Formulation of the fundamental laws of nature
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The first and fundamental law of nature is to seek peace and follow it.
And because the condition of man (as hath been declared in the precedent chapter) is a condition of war of every one against every one, in which case every one is governed by his own reason, and there is nothing he can make use of that may not be a help unto him in preserving his life against his enemies; it followeth that in such a condition every man has a right to every thing, even to one another's body. And therefore, as long as this natural right of every man to every thing endureth, there can be no security to any man, how strong or wise soever he be, of living out the time which nature ordinarily alloweth men to live. And consequently it is a precept, or general rule of reason: that every man ought to endeavour peace, as far as he has hope of obtaining it; and when he cannot obtain it, that he may seek and use all helps and advantages of war. The first branch of which rule containeth the first and fundamental law of nature, which is: to seek peace and follow it. The second, the sum of the right of nature, which is: by all means we can to defend ourselves.
Hobbes, Lev XIV 4
The second law of nature is to claim only so much liberty against others as one would allow others against himself.
From this fundamental law of nature, by which men are commanded to endeavour peace, is derived this second law: that a man be willing, when others are so too, as far forth as for peace and defence of himself he shall think it necessary, to lay down this right to all things; and be contented with so much liberty against other men as he would allow other men against himself. For as long as every man holdeth this right, of doing anything he liketh; so long are all men in the condition of war. But if other men will not lay down their right, as well as he, then there is no reason for anyone to divest himself of his: for that were to expose himself to prey, which no man is bound to, rather than to dispose himself to peace. This is that law of the gospel: Whatsoever you require that others should do to you, that do ye to them. And that law of all men, quod tibi fieri non vis, alteri ne feceris.
To lay down a man's right to anything is to divest himself of the liberty of hindering another of the benefit of his own right to the same. For he that renounceth or passeth away his right giveth not to any other man a right which he had not before, because there is nothing to which every man had not right by nature, but only standeth out of his way that he may enjoy his own original right without hindrance from him, not without hindrance from another. So that the effect which redoundeth to one man by another man's defect of right is but so much diminution of impediments to the use of his own right original.
Hobbes, Lev XIV 5-6
The third law of nature is to keep your contracts, i.e., be just.
FROM that law of nature by which we are obliged to transfer to another such rights as, being retained, hinder the peace of mankind, there followeth a third; which is this: that men perform their covenants made; without which covenants are in vain, and but empty words; and the right of all men to all things remaining, we are still in the condition of war.
And in this law of nature consisteth the fountain and original of justice. For where no covenant hath preceded, there hath no right been transferred, and every man has right to everything and consequently, no action can be unjust. But when a covenant is made, then to break it is unjust and the definition of injustice is no other than the not performance of covenant. And whatsoever is not unjust is just.
Hobbes, Lev XV 1-2