The main thesis contained in the Theory of Science consists in a clear distiction between psychology and logic. This work, as well as Bolzano’s other works on logic, was given little consideration by his contemporaries. Husserl was the first to point out the exceptional importance of Bolzano’s conception, considering him as “one of the greatest logicians of all times”.
In Bolzano’s view, logic is “a theory of science” — Wissenschaftslehre. which explains the title of the above cited treatise on logic.
The work is divided into five parts:
(1) Fundamentallehre — fundamental theory. In this part Bolzano points out that truths must be considered in themselves — Wahrheiten an sich, separating the logical content from the corresponding logical process.
(2) Elementarlehre — elementary theory. In this part he treats of the theory of representations of sentences and deductions. Here also Bolzano admits, as he did for truth, that there are “representations in themselves — Vorstellungen an sich and “sentences in themselves” — Sätzen an Sich.
(3) Erkenntnislehre — the theory of knowledge. That is the theory of the conditions that truth must conform to in relation to human intelligence.
(4) Erfindungskunst — the art of discovering truth.
(5) Eigentliche Wissenschaftslehre — the theory of science proper. This part is concerned with “truth” in the field of special sciences.
The three fundamental concepts on which Bolzano’s theory is based are: “sentence in itself”, “representation in itself”, and “truth in itself”.
By “sentence in itself” he understands that which can be thought in a sentence, irrespective of the fact whether this sentence has been thought or not, expressed or not. In this way, he marks a fundamental distinction between thinking a sentence and the sentence itself. The “sentence in itself” is neither representation, nor judgement; Bolzano does not specify what such a sentence is, but he says what it is not. A “sentence in itself” has no existence whatsoever, since only thought sentences or asserted sentences exist in the mind of the one who thinks; the sentence is the content of thought, which content has no real existence. So, for instance, the sentence “life is not the greatest good of all” is a “sentence in itself”, when we consider only its significant content — its sense —, irrespective of the fact whether it is true or false.
As to the “representation in itself”, this does not exist in us, it exists independently of the subject’s consciousness; therefore, although several subjects may have the same representation, it is not multiplied but unique, and this is, in fact, Bolzano’s argument in favour of the objectivity of representation. Let us take the above quoted sentence, “life is not the greatest good of all” ; “life” and “the greatest good of all” are representations in themselves and are elements of the given sentence. The sum of representations in a sentence forms its content. This “objective representation” does not need, like the “proposition in itself” or the objective proposition, a subject who should think of, or express it but, like the latter, “it is not anything existing and yet it is a certain something” — Zwar nicht als etwas Seiendes, aber doch als ein gewisses Etwas (Wissenschaftslehre, vol. 1, p. 217). More precisely “representation in itself” consists of something but not of something existing. Therefore “representations in themselves” are neither true nor false.
The third of Bolzano’s concepts is “truth in itself”, which expresses something as it is, irrespective of whether it was or not thought or expressed by some one. The object of truth needs nothing of what exists. So, for instance, the truth that “truth is nothing existing”, does not require any real object (op. cit., vol. I, p. 112).
After this analysis of significations Bolzano proceeds to the examination of other logical concepts, of logical value, logic relation and deduction, and he comes to the conclusion that logic is a science of meaning. This is pure logic — Die reine Logik — independent of psychology, with an a priori value, but not in the Kantian sense.
Husserl will be influenced by these basic ideas of Bolzano’s philosophy and in this way will attempt to definitely eliminate psychologism in logic.”
From: Anton Dumitriu, History of Logic, Tubridge Wells; Abacus Press, Vol. III, pp. 354-355