|Lecture I||The Rejection of Metaphysics|
|Section 3||Problems of Reality|
|Section 5||Metaphysics as Expression|
|Section 7||Logical Analysis|
|Lecture II||Logical Syntax of Language|
|Section 1||"Formal" Theory|
|Section 2||Formation Rules|
|Section 3||Transformation Rules|
|Section 4||Syntactical Terms|
|Section 7||Pseudo-Object Sentences|
|Section 8||The Material and the Formal Modes of Speech|
|Lecture III||Syntax as the Method of Philosophy|
|Section 1||The Material Mode of Speech|
|Section 3||Relativity in Regard to Language|
|Section 6||Natural Philosophy|
|Section 7||What Physicalism Asserts|
|Section 8||What Physicalism Does not Assert|
|Section 9||The Unity of Science|
The purpose of Logical Analysis is to analyse assertions and make clear their sense, which involves determining their method of verification. Some propositions can be directly verified, others are to be verified indirectly, by directly verifying propositions deduced from them. Indirectly verifiable propositions cannot be conclusively verified. Propositions which have no verifiable consequences are without sense, "nothing but an empty series of words".
|EXPRESSIVE FUNCTION of LANGUAGE||REPRESENTATIVE FUNCTION of LANGUAGE|
(= The System of Theoretical Knowledge)
Wittgenstein's view that the Tractatus is meaningless is rejected, and this lecture is affirmed to be an example of logical analysis. It is the purpose of the following lectures to give reasons for this claim, to show a way of formulating the results of logical analysis, and thus to exhibit an exact method of philosophy. (from which we may infer that logical analysis goes beyond characterising a proposition as logical or scientific, by providing a formal translation of the proposition.)
Thus, formation rules correspond to grammar and transformation rules correspond to logic, both of which have a purely formal character. The word "sentence" is preferred to "proposition" because of the concern for syntax rather than semantics.
"true" and "false" cannot be defined syntactically, but where a sentence is true or false "only by reason of rules of the language" then it is termed valid or contravalid respectively. A sentence A is valid if it is a consequence of the null class of premises, and is contravalid if every sentence of the language is a consequence of A. A sentence is determinate if it is either valid or contradictory and indeterminate otherwise.
C is an L-consequence of P if it is derivable from P using only L-rules. If C is a consequence but not an L-consequence, then it is a P-consequence. Other L- and P- terms may be defined analogously, e.g. a sentence is L-valid or analytic if it is an L-consequence of the null class of premises. Similarly L-contravalid or contradicatory, L-determinate (analytic or contradictory), L-indeterminate or synthetic.
The totality of sentences may be shown thus:
Two sentences are called equipollent if they have the same content.
Two expressions are called mutually synonymous if the content of any sentence containing one of them is not changed if we replace that expression by the other.
Sentences containing irreducible references to not syntactic objects are called real object-sentences. There is another class of sentences which are like object-sentences in their form but like syntactical sentences in their content. These are called pseudo-object-sentences.
Next there is an explanation of how pseudo-object-sentences can be recast in a way which makes it clear that their content is syntactic. I'm afraid this doesn't hang together for me so I can't do a precis.
This difference in mode of expression is designated by the phrases material mode of speech and formal mode of speech. In the former there are apparent references to real objects, in the latter these are not present or have been eliminated. e.g. "The morning star and the evening star are identical." is in the material mode, and can be translated into the formal mode as "The words 'evening star' and 'morning star' are synonymous".
Sentences in the material mode are deceptive in that they appear to refer to real objects but do not really do so. Most of the statements of philosophy are of this kind.
A lot of philosophical confusion results from the deceptive form of syntactical sentences expressed in the material mode. Idle philosophical controversies can be resolved by translating these confusing theses into the formal mode.
Often the material mode involves reference to abstract objects such as numbers. Statements about such abstract entities can be replaced by statements which are about the kind of syntactic object used to refer to them. e.g. "7 is a number" can be translated into "'7' is a numerical sign". This process can be adapted to all kinds of abstract object.
Similarly, talk about meanings (which are themselves abstract objects) can be translated into the syntactical analogues of semantic terms, such as equipollent and synonymous.
By these means logical analysis will be able to convert logical statements into purely syntactic forms, permitting their status to be established by syntactical methods. Of course this doesn't apply to the real-object statements of the empirical sciences.
Similar considerations apply to physical as well as logical modalities. e.g. "The state of a particular solid iron ball swimming on the water is a physical impossibility" can be translated as "The sentence 'This solid iron ball is swimming on the water' is contravalid" (actually P-contravalid).
In general modal sentences are expressed in the material mode and can be translated into the formal mode using the following table:
|Modality||Parallel syntactical terms|
|log. or phys. impossible||contradictory||contravalid|
|log. or phys. possible||non-contradictory||non-contravalid|
|log. or phys. necessary||analytic||valid|
|log. or phys. contingent||synthetic||indeterminate|
For example, a dispute between Russell and Hilbert about what numbers are, can be seen to be spurious since on translation their relative claims can be seen to be claims about what numbers are in distinct formal languages, and the claims are therefore not incompatible.
It is advisable therefore to use the material mode with caution and to translate back into the formal mode at key points in discussion. Faced with someone unwilling to undertake this kind of explication, withdrawing from the debate may be the best policy.
Hence epistemology - (as philosophy) - is a part of syntax.
The physical language of science is a universal language comprehending the contents of all other scientific languages.
Every sentence of any branch of science is equipollent to some sentence of the physical language.
Syntactically: the terms of all branches of science are logically uniform.
The method of logical syntax, that is, the analysis of the formal structure of language as a system of rules, is the only method of philosophy.