Less is Different: Emergence and Reduction Reconciled
Less is Different: Emergence and Reduction Reconciled
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少即是不同：出现与减少的协调
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Butterfield
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作者：
J. Butterfield
这是另一篇论文的姊妹篇。他们一起反驳了两个关于涌现的广泛的哲学学说。第一个也是主要的学说是，涌现与还原是不相容的。第二个是，涌现是随附性，或者更准确地说，随附性没有减少。在其他文件中，我发展这些反驳一般条款，强调第二个反驳。在这里，我讨论物理学的情况，强调第一个反驳。我专注于理论之间的限制关系，并用四个例子来说明我的主张，每个例子都是一个模型或建模框架，来自成熟的数学或物理学。我认为，还原本质上就是演绎。我的第一个反驳的主要思想将是在取某个参数的极限后执行演绎。因此，我的第一个主要主张是，在我的四个例子（以及许多其他例子）中，我们可以通过取参数N的极限N→∞来推导出一种新颖而鲁棒的行为。但另一方面，这并不表明N=∞极限是“物理上真实的”，正如一些作者所声称的那样。因为我的第二个主要主张是，在这些相同的例子中，在我们到达极限之前，即对于有限N，存在一种较弱的、但仍然生动的、新颖的和鲁棒的行为。正是这种较弱的行为在物理上是真实的，我举的例子有：任意函数的方法（概率论）;分形（几何学）;无限系统的超选择（量子论）;无限系统的相变（统计力学）。
This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics).