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The judge and jurist Oliver Wendell Holmes Jr very aptly summed up the way such development works in his book The Common Law (1881). He noted:

The life of the law has not been logic: it has been experience. The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellowmen, have had a good deal more to do than the syllogism in determining the rules by which men should be governed.

Source: P131, How the Law Works, Gary Slapper

I recognise the form of a syllogism from my math studies, but I'm guessing that the meaning here should be Definition 1.1? Yet I doubt this, because deduction doesn't always determine 'the rules ...'?

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Simplifying the sentence may help clarify:

The life of the law has not been logic: it has been experience. [This list of experiences] have done more than [logical structures, e.g.] the syllogism, to determine the rules by which men should be governed.

Your statement above is correct - logical deduction doesn't necessarily determine the rules. This is also what Judge Holmes was saying. He's using "syllogism" as an example of a logical structure that could be used in determining the law, but which in his view is overshadowed by theories, policy choices, or prejudices of the time.

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The author is pointing back to the previous sentence. The "life" of the law - how it is exercised - is based on experience, not logic. As a syllogism is a logical structure, all of the items he has listed are experiential and take precedence over the logic. He is contrasting the content (logic) of the law with its application.

For example, the law might state that the posted speed limit on a particular stretch of road is 45 miles per hour. However, this road leads to a hospital. So the application of the law - from a perspective of experience - may take this into account when handing down a verdict for a particular offender who happened to be rushing his child to the emergency room. The syllogism of law states an absolute; experience gives it flexibility.

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