In the context of Frege, what is the idea behind conceptual analysis in simple words?

Question

I am reading this Stanford entry behind the Hilbert-Frege debate. I get confused everytime the phrase "Conceptual Analysis mentioned". Here are some extracts:

The idea that Frege takes logical entailment to be sensitive to conceptual analysis in the way just suggested is taken, on this account, to be evident in the strategy Frege employs in his life-long attempt to demonstrate his logicist thesis, the thesis that the truths of arithmetic are provable from pure logic. In the course of that project, Frege regularly provides demonstrations that a given thought τ follows logically from a set T of thoughts, in a way that involves two steps. First, Frege subjects τ and/or the members of T to conceptual analysis, bringing out previously-unrecognized conceptual complexity in those thoughts.

Answer 1

Nice question, that Routledge knows the answer to

A distinction must be made between the philosophical theory of conceptual > analysis and the historical philosophical movement of Conceptual Analysis.

The theory of conceptual analysis holds that concepts – general meanings of linguistic predicates – are the fundamental objects of philosophical inquiry, and that insights into conceptual contents are expressed in necessary ’conceptual truths’ (analytic propositions). There are two methods for obtaining these truths:

• direct a priori definition of concepts;

• indirect ’transcendental’ argumentation.

The movement of Conceptual Analysis arose at Cambridge during the first half of the twentieth century, and flourished at Oxford and many American departments of philosophy in the 1950s and early 1960s. In the USA its doctrines came under heavy criticism, and its proponents were not able to respond effectively; by the end of the 1970s the movement was widely regarded as defunct

As is well known

There’s something to it, but probably not much. ‘Transcendental’ arguments used to run: ‘If it weren’t that P, we couldn’t know that Q; and we do know that Q; therefore P.’ Philosophical fashion now prefers: ‘If it weren’t that P, we couldn’t say (or think or judge) that Q; but we do say (or think or judge) that Q; therefore P.’

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Ignore this bit if you don't like ad libbing, and I'm sure someone can provide an actual example and one that is much prettier.

So we might, e.g., construct some definitions:

• Metaphysical questions are philosophical questions.
• "What is metaphysics" is a metaphysical question.

Draw an inference from their conjunction:

• "What is metaphysics" is a philosophical question.

Then ask what must be the case if we can think or say or judge that conclusion (this last step may be less obvious, but hopefully you'll agree that if you can judge that some question is a philosophical question, then you have means to do so and):

• philosophy has a definition.

Answer 2

Frege had a very strong sense of syntax, to the point that he used a very nonstandard form of notational ambience (the two-dimensionality of the Begriffsschrift) thereby the by. For many of us, conceptual analysis might be thought of as replacing a single word by a linear list of other words, but for Frege, the law of identity was multidimensionally caught up in other syntactic laws and so analysis of conceptual identities could easily translate into a more expansive, you might say graph-theoretic, representation.

Or (without duplicating his style directly, since I don't know it) consider the Fregean account of an empty set. The easiest thing is to just write down the empty inset notation {}, but the Fregean thinks there's an explanation, so to say, for "why" the set is empty. The definition is, "There exists a set Ø such that for all x, x is an element of Ø if and only if x is not self-identical." Of course, everything is self-identical, and nothing is otherwise; hence Ø must be empty.

So Frege sees conceptual identities as many-faceted per their syntax, and his brand of analysis has a more "mechanical" feel to it than the "organic" meditations of e.g. Socrates in the Meno.