Show me a neuron (or brain) whose generation of a behavior is independent of the sum of its biological past, and for the purposes of this book, you’ve demonstrated free will. The point of the first half of this book is to establish that this can’t be shown."
(Sapolsky, Robert M. Determined: A Science of Life without Free Will. New York: Penguin, 2023. pp. 14-5)