The negative commandments are simply injunctions against particular actions, instructions to refrain from doing.
The positive mitzvot, which are actually considered to be on a lower level, are defined in straightforward, clear terms.
It appears that precisely because of their superiority, the negative mitzvot cannot be so plainly defined.
We do not have the means to understand them properly and cannot be quite so explicit.
We can however reach them by a negative route, through a process of elimination-by knowing what is prohibited.
This definition through negation is of course very partial and unsatisfactory.
It offers no more than a general concept of what the situation requires.
It provides the framework without which action is either possible or impossible.
But altogether, a positive definition is often unavailable and a negative definition is often more feasible as, for example, when trying to define a state of war or peace (peace is when there is no war and visa versa).
And there are qualifications that are certainly positive but we do not quite know exactly what they mean, such as eternity, and the like.
The negative definition may thus prove an advantage in many cases.
What we are given as a negative mitzvah is a statement of boundaries within which we can or cannot act.
It does not provide anything that we can be absolutely sure of.
Just as in the biblical phrase describing the wilderness as a land not sown (Jeremiah 2:2), what is implied is not a negative action but a statement to the effect that the land was sown with nothing.
This follows the pattern of Creation, that in the beginning there was darkness and then light, that chaos precedes form.
It is the concept maintaining that there has to be a compression, an abatement of infinitude, a tzimtzum, for anything to exist–that light is a contraction of darkness.
It's as though the darkness is squeezed until light comes out of it.
Creation precedes formation.
In our daily prayers, we say: (He who) forms light and creates darkness.
Light is one of the formations that comes out of the dark, just as a potter shapes a particular form (light) out of the amorphous clay, which is darkness.
–Rabbi Adin Steinsaltz
From "The Way of the Soul and Torah" in The Candle of God by Rabbi Adin Steinsaltz