少是不同的：出现和减少
Less is Different: Emergence and Reduction Reconciled
摘要：
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，突现是随附性，或者更确切地说，是没有减少的随附性。在另一份文件中，我一般地发展这些反驳，强调第二个反驳。在这里，我讨论物理学中的情况，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。我把涌现看作是相对于某个比较类来说新颖而健壮的行为。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趋于无穷大，推导出一种新颖而鲁棒的行为。但另一方面，这并不表明无限极限是“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。我举的例子是：任意函数法（概率论）;分形（几何学）;无限系统的超选择（量子理论）;无限系统的相变（统计力学）。
英文摘要：
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 goes to infinity, of a parameter N. But on the other hand, this does not show that that the infinite 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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
