When you see X ⊃ Y, you are to read "X implies Y" or "If X, then Y." Sometimes you may see the modern form, X —> Y, in my comments.
When you see X ≡ Y, you should read "X equivalent to Y" or "X strictly implies Y" or "If and only if X, then Y" or "If X, then Y and if Y, then X" (these forms are sometimes shortened to "iff"). "X ≡ Y" can also be read: "Y is necessary for X and X is sufficient for Y." Occasionally one also sees "X ≡ Y" interpreted as "Y holds just in case X holds" or "Y holds only in case X holds" and the converse, "X holds just in case Y holds." Sometimes my comments use the modern X <—> Y.
For the quantifier all, you will see ( ), as in (x)Fx. In my comments I sometimes use the modern symbol ∀, as in ∀xFx. The existential quantifer ∃, as in ∃xFx, is used in W's text and in my comments. P●Q should be read "P and Q." Often the dot is dropped, as in PQ. Occasionally dots are used instead of parentheses.
11 The world is everything that is the case.
1.1
The world is the totality of facts, not of things.
Do we have here an indication of naive realism? Well, at least W's world is defined as composed of facts, which must be mental in nature. That is, a fact is considered to carry the the truth value true. It tells the hearer something about his world that holds or doesn't accord with what we call reality. Non-facts I presume are propositions or relations that are regarded as not true or as presenting a silly association.
1.11
The world is determined by the facts, and by these being all the facts.
1.12
For the totality of facts determines both what is the case, and also all that is not the case.
1.13
The facts in logical space are the world.
Logical space? Is this a Platonic space of pure forms? Yes, I would say it is. I daresay Plato would argue that his pure forms are equivalent to W's pure logical forms.
1.2
The world divides into facts.
I agree that the human mind carves up Creation into little mental compartments for utilitarian reasons (homeostasis).
1.21
Any one can either be the case or not be the case, and everything else remain the same.
Yes, the mind holds input from the environment constant while it considers a particular "fact" as either true or false.
1. The decimal figures as numbers of the separate propositions indicate the logical importance of the propositions, the emphasis laid upon them in my exposition. The propositions n.1, n.2, n.3, etc., are comments on proposition No. n; the propositions n.m1, n.m2, etc., are comments on the proposition No. n.m; and so on.
1.1
The world is the totality of facts, not of things.
Do we have here an indication of naive realism? Well, at least W's world is defined as composed of facts, which must be mental in nature. That is, a fact is considered to carry the the truth value true. It tells the hearer something about his world that holds or doesn't accord with what we call reality. Non-facts I presume are propositions or relations that are regarded as not true or as presenting a silly association.
The world is determined by the facts, and by these being all the facts.
1.12
For the totality of facts determines both what is the case, and also all that is not the case.
1.13
The facts in logical space are the world.
Logical space? Is this a Platonic space of pure forms? Yes, I would say it is. I daresay Plato would argue that his pure forms are equivalent to W's pure logical forms.
The world divides into facts.
I agree that the human mind carves up Creation into little mental compartments for utilitarian reasons (homeostasis).
Any one can either be the case or not be the case, and everything else remain the same.
Yes, the mind holds input from the environment constant while it considers a particular "fact" as either true or false.
1. The decimal figures as numbers of the separate propositions indicate the logical importance of the propositions, the emphasis laid upon them in my exposition. The propositions n.1, n.2, n.3, etc., are comments on proposition No. n; the propositions n.m1, n.m2, etc., are comments on the proposition No. n.m; and so on.
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