It is relatively easy to answer this question in a loose way, and we all know it pretty readily. If you want to be very loose in defining, you might just say “killing a person”. But we also all know that this isn’t really enough, that there is more needed to distinguish the act of murder from killing a person, because we all know that some instances of killing a person are not murder, and others are.
But before drawing out the details for that (or, according to some, obfuscating them), let’s take 2 moments to ask a prior question: what do we mean by “definition”?
Going all the way back to the beginnings of western philosophy, with Socrates and Plato in the “Meno”, we realize that when you define a general term, it isn’t just a matter of enumerating instances that fall in that category. The meaning of “virtue” is not “justice, and prudence, and courage, and honesty…” as Meno’s slave comes to see. The definition states the conceptual relationships of that notion “virtue”. If I come home and see a box of stuff in the hallway, I might say “what’s this”. The answer “it’s a collection of a knife, a stuffed animal, a yo-yo, a teapot, and 5 cloth napkins” might be true but not particularly helpful, for it doesn’t tell me what I want to understand. The answer “it’s the box of stuff going to the white elephant sale” provides the ratio under which the collection becomes intelligible as a collection. This is more what we mean by a definition.
Aristotle advanced our understanding of defining with his laying out the 4 distinct kinds of cause – matter, form, agent, and end – and then clarifying that of these causes of a thing, the first two are intrinsic causes while the latter 2 are extrinsic. When possible, the most fulsome sort of definition includes all of them rather than only some. This is why St. Thomas, in identifying the meaning of the term “law”, in the first question in the treatise on law, (Q. 90 of Prima Secundae) uses 4 articles to lay out the 4 causes, and then at the end says therefore, law is “nothing else than…” an ordinance of reason, for the common good, by him who has the care of the common good, promulgated. He is explicitly covering the 4 causes in the definition.
But to get back to the intrinsic causes of a thing, the form and the matter, which Aristotle says constitutes the NATURE of the thing, the form is the more critical than the matter. These together both tell us the “what it is” of the thing, rather than “who made it” or “why they did”. And then the philosopher Porphyry explicated Aristotle’s notion of identifying the whatness of the thing in stating the genus in which it is found and the specific difference which nails down its nature specifically within the genus: in the genus created substances, there are bodily beings and non-bodily beings (angels). In bodily beings, there are living and non-living things. In living things there are plants and animals. In the genus animals there are vertebrates and non-vertebrates. Within the former there are mammals and birds and reptiles and amphibians and fish. And within mammals (eventually) there are rational animals. The what it is of man is something like “rational primate”, to give the nearest genus. But since there aren’t any instances of rational reptiles, or rational birds, or rational starfish, we could also (loosely) say man is rational vertebrate, or just rational animal. The term “rational” is the specific difference that gives us the intelligibility of the classification “man” from the rest of the genus. If there were rational animals in other genera, we would have to be more careful, and we would have to state the nearest and lowest genus in which man is found to really define it, otherwise the definition would end up not with ONE specific difference, but many. And this is less intelligible.
So a definition is better when it positively identifies the specific difference rather than tries to distinguish negatively by saying “well, it’s in this genus but it isn’t A, B, or C in the genus." Such may be used for loose work, but it is less than ideal for defining. Ideally, we pinpoint under a single concept the specific difference that separates it from all the other members of the genus – if you need more than one concept to do so, it may be that you haven’t yet identified the lowest genus in which the species is distinct and separable notionally. You have more work to do.
The genus and specific difference of a natural substance like a plant or animal is often a little clearer than more abstract categories, like “virtue”. So we might have trouble defining some things, like kinds of actions, because they only imperfectly fall into the above structure of higher and lower genera, of saying “what it is” using the 4 causes, and for its nature giving its lowest genus and specific difference.
Returning to murder: we know it must be the act of a human (or at least a rational being) – animals cannot commit murder.
We know it must be an act that flows from the will upon rational apprehension – accidents are not murder. The killing must be in the object of the act willed. It is possible that the genus that expresses these two notions is "homicide" but I am not sure (the legal meaning of homicide varies from place to place). So for the moment let's just take it that we have narrowed down the genus by saying it is a human chosen act of killing a person.
A. We know that it isn’t murder if it is an executioner carrying out a just sentence for a capital crime. But (to be cautious here): just because someone is justly convicted of a capital crime and is justly condemned, not anyone take it upon himself to be the killer – Joe Q. deciding on his own to kill the guy doesn’t dispense Joe from being a murderer. (On the contrary, Augustine says (De Civ. Dei i) [Can. Quicumque percutit, caus. xxiii, qu. 8: "A man who, without exercising public authority, kills an evil-doer, shall be judged guilty of murder, and all the more, since he has dared to usurp a power which God has not given him.")
B. We don’t ascribe murder to a soldier lawfully performing his duties in the battlefield by
killing enemy soldiers.
C. It isn’t murder if you kill an attacker in defending yourself. Or if a policeman kills the guy attacking you.
Taking these all together, we might be tempted to construct a definition that lays out something like “a human, chosen act of killing a person that isn’t A, B, or C” but we have due reason to think that such a definition is less than ideal – it fails to identify the ratio, the specific difference of the act as a single coherent concept that says what it is rather than what it isn't. It is a definition more in the form of an enumeration (negatively) than in the form of a specific difference under the genus. Maybe that’s the best we can do, but we shouldn’t assume it first off.
Some people suggest that it is better to state it as “a human, chosen act of killing a person whose life you have no right to take.” This does encapsulate scenarios A, B, and C under a single conceptual difference, but – without at least an allusion to what might formulate the basis of a “right to take lives” it seems less than complete.
So, a better result would be a definition that uses the principle under which man doesn’t have the right to take another’s life – a principle that harbors within itself its own limitations (the guilty, soldiers in combat, self-defense) by nature rather than by accidental enumeration. This would allow us to state the specific difference by an integrated intelligible notion.
St. Thomas helps out here, he gives us insight on what it is that makes it that we don’t have the right to take lives:
it is lawful to kill an evildoer in so far as it is directed to the welfare of the whole community,
It is altogether unlawful to kill oneself, for three reasons. First, because everything naturally loves itself, the result being that everything naturally keeps itself in being, and resists corruptions so far as it can. Wherefore suicide is contrary to the inclination of nature, and to charity whereby every man should love himself. Hence suicide is always a mortal sin, as being contrary to the natural law and to charity. Secondly, because every part, as such, belongs to the whole. Now everyman is part of the community, and so, as such, he belongs to the community. Hence by killing himself he injures the community, as the Philosopher declares (Ethic. v, 11). Thirdly, because life is God's gift to man, and is subject to His power, Who kills and makes to live. Hence whoever takes his own life, sins against God, even as he who kills another's slave, sins against that slave's master, and as he who usurps to himself judgment of a matter not entrusted to him. For it belongs to God alone to pronounce sentence of death and life, according to Deuteronomy 32:39, "I will kill and I will make to live."
Man is made master of himself through his free-will: wherefore he can lawfully dispose of himself as to those matters which pertain to this life which is ruled by man's free-will. But the passage from this life to another and happier one is subject not to man's free-will but to the power of God.
Through reason and free will, man is master of himself within limits, under God and the nature with which he was created. Thus man can dispose of himself within those limits, and outside those limits he is constrained by law (either the natural law or the divine law). Through man’s nature, he is a social being, and as social it is according to his nature that he have care for and charity for his neighbor. Also through his nature, his likeness to God (in His image) as rational being, is a nature to be loved and protected, so we ought to love our neighbor (loved secondarily on account of loving God primarily – which is charity). Though a man ought to love himself as his closest of neighbors (and this is why he ought to protect himself against an attacker, see article 7, Q 64). In all cases, then, what sets a man off from the animals (who may be killed at our choice) is that man is the sort of thing (like to God) who ought to be loved in himself rather than simply be used. All of the acts of A, B, and C above (which are killing but not murder) are cases in which killing a man occurs when you have an _ordered_ love of men, not a disordered love of them, and this order stems from man’s relation to God (who is the exemplar source of all ordering principles). All the acts of reprehensible killing, without exception, defy that orderliness of man as related and ordered to God under His image.
So, one way to suggest a defining expression that is positive and identifies a specific difference that is so by nature rather than an accidental enumeration is this: murder is the human willed act of killing a man contrary to the orderly love of man as under the image of God.
An act of this sort is intrinsically evil. It is disordered in its object. It is wrong without exception. It is that lovable imago dei that forms the basis of protection of the man who is innocent, and which bears its own inherent limits regarding the guilty and enemy soldiers:
Now every individual person is compared to the whole community, as part to whole. Therefore if a man be dangerous and infectious to the community, on account of some sin, it is praiseworthy and advantageous that he be killed in order to safeguard the common good, since "a little leaven corrupteth the whole lump" (1 Corinthians 5:6).
In killing the guilty, it is not that the guilty are no longer loved as men, but that the love of the common good of all calls for their death. In killing enemy soldiers, you do not treat them as cattle, but rather you bear out the love of your near neighbors (and yourself) who bear the image of God more by not letting them be killed. The love of man under our love of God requires killing some, and this is loving the best good more than a lesser good.