Combining Texts

All the ideas for 'fragments/reports', 'Symbolic Reasoning' and 'works'

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4 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
21548 The null class is the class with all the non-existents as its members [MacColl, by Lackey]
     Full Idea: In 1905 the Scottish logician Hugh MacColl published a paper in which he argued that the null class in logic should be taken as the class with all the non-existents as its members.
     From: report of Hugh MacColl (Symbolic Reasoning [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.95
     A reaction: For the null object (zero) Frege just chose one sample concept with an empty extension. MacColl's set seems to have a lot of members, given that it is 'null'. How many, I wonder? Russell responded to this paper.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
17743 De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki]
     Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'.
     From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1
     A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.