The main work of Bolzano, Wissenschaftslehre, was first published in four volumes: Wissenschaftslehre: Versuch einer ausführlichen
und grösstetheils neuen Darstellung der Logik, mit steter Rücksicht auf deren bisherige Bearbeiter. Herausgegeben von mehren seiner Freunde. Mit einer Vorrede von Dr. J. Cr. Heinroth. -
Critical edition edited by Jan Berg: Gesamtausgabe - Voll.11-14 (1985-2000).
Vol. I XVI+571 , vol. II VIII+568+, vol. III VIII+575 and vol. IV XX+683 pages; the work is composed of five book in 718 paragraphs.
Summary (from the translations of Rolf George [George 1972] and Jan Berg [Berg 1973]; the citations by Bolzano are from the Introduction, 15):
Introduction (1-16). Logic as a theory of science
Book One: Theory of Fundamentals Truths (17-45) "including the proof that there are truths in themselves and that we humans also have the capacity to know them"
Purpose, Contents and Divisions of this Book (17)
Refutation of some Objections (18)
Part One: Of the Existence of Truths in Themselves (19-33)
Part Two: Of the Recognizability of Truth (34-45)
Book Two: Theory of Elements "or the theory of ideas, propositions, true propositions and inferences in and of themselves"
Purpose, Contents, and Sections of this Book (46)
Part One: Of Ideas in Themselves (47-114)
Appendix: Earlier Treatment of the Subject Matter of this Part (115-120)
Part Two: Of Propositions in Themselves (121-184)
Appendix: Earlier Treatment of the Subject Matter of this Part (185-194)
Part Third: Of True Propositions (195-222)
Part Fourth: Of Arguments (223-253)
Appendix: Earlier Treatment of the Subject Matter of this Part (254-268)
Book Three: Theory of Knowledge "or concerning the conditions underlying the possibility of knowing the truth, particularly among us humans"
Purpose, Content, and Divisions of this Book (269)
Part One: Of Ideas (270-289)
Part Two: Of Judgments (290-306)
Part Third: Of the Relation between Judgments and Truth (307-316)
Part Fourth: Of Certainty, Probability and Confidence in Judgments (317-321)
Book Four: The Art of Invention (322-391) "or rules to be observed in the enterprise of thought when it is aimed at discovering the truth"
Book Five: Theory of Science proper (392-718) "or rules that must be observed in dividing up the domain of truth generally into particular sciences and in presenting those sciences
in specialized scholarly treatises."
1. What the Author Understands by Theory of Science
Suppose that all truths which are now, or eve were, known to any man were somehow collected together, e.g. compiled in a single book; I would call such an aggregate the sum of all
human knowledge. Compared to the immense domain of truths in themselves, most of which are altogether unknown, this sum is very small; but it is large, ever too large a sum for the mental capacity of
any man.(...)4. It should be possible through some reflection t find the rules which we must follow in dividing the total domain of truth into individual sciences and which must govern the writing of
the respective treatises. There can also be no doubt that the sum of these rules itself deserves to be called a science, since it is clearly worth while to collect the most important part of the in a
special book, and to order the and provide proofs for them so that everyone can understand and accept them with conviction. I allow myself to call it the theory of science [Wissenschaftslehre], since it is the science which teaches us to represent other sciences (actually only their treatises) (...) [Berg 1973]
15. General Outline of this Treatise
It is desirable that the theory of science proper should be preceded by a discussion of rules to be followed in the discovery of truths: heuretic. Heuretic seems to require an
antecedent discussion of the general conditions of human knowledge: epistemology. Epistemology can be fruitfully developed only if it is preceded by the theory of ideas, propositions and deductions:
the theory of elements. The latter will be preceded by a theory of fundamentals in which it is proved that there are truths and propositions in themselves. [George 1972].
19. What the author Means by a Proposition in Itself
In order to indicate as clearly as possible to my readers what I mean by a proposition in itself (Satz an sich), I shall begin by explaining first what I
call as assertion or a proposition expressed in words. I use this term to designate a verbal statement (most often consisting f several, but at times of just a single word) if it is an instrument of
asserting or maintaining something, if it is therefore always either true or false, on of the two, in the ordinary sense of these words, if it (as can also say) must be either correct or incorrect
(...) But I also call the following sequence of words a proposition: 'Squares are round'. For through this form of words something is also stated or asserted, although something false and incorrect.
On the other hand, I do not call the following expressions propositions: 'The omnipresent God', 'A round square'. For though these expressions something is indeed represented but nothing is stated or
asserted. Consequently one can, strictly speaking, neither say that there is anything thru, nor that is anything false in them. [Berg 1973].
67. Ideas without Referents
It is true that most ideas have some, or even infinitely many, referents. Still, there are also ideas that have no referent at all, and thus do not have an extension. The clearest
case seems to be that of the concept designated by the word 'nothing'. It seems absurd to me to say that this concept, has an object too, i.e. a something that it represents. Somebody might in turn
find it absurd that an idea or representation should have no object at all, and thus represent nothing, but the reason for this is in all likelihood that he means by ideas merely mental ideas, i.e.
thoughts, and that he identifies the content of these mental ideas (i.e. the ideas in themselves) with their objects. It is reasonable to say that the thought 'nothing' has a content, namely the
objective concept 'nothing' itself; but that the latter should also refer to a certain object, is an assertion that can hardly be justified. The same holds of the ideas 'a round square', 'green
virtue', etc. We do and must think something by these expressions, but this is not the object of these ideas, but the ideas in themselves. Incidentally, it is evident from these ideas themselves that
no object can correspond to them, since they would attribute contradictory properties to it. However, there are probably also ideas that lack reference, not because they attribute contradictory
properties to their objects, but for some other reason. Thus the ideas 'golden mountain', 'a presently blooming vine' are perhaps without object, although they do not contain a contradiction.
NOTE. It might be objected that ideas of which I have said that they lack reference must nonetheless have extensions, since they are occasionally compared with respect to their
extensions, and some of them called wider than others. For example we find it quite proper to say that a person who shows the impossibility of round polygons achieves more than one who merely shows
the impossibility of round squares, since the latter follows from the former, but not conversely. This conclusion seems to be valid only if it is assumed that the concept of a round polygon is wider
than that of a round square. I admit that the impossibility of round squares can be inferred from the possibility of round polygons in general. I deny, however, that for this inference we need the
minor premise 'round squares are a kind of round polygon', and that we thus have to attribute an extension to these two concepts in order to draw the above conclusion. It is after all the case that
the assertion that no round polygons are possible follows from the proposition 'No polygon is round'. (Or every polygon is something that is not round.) Hence the conclusion that no square is round,
and thus that round squares are impossible, follows from the minor premise that all squares (not only the round ones that do not exist) are also polygons. Moreover, in 108 I shall discuss a sense in
which the relation of subordination can also be applied to ideas that do not have reference. [George 1972]