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In this question I suggested that logic is almost only ever used in philosophy as a means to present an argument. By implication, I meant that every formal argument can be stated informally, and that the two are usually studied / presented side by side.

Is it true that symbolic logic as it appears in philosophy is always one way of stating something among others?

And how often does a formal language appear in the literature without that explanation?

I am not suggesting that formalization has no use, indeed it can help the reader follow the argument. But has anything appeared in contemporary philosophy itself as a direct result of symbolic logic, even appeared with that language as a necessary condition?

Thank you.

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  • Are you asking is formal logic necessary to any philosophical purposes that informal logic would not suffice for? It would seem like there would be a wealth of answers to that question... Jan 26 '15 at 16:14
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Logic is intended to remove the ambiguity of natural grammar, and the elusiveness in argumentation (omitted steps). It is a means of avoiding mistakes, but it is hard to read. Natural languages are more convenient to convey ideas, and indispensable in philosophy when the aim is clarifying concepts rather than producing formal arguments. (As a mathematician you should be familiar with that: natural language can be used to convey informally the "spirit" or strategy in a demonstration).

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Hegel has an onto-logic which he uses to develop his mythic history of philosophy; ie Non-Being & Being (Parmenides) gives Becoming (Heraclitus).

As Quen_tin points out, formal logic, operates as a formal grammar of reasoning, a perspective that became important in the line of development of Frege-Russell-Wittgenstein; language becomes a logic. A different perspective is that of Derrida, where the world becomes a text (its an inversion of Wittgensteins perspective); in Christian theology one has the Word and logos.

Its worth bearing in mind that ambiguity can be useful; for example the Cretan Liar paradox inspired Gödel to his completeness proofs, and there is a different solution to it using paraconsistent logic - since the history of this hasn't been written, its hard to discern to what extent, if any, this inspired its development.

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