Notes Dictated to G.E. Moore in Norway: Difference between revisions
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(1) Take ''ϕ''x. We want to explain the meaning of 'In "''ϕ''x" a ''thing'' symbolizes'. The analysis is:— | (1) Take ''ϕ''x. We want to explain the meaning of 'In "''ϕ''x" a ''thing'' symbolizes'. The analysis is:— | ||
{{p indent|(∃y) . y symbolizes . y = "x" . "''ϕ''x"}} | {{p indent|(∃y) . y symbolizes . y <nowiki>=</nowiki> "x" . "''ϕ''x"}} | ||
["x" is the name of y: "''ϕ''x" = '"''ϕ''" is at [the] left of "x"' and ''says'' ''ϕ''x.] | ["x" is the name of y: "''ϕ''x" = '"''ϕ''" is at [the] left of "x"' and ''says'' ''ϕ''x.] | ||
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(2) The point can here be brought out as follows. Take ''ϕ''a and ''ϕ''A: and ask what is meant by saying, "There is a thing in ''ϕ''a, and a complex in ''ϕ''A"? | (2) The point can here be brought out as follows. Take ''ϕ''a and ''ϕ''A: and ask what is meant by saying, "There is a thing in ''ϕ''a, and a complex in ''ϕ''A"? | ||
{{p indent|(1) means: (∃x) . ''ϕ''x . x = a}} | {{p indent|(1) means: (∃x) . ''ϕ''x . x <nowiki>=</nowiki> a}} | ||
{{p indent|(2) means: (∃x, ''ψξ'') . ''ϕ''A = ''ψ''x . ''ϕ''x.<!--<ref>''ξ'' is Frege's mark of an ''Argumentstelle'', to show that ''ψ'' is a ''Funktionsbuchstabe''. [''Edd''.]</ref>-->}} | {{p indent|(2) means: (∃x, ''ψξ'') . ''ϕ''A <nowiki>=</nowiki> ''ψ''x . ''ϕ''x.<!--<ref>''ξ'' is Frege's mark of an ''Argumentstelle'', to show that ''ψ'' is a ''Funktionsbuchstabe''. [''Edd''.]</ref>-->}} | ||
''Use of logical propositions''. You may have one so complicated that you cannot, by looking at it, see that it is a tautology; but you have shewn that it can be derived by certain operations from certain other propositions according to our rule for constructing tautologies; and hence you are enabled to see that one thing follows from another, when you would not have been able to see it otherwise. E.g., if our tautology is of [the] form p ⊃ q you can see that q follows from p; and so on. | ''Use of logical propositions''. You may have one so complicated that you cannot, by looking at it, see that it is a tautology; but you have shewn that it can be derived by certain operations from certain other propositions according to our rule for constructing tautologies; and hence you are enabled to see that one thing follows from another, when you would not have been able to see it otherwise. E.g., if our tautology is of [the] form p ⊃ q you can see that q follows from p; and so on. | ||
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''ϕ'' cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ''ψ''x is ''that'' ''ψ'' stands to the left of a name form, and another symbol ''ϕ'' cannot possibly stand to the left of such a ''fact'': if it could, we should have an illogical language, which is impossible. | ''ϕ'' cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ''ψ''x is ''that'' ''ψ'' stands to the left of a name form, and another symbol ''ϕ'' cannot possibly stand to the left of such a ''fact'': if it could, we should have an illogical language, which is impossible. | ||
{{p indent|p is false = ~(p is true) Def.}} | {{p indent|p is false <nowiki>=</nowiki> ~(p is true) Def.}} | ||
It is very important that the apparent logical relations ∨, ⊃, etc. need brackets, dots, etc., i.e. have "ranges"; which by itself shews they are not relations. This fact has been overlooked, because it is so universal —the very thing which makes it so important. <!--[''Cf''. 5.461.]--> | It is very important that the apparent logical relations ∨, ⊃, etc. need brackets, dots, etc., i.e. have "ranges"; which by itself shews they are not relations. This fact has been overlooked, because it is so universal —the very thing which makes it so important. <!--[''Cf''. 5.461.]--> | ||