www.TheLogician.net © Avi Sion - all rights reserved
© Avi Sion
All rights reserved
Sundry notes and essays on Logic
© Avi Sion: 2003, 2005. All rights reserved.
Part II, Chapter 8: (Chapter 14 in 2008 reprint)
essay was developed in 2003 and 2005 from notes written in March 1998, after
attending a lecture about Bernhard Bolzano (Bohemia, 1781-1848), a logician
I’d never heard of at the time, given by Professors Barnes and Mulligan of
I was disappointed by their seeming inability to unravel for their students the
confusions in Bolzano’s approach. Needless to say, I am here only concerned
with specific proposed logic concepts of his, and do not intend any criticism of
his mathematics or other writings.
would like to propose here a brief critique of Bolzano’s concepts for
In common discourse, the term “proposition” is used in relation to an act of consciousness, which may or not be expressed in words – it is never used with reference to the object of such act, be that object real or imaginary.
The underlying object of a proposition, it should be stressed, is essentially relational. Categorical propositions concern relations between subjects and predicates (whether the latter concern attributes, actions, or any other category); hypothetical propositions concern those between prior propositions (categorical or otherwise); and so forth.
Bolzano takes off from the expressions “a proposition apprehended” or “a proposition uttered”, to suggest a concept of “proposition” without any such specification (tout-court), or “proposition-in-itself”, or again “objective proposition”. However, to begin with, that leap is illicit: from the given concepts, we would only normally elicit a genus “proposition”, and not a concept other than or beyond the given two, as he attempts to do here.
The concept he refers to, I submit, is none other than that of the object of the thought or spoken proposition, i.e. what it tells us. The situation he is considering is, quite simply, that of an object that has not yet been apprehended or thought, and which perhaps never will be. We can quite imagine such a situation, as there are objects we are conscious of today which we ignored yesterday, or that we are aware of but other people are not – and, in view of our cognitive and existential limitations, by extrapolation, we can well assume that there are objects none of us will ever get to apprehend.
We could, in the limit, refer to such objects as “potential but unactualized propositions”. This is assuming that all objects are in principle knowable, which proposition is open to much doubt or at any rate hard to demonstrate – but let us, for the sake of argument (as it is not the essence of the issue here), accept it as conceivable. Such doubt should dissuade us to apply the term “proposition” to objects of this sort (i.e. unknown objects); but in any event, we can in no wise omit to specify that such propositions are to be distinguished from actual propositions by being merely potential.
It follows that the term “propositions-in-themselves” is a misnomer. The correct term would be simply “propositions”, provided we had previously clearly defined this term as including both actual propositions (thought or spoken) and potential-but-not-actual propositions. Propositions so defined are true if they are realistic (i.e., in common parlance, if they have a correspondent in reality – but, in a more scientific approach, roughly put, if in the given context of information they are best classified as thus), and they are false if their content is (or is found to be) merely imaginary.
Note also: one cannot discuss what Bolzano calls a “proposition-in-itself” without expressing it in thought or speech (witness his own definition of them as “assertions”). For this reason, too, the term he proposes is misleading: we might only, at best, accept the label “potential but not actual propositions”.
Briefly put, then, actual propositions would be called true or false if they are real or imagined, respectively; whereas potential-but-not-actual propositions would be called true or false if they are real or imaginable, respectively. Thus, the definition of truth is the same in both cases, but that of falsehood is slightly different: for actuals, it is actual imagination; whereas for merely-potentials, it is the mere potential of imagination.
Concerning the latter, it should be added that the existence of an object not yet encountered is hypothetical. It is an inductive extrapolation from our past cognitions, from the fact that in the course of our lives we have come to know new objects previously unknown, or that we know things others ignore or others claim to know things we ignore.
There is therefore no call for a varied terminology regarding truth and falsehood, as suggested by Bolzano. No need to get into a deeper discussion regarding the concepts of truth and falsehood, here.
With regard to the thesis by Bolzano (and others) that propositions are subdivided into terms (i.e. that ideas are parts of propositions), I will not here comment.
let me mention my agreement that not all propositions are of the form “S is
P”. This form is reserved for the expression of a specific kind of relation,
viz. the classificatory
(broadly-speaking). A colloquial proposition like “it rains” attempts to
express in such habitual form an event. More precise would be something like
“Water is dripping or pouring down from the clouds in the sky”. But the
“it” involved may not be the sky, but simply the screen in front of our face
in which the event of raining water occurs.
Turning now to Bolzano’s treatment of “ideas” - the issues are very similar.
It is clear in the above that I am using the term “object” (which, in my view is best retained, without expanding the term “proposition” as suggested by Bolzano) as widely as possible.
Now, a proposition (in the normal sense, or a thought/spoken proposition in Bolzano) is assertoric, essentially in that it claims that the event or relation it expresses really exists. If, “in fact” (i.e. in the widest possible context of phenomenal knowledge) it does exist, the proposition is said to be true; otherwise, the event or relation it asserts is regarded to have been a mere product of the imagination, an illusion, and the proposition is said to be false.
Similarly for a term (or phrase), thought or spoken. It may refer to something “in fact” existing, or it may be a mere construct of the imagination. In the former case, it indeed has an object; in the latter case, it gives the illusion of having an object, but doesn’t. Thus, “ideas” (if we must use this tortured word) are like propositions exactly, in that they implicitly assert an existence, though they may in fact merely refer to a construct.
As we saw, a relational object, be it real (demonstrable) or imaginable, which has not been thought or uttered (in theory – though that is precisely what we are doing the moment we but mention it for the present discussion), cannot be called a “proposition” (and much less a “proposition-in-itself”, implying it to be even more of a proposition than a merely actual proposition!). It is sensu stricto erroneous to call it that; at best (though preferably not), we might refer to it as a “potential but unactualized proposition”.
Likewise, the object, real or imaginable, of an “idea” cannot properly be called an idea until a perceptual or conceptual cognition of the object actualizes as such. Here again, if we wanted to be very generous, we might refer to “potential but unactualized ideas”, but certainly not to “ideas-in-themselves”.
The proof that this proposal of Bolzano’s is confusing and unacceptable is that it leads to a distinction (made by him) between an “idea-in-itself” and its “object”! Once the verbal difference is generated, a corresponding material difference is presumed, even though in fact the object of both these terms is one and the same.
The examples brought to bear by Bolzano are not convincing, but emerge from yet more confusions in his mind. He does not realize that an empty class is a mental (imaginary) construct without demonstrable (real) referents. He does not understand that a general idea is not an “idea-in-itself” with many objects – but more simply a concept in relation to which all the objects referred to count as “one”, due to their abstract commonalities.
Bolzano’s expression “ideas-in-themselves” is as artificial and confusing a term as “propositions-in-themselves”. It refers at best to “ideas” defined as including both actual ideas (i.e. which have been thought or spoken, rightly or wrongly) and potential but not actual ideas (which could be thought or spoken, rightly or wrongly, but have not been).
But to think of objects or constructs which have not been apprehended or uttered as “ideas”, let alone “ideas-in-themselves”, is not advisable. The danger being that of reification – once a term is introduced, it is taken to refer to something additional. This is exactly what happened with Bolzano: the idea-in-itself is thenceforth distinct from the object.
It should be added that the expression “having an object”, which Bolzano uses, is ambiguous. All more or less meaningful terms, phrases or propositions have an object of sorts – but these objects are not epistemologically or ontologically always on the same plane.
Sometimes the object referred to is no more than a name or verbal construct; sometimes, it is a vague or clear mental image, a set of imagined sights and sounds. Sometimes, the word refers us to a hypothetical entity within a complex scientific theory, a conceptual construct at different stages of validation; sometimes, the object is a perceptible or very well established material body. Thus, the “object” referred to could in fact be anything from a reality to an illusion, including all the intermediate statuses of appearance in between.
As our above clarification implies, “ideas” as Bolzano presents them are in fact one and the same as “objects” (in the wide sense including “real objects” and “imaginary constructs”, of course), whether they come to mind or remain unknown. But Bolzano’s hunt for examples to support his discriminative thesis diverts the discussion, raising issues regarding the statuses of empty classes and general classes.
Empty classes, in my view, roughly put, are mental constructs based on conceptual manipulations (which may be based in whole or in part on perceptual rearrangements). They are indeed “ideas”, but their objects are not “real objects” only at best “imaginary constructs”. They are empty of objective content, though they emerge from some fantasy (and in this latter sense – alone – have a content of sorts).
In the case of concrete individuals or limited groups, the idea “refers to” or “means” certain objects. In the case of general classes, we suppose the idea-object relationship to be the same, though the object (a universal or an open-ended group) is more difficult to pinpoint and understand. They are supposed “abstractions”– projected common factors, based on our apparent capacity to measure the underlying units against each other.
But in any case, the distinction has no bearing on the issue of Bolzano’s split between idea (in the large sense adopted for him) and object, because his discussion started with a broad concept of object such as to include any type of object. He was only concerned thus far with whether the object was thought/uttered or not.
He cannot now change the sense of his term, so that singular and plural objects acquire distinct properties in this respect! Indeed, rather he should have at this stage gone into the varieties in his use of the term object, distinguishing between those that are imaginary from those that are demonstrable, and so forth. All this goes to show that he got caught up in misleading categorizations.
Bolzano’s consideration of compound terms (say, “XY” – e.g. “blue
flower”) as not propositions, and therefore neither true nor false, is also
misleading. Terms, single or compound, are not per se true or false, but
if they imply a proposition (such as “Xs exist” or “some things are
Y” or “there are Xs that are Y”) they suggest or presuppose some truth or
falsehood. Note well: the proposition concerned may be true (as in the case of
“some flowers are blue”), or it may well be false (as in the case of
“some flowers are talkative”).
Once we have understood what it is that Bolzano has in mind when he refers to “propositions-in-themselves”, it is relatively easy to resolve his questions concerning their being in time or beyond time.
That actual propositions exist in time is not open to doubt, they come to be when they are thought (and occasionally, spoken) and cease to be when they are no longer thought (let alone spoken). This refers to the mode of existence we call actuality, specifically.
We may say that in the mode of existence we call potentiality, they existed before they were ever thought/spoken (else they would never have been), and also will exist after they are last thought/spoken, at least so long as it is still potential for anyone to think/speak them.
But in any case, this potential mode of existence is not an actual mode of existence. Similarly for propositions that are potential but have never been actualized. If our definition of timelessness is such that it refers to the existence of things in the weaker mode of being that we call potentiality, then this is indeed “outside time”.
In other words, the issue raised by Bolzano is not specific to this area of discussion, but concerns all cases of “potentiality”. The important thing is not to permit ourselves equivocations and confuse the terms “exists actually” and “exists potentially”.
The following may be added, regarding the temporality or timelessness of his “propositions in themselves”.
Consider a proposition that is not actual (only potential) – i.e. which no one has wordlessly thought or explicitly formulated:
Ř Does it exist? Only, at best, potentially (by our premise).
Ř Did it begin to exist? Not yet, though it might one day become actual.
Ř Did it always exist? Only as a potential of the universe, since (by definition) it has not yet actualized.
Ř Is it “outside time” No, insofar as its existence is possible only within this universe.
Here again, then, Bolzano is misappropriating a concept. The issue of time raised here (as already pointed out) is applicable not only to “propositions in themselves” (supposing that we at all grant the concept), but to all unactualized potentialities.
In my Future Logic, I show that we cannot regard such potentialities as ‘casting an actual shadow’ into the ‘nature’ of the thing, i.e. into some static essence; instead, we must regard potentiality as another, lighter form or degree of being. This, I may add, is not timelessness, since some potentialities are irretrievably lost anyway, i.e. there exists a phenomenon of ‘loss of powers’.
 Based on a reading of: A. Wedberg’s A History of Philosophy (Oxford: Clarendon, 1984). Vol. 3, pp. 57-61.
 Which I believe Bolzano presented in 1837, in his An Attempt at a New Presentation of Logic.
 Or is it Wedberg? p. 59.
 I refer you to my work, Future Logic, e.g. chapter 21.
 See Future logic, e.g. p. 248, showing the impossibility in certain cases of such processes.
 I refer you to the examples given by Wedberg in this context.
 But the concept can be criticized further - it is not the issue here, so I won't.
 For further discussion of this point, again see Future Logic, e.g. pp. 413-415.
 See chapter 45.3 on Impermutability.
 The reverse phenomenon of ‘acquisition of powers’ could also be pointed to as an argument in favor of the idea that existence has degrees. Some potentialities are more remote than others, requiring more work to be brought into near actuality (readiness or immediate power) or into full actuality (actualization). This concept is usually applied to volitional contexts, but sometimes also more broadly.