Keywords

Mathematics Subject Classification

1 Introduction

This paper is strongly inspired by John Corcoran’s work [8]. The passage, crucial for my further considerations, runs as follows (p. 72):

A judgment is a private epistemic event that results in a new belief and a statement a public pragmatic event, an act of writing or speaking. Both are made by a unique person at a unique time and place. [...]. In contrast propositions and sentences are timeless and placeless abstractions. A proposition is an intensional entity; in some cases it is a meaning of a sentence: it is a meaning composed of concepts, a complex sense composed of simpler senses. A [declarative] sentence is a linguistic entity. A written sentence is a string of characters; it is composed of character-strings – usually words or “symbols” that can be used to express meanings, but which are not in themselves meaningful. A spoken sentence is composed of [articulate] sounds. Only proposition is properly said to be true or to be false – although in some contexts, or with suitable qualifications, judgements, statements or even sentences may be said to be true or false in appropriate derivative senses. Propositions are true in virtue of facts, which are either timeless or temporal subsystems of the universe.

In my further considerations, I will focus on sentences and propositions – statements and judgments will mentioned occasionally only. Since I am interested in epistemological truth-bearers, facts are neglected entirely – the phrase “true fact” means (perhaps except some cases of emphasis) the same as “fact” (“true” is redundant in “true fact”). Note that if we select, for instance, propositions or sentences as truth-bearers, the context “true proposition (sentence)” has a different meaning than the noun “proposition (sentence).” Eventually, one can discuss the so-called ontological truth-bearers, but this issue is out of the present paper.

Corcoran is fairly conscious that the words “judgment,” “proposition,” “sentence,” “statement,” and “fact” (italicized to emphasize their centrality in the above quotation as well in the entire paper [8]) are vague and ambiguous. Omitting various ontological complications associated with being timeless and placeless, it can be easily illustrated by an obvious openness of such phrases occurring in Corcoran’s text as “in some contexts” (which, please give examples, one might ask), “with suitable qualifications” (please describe them in a way, one might remark), or “in appropriate derivative senses” (the same request as in the preceding example). In fact, many Corcoran’s explanations and settings could be taken as regulative stipulations or even definitions. For instance, when he quotes J. L. Austin (p. 74) that sentences are made up of words, statements are made in words, or that statements are made, but sentences are used, these assertions function as attempts to illuminate the related concepts (see [4] as the original source). On my part (I do not pretend to be an expert in the native ordinary English), Austin’s proposals are somehow artificial. I see nothing wrong in saying that sentences are made in words, but statements are made of words or saying that someone used a statement made by a different person earlier. To allude to Ryle’s idea of the standard use of ordinary expressions (see [30]), I do not think that my examples violate the ordinary use in English.

I do not believe that it is possible to formulate a theory, which would solve all (or even most) philosophical troubles generated by the concepts of sentence and proposition. One reason consists in entanglement of both notions in basic ontological and epistemological controversies, like those between realism (Platonism) and nominalism or rationalism and empiricism. Another important factor should be considered is connected with the fact that both words “sentence” and “proposition,” as well as their non-English counterparts, function in definite common (ethnic, ordinary, natural) languages, which cause that their meanings are not equivalent. As the title announces, I will explore the perspective of Polish as a possible semantic framework. Doing so, I do not suggest that my native language better than other linguistic schemes. Yet, since English perspective is so heavily dominant in contemporary philosophy, it is perhaps interesting to take into account other languages. As far as the issue concerns Polish, we have an additional motive to consider this language very seriously. Tarski’s semantic theory of truth was originally formulated in Polish [see [32]), then expressed in German (see [32]), and finally presented in English (see [35, 36]). I will try to document that some frequent misinterpretations of this influential conception, logical as well as philosophical, stem from the fact that some features of Polish disappear via comments made in other languages, particularly English. To anticipate, I have in my mind the relation between formal and formalized languages and the problem whether sentences are meaningful. Assuming that A is a truth-bearer, we have the explanation:

  • (*) “A is true” means that A says (asserts, states, etc.) so and so and it is so and so,

for instance, if A = “snow is white,” we obtain “snow is white” is true if and only if snow is white – (*) does not require an appeal to facts – this an additional reason to omit considerations on facts.

A digression. One might contest the explanations made at the end of the last paragraph referring to Tarski’s remarks in ([35], pp. 666–667 and [36], pp. 153, 155) (page-reference to Eng. tr. and reprint, respectively; similarly in other cases if the translation or a reprint is mentioned in references at the end of this paper) in which he informally explains the meaning of “is true” by reference to facts, existing states of affairs, agreement, or correspondence with reality. Yet he writes ([35], p. 667):

The truth of a sentence consists in its conformity with (or correspondence to) reality.

[...]

A sentence is true if it designates an existing state of affairs.

[...]

However, all these formulation s can lead to various misunderstanding, for none of them is succiciently precise and clear (though this applies much less to the original Aristotelian formulation that to either of the others; at any rate, none of them can be considered a satisfactory definition of truth.

Tarski considered (*) as equivalent to Aristotle’s view and the intuitive prototype of the semantic theory of truth, equivalent to the T-scheme (A is true if and only if A – it is so-called naive version; he was skeptical about the quoted formulations as good definitions. Thus, taking (*) as basic is not at odds with Tarski’s intentions. Let me add that this formula was commonly used by Polish logicians and philosophers in their preliminary explanations of the concept of truth. The end of digression.

2 Some Preliminary Remarks About Polish Words Zdanie and Sąd

My earlier remark about the reasons to taking into account Polish should not be understood as the claim that the usage of words in this language is radically different than in English. In particular, it concerns the words zdanie and sąd, that is, Polish counterparts of “sentence” and “proposition.” According to elementary explanations following Polish language dictionaries, the term zdanie (sententia in Latin) has the following meanings:

  1. (i)

    An utterance having a predicate.

  2. (ii)

    An opinion (opinia in Polish).

  3. (iii)

    An utterance employed for communicating a content and determined by formal constraints.

The points (i) and (iii) are qualified as linguistic. Clearly, they are not equivalent, because the former is syntactic, but the latter is semantic with a syntactic parameter. In English, we have

  1. (iv)

    A set of words that is complete in itself, typically containing a subject and predicate, conveying a statement, question, exclamation, or command.

Polish grammar divides sentences into three categories, namely, declaratives, questions, and imperatives. The same classification is suggested by (iv) (we can ignore exclamations).

Corcoran, to repeat, says that a sentence is a linguistic entity (although he uses the adjective “declarative,” his explanations can be extended to questions and imperatives), and this can be correlated with (i). He adds that sentences can be used to express meanings, what makes his account close to (iii). On the other hand, nothing suggests in (ii) and (iii) that sentences (zdania) are not in themselves meaningful. Now, as far as the issue concerns (iv), it can be understood purely syntactically as having the grammatical form of declaratives, questions, or imperatives or semantically as expressing contents which are conveyed by related sentential forms. Since “or” is not exclusive, we obtain an equivalent of Corcoran’s account of sentences. Thus, zdanie refers to a linguistic entity satisfying some formal constraints and having a meaning (content). Perhaps, an interesting fact is that we can say in Polish “mieć zdanie,” that is, to have an opinion, although it cannot be translated by “to have a sentence.” According to Polish, an opinion consists of a sequence of sentences, but in English, we should say that statements, judgments, etc. are its element. The situation is more complicated, if we take legal contexts into account. Although in English, we have that a sentence is the punishment assigned to a defendant found guilty by a court or fixed by law for a particular offense (the context “to have a sentence” is legitimate), the noun zdanie cannot be used in such contexts; the word wyrok functions in legal issues and has no etymological connections with zdanie, although every court’s decision is expressed in sentences.

The noun sąd refers to court, but we can find explanations, like this (Polish Wikipedia, https://pl.wikipedia.org/wiki/S%C4%85d_(logika):

A proposition in the logical sense (frequently briefly: a proposition) – the meaning of a sentence in the logical sense, that is, true or false. The same proposition corresponds different sentences having the same logical meaning (for example, sentences uttered in various languages). Propositions in the logical sense are contrasted with propositions in the psychological sense being mental states corresponding with propositions in the logical sense. Truth and falsity are properties of propositions in logical the sense, similarly as they are attributes of sentences. A true proposition is the meaning of a true sentence, and false proposition is the meaning of a false sentences.

The entry from Polish Wikipedia can be compared with the following (https://en.wikipedia.org/wiki/Proposition):

In linguistics and philosophy, a proposition is the meaning of a declarative sentence, where “meaning” is understood to be a nonlinguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the nonlinguistic bearer of truth or falsity which makes any sentence that expresses it either true or false. While the term “proposition” may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term [...] refers exclusively to the nonlinguistic meaning behind the statement. The term is often used very broadly and can also refer to various related concepts, both in the history of philosophy and in contemporary analytic philosophy. [...]. Since propositions are defined as the sharable objects of attitudes and the primary bearers of truth and falsity, this means that the term “proposition” does not refer to particular thoughts or particular utterances (which are not sharable across different instances), nor does it refer to concrete events or facts (which cannot be false).

A comparison of both above quotations shows that the latter is not only longer but also points out more issues. Two crucial differences are (a) Polish explanation distinguishes propositions in two senses, logical and psychological – English does not mention this distinction, and (b) English explanation says that propositions are nonlinguistic bearers of truth and falsity; Polish does not consider propositions as nonlinguistic items (see the next section for a fuller explanation). Still, one terminological remark is in order. Polish has the simple words sądzić and sądzenie etymologically connected with sąd (I neglect legal uses). The former (a verb) can be translated into English as to judge, to think, to believe, etc., but not as “to propose.” Sądzić (and sądzenie as a gerund, translated as judging, thinking, believing, etc., but not proposing) refers to acts of making propositions, which result in propositions as their products (see sect. 4 for a more extensive treatment).

These linguistic observations are coherent with more philosophical explanations (see (i) [9], p. 949, [48], p. 1196; both writings are unpublished – written in the early 1940s):

  1. (i)

    A sentence is a pronouncement of a thought, more strictly a direct or indirect pronouncement of a thinking person. All and only these inscriptions (more generally: utterances) are sentences, which are true or false, however also commands and questions are regarded as sentences. The last two categories are contrasted with declarative sentences. We will exclusively deal with declarative sentences, because only they are true or false – only these are sentences in our understanding, and we will call them sentences for simplicity, remembering that we understand by “sentence”, what is commonly understood by “declarative sentence” or “logical sentence”.

  2. (ii)

    We distinguish propositions in the psychological sense and propositions in the logical sense. The former are certain psychological phenomena, thoughts consisting in inner convictions that there is so and so or is not. Such thoughts are expressible by declarative sentences. If we express a proposition in a sentence, which can be understood by a group of persons in a univocal manner, we create conditions for speaking on propositions in the logical sense. When the same sentence is written or heard by some group of persons as understandable, in spite that we have so many thoughts (judgements), that is psychological sentences as many related persons, but the content of thought, provided that it is not ambiguous, is the same for all persons in question. This content is called – the proposition in the logical sense. This difference can express otherwise as well. The thought of a subject being the basis of understanding of an expression at a certain time, we call the psychological meaning of a given expression at this time, and there so many psychological meaning as many are users of the expression in question; it can also happen in the case of an individual person, provided that he or she employs a given expression many times. The content common for all these expressions, co-ordinated with a given expression in a language, is called the linguistic meaning of this expression. Remembering the difference between the psychological meaning and the linguistic meaning, it is possible to define propositions in the psychological sense as psychological meanings of sentences, and propositions in the logical sense as linguistic meanings of sentences. Speaking about sentences, we mainly mean declarative ones, and exclude questions and commands, because only declaratives are true or false.

Both last quotations stress a close connection between sentences, propositions, and language. This is the essence of what I term as the linguistic theory of propositions.

3 Some General Philosophical Remarks

I do not claim that using English as the linguistic basis of philosophy forces the nonlinguistic account of propositions (see [11] as an example) as well as that other languages exclude it – Bolzano’s Sätze an sich (propositions in themselves; also translated as sentences in themselves) and Frege’s Gedanken (thoughts; the capital at the beginning of this word is justified by its Platonic flavor) are primary examples in German. One might introduce similar entities into an arbitrary language by suitable stipulations. The duality in question can be illustrated by Rudolf Carnap’s views. The concept of proposition does not occur in [5] – it is not surprising for the content of this book entirely dealing with syntactic issues. In [6], p. 18, propositions are understood as designate of sentences. In particular, logically equivalent sentences designate the same propositions (p. 92). Carnap observes (p. 235) that the term proposition “is used for two different concepts,” namely, for certain expressions [declarative sentences] (I) and for their designate (II)” – Bolzano’s Sätze an sich, Meinong’s Objectives, or Wittgenstein’s states of affairs are mentioned by Carnap as instantiations of II. In [7], p. 27, Carnap identifies propositions with intensions of sentences, contrasted with their extensions (truth-values) and adds that “the term “proposition” [...] is used neither for a subjective, mental occurrence, but rather for something objective that may or may be not be exemplified in nature.” This means that Carnap rejected the meaning (I) listed in [6] and opted for (II). Unfortunately, the phrase “rather for something objective” does not clarify the ontological nature of propositions in a satisfactory way.

Returning to (a) and (b) from the end of the preceding section, since judgments (statements, thoughts, etc.) can be regarded as propositions in the psychological sense, the distinction expressed in the point (a) can be easily embedded into English way of speaking, although Carnap, for example, strongly protested against considering propositions as psychological items. The difference (b) cannot be solved by terminological or classificatory proposals. In fact, (b) concerns the ontological issue, that is, the question of how propositions exist. Answers are very different (see [23, 24] for systematic surveys and [26, 27, 43] for historical information). The nonlinguistic variety of conceptions of propositions covers, for instance, the views that they are (the list is not exhaustive – see examples given by Carnap; particular views are not exclusive mutually) facts, states of affairs, Platonic-like entities (timeless and placeless), or sets of possible worlds. Since I am interested in Polish view as presented in https://pl.wikipedia.org/wiki/S%C4%85d_(logika), I will not enter into an analysis of arguments pro and contra of nonlinguistic account. Polish logicians and philosophers (see the next section for more details) maintain (the same holds presently in Polish philosophical literature) that propositions exist as linguistic entities or, at least, as items inherently connected with a language, more specifically with sentences. In other words, propositions are language-dependent items.

The view pointed out in the last sentence of the preceding paragraph can be termed as linguistic theory of propositions. It is a kind of the deflationary approach to propositions to use Andrea Iacona’s terminology (see [11]), because they are reduced in a sense to sentences – the fundamental point consists that sentences are meaningful by assumption. Consequently, propositions are meaningful sentences or meanings of sentences (it justifies to use the names “sentences” and “propositions” as equivalent). Henryk Greniewski offers a nice expression of this idea in [10], pp. 11, 12) in the following words:

The principle. Every expression of an arbitrary language has two sides [...] material [and], [...] significative (that is related to understanding).

The material side of an arbitrary expression belonging to any graphical language is an insctiption or drawing. The material side of an arbitrary expression belonging to an acoustic language is a series of sounds. However, not every inscription is a material side of an expression belonging to this or that language as well as not every series of sounds is a material side of an expression belonging to this or that language. [...].

Explanation. The expression A is synonymous with the expression B if and only if, if understanding of A is identical with understanding of B. [...]. In other words, two expressions are synonymous if they have the same understanding. The significative sides (that is understandings) of expressions are the only factors which influence being synonymous or not – their material sides has no influence in this respect.

Of course, one could observe that the above explanation is essentially insufficient, because the concept of meaning remains still unclear. In fact, Greniewski defines the meaning as the class of abstractions from the relation of the same understanding. Although the technique of this explanation looks very formal, it is pragmatic in its very nature. In fact, the notion of understanding becomes the primitive term of the entire construction – for this reason, the definition in question is semiotic (semantic in the wide sense) due to its pragmatic flavor.

We can generalize Greniewski’s approach and say that the meaning of an expression A is the property of this expression which generates its understanding by users of a given language community. I do not claim that it is the only way of defining the concept of meaning and that it answers to all problems, ontological or epistemological, related to the notion of meaning and discussed in the contemporary philosophical literature, particularly in analytic philosophy. Yet, I am inclined to think that any other attempt, for instance, by appealing to denotations of expressions, their structure, their interpretations, their senses, or their uses can be employed in introducing the significative side of expressions as occurring in every expression together with their material side. This distinction can cooperate with any concrete definition of meaning – note that no conception of meaning gained a common acceptance in philosophy or linguistics. Thus, every linguistic expression is a unit having material (syntactic) aspect and significative (semantic sensu largo) aspect – this statement is the core of “Polish” way of speaking about propositions as language-dependent entities. In particular, sentences are always equipped with meaning (sense), that is, always meaningful (the problem of the so-called purely formal languages will be briefly discussed in Sect. 3.6). Carnap in [6], p. 238 remarks:

Some authors [Carnap does not give examples] use the term ‘proposition’ for meaning but with qualification that it applies to sentences and insofar as these are not regarded as from a merely formal point of view but as having a meaning – in our terminology, sentences in semantics, not in syntax. This use seems to go back to Aristotle. Following Schlick I used this term in this way [...]. But it now seems to me preferable to use in the meaning II, and to use only one term (namely ‘sentence’) for I both in calculi and in semantical systems.

Greniewski is close to Carnap except considering the distinction of sentences in semantics and sentences in syntax (the former does not use this terminology).

Some problems and roles of propositions listed in the recent philosophical literature and typically attributed to the nonlinguistic theory can be easily captured by or translated into the linguistic approach. Consider, for instance, the following general outline opening the survey [23]:

The term ‘proposition’ has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other “propositional attitudes” (i.e., what is believed, doubted, etc.), the referents of that-clauses, and the meanings of sentences.

We can say without violating respective philosophical or ordinary intuitions that sentences (as meaningful entities) are bearers of truth-values or meanings of sentences. Furthermore, although we cannot directly say that sentences are objects of propositional attitudes or referents of that-clauses, it seems fairly admissible to speak that oratio obliqua formed by suitable that-clauses refers to propositional attitudes and their objects. I do not think that this terminology solves all problems related to semantics of intensional contexts, but my intention is to show that we do not lose anything important by substituting “meaningful sentences” for “propositions.” In fact, the locution

  1. 1.

    The sentence “that logic is a very good device of philosophy” as a proper part of the sentence “John thinks that logic is a very good device of philosophy” refers to logic as being a good device of philosophy.

expresses the same what

  1. 2.

    The sentence “that logic is a very good device of philosophy” as a proper part of the sentence “John thinks that logic is a very good device of philosophy” refers to the proposition that logic is a good device of philosophy.

If we agree that (1) and (2) are pragmatically equivalent, propositions as references of sentences are dispensable.

4 Polish Philosophers and Logicians on Propositions

4.1 Kazimierz Twardowski

Twardowski, looking for sources of relativism in the truth-theory (he rejects this view), writes in [37], pp. 148–149 (see also [42], Chap. 6):

[...] the relativists [do] not acknowledge the distinction between a statement (enuntatio, Aussage), a sentence which expresses a judgement and a judgment itself as a mental product. [...]. For although there is a very intimate connection between a judgment on the one hand and statement, which is the external expressions of the judgment on the other, the statement is not nonetheless not identical with the judgment [...].

Twardowski argues that sentences (powiedzenia in Polish version of [36]) can be elliptical due to possible occurrences of indexicals in them, but judgments (Urteile in German, sądy in Polish) have always completely determinate meanings. Now, only judgments are primary bearers of truth; eventually, logical values can be attributed to sentences without any indexical content. In the latter case, sentences are correlated (not identical) with judgments which they express. Truth is always absolute, but the impression of the existence of “relative” truths results from occasionality of some sentences, like “Today is raining.” Twardowski’s general approach to propositions (I prefer this label) occurs in [38], p. 12. He writes:

When we speak, we employ sentences [zdania]. [...]. Sentences can express questions [...], wishes [...], eventually assertions or denials. A sentence, expressing an assertion or denial is called a declarative sentence [powiedzenie in this context]. Thus, every declarative sentence is a sentence, but not every sentence is a declarative sentence. [...]. Assertions and denials expressed by declaratives we call propositions. Propositions and declaratives should be sharply distinguished. A proposition is a mental activity, but a declarative sentences is its external expression this activity; a proposition is something psychical, spiritual, but declaratives appear as physical, sensual.

The difference between sentences and declaratives is not particularly important – it can be considered as related to the distinction between sentences in the grammatical sense and sentences in the logical sense. Much more essential is psychologism evident in Twardowski’s explanation of the nature of propositions (see also [41], pp. 25–35).

Twardowski tried to overcome psychologism in [40] via the distinction of actions and products (see [42], Chap. 4). He writes at the beginning (p. 104):

Of the two expressions that make up such parts as “to walk/the walk”, to race/the race”, “to sing/the song”, “to speak/the speech”, “to think/the though”, “to err/the error”, “to judge/the judgment”, “to bend/the bend” – the first denotes some sort of action. The task of the following expositions is to analyze how the meaning of the second expression in each such pair is related to the meaning of the first.

All examples given by Twardowski fall under the scheme:

  1. 3.

    <A, P>,

in which the letter A symbolizes an action and the letter P the related product. The main intuition associated with (3) suggests that a given instance of A produces a given instance of B. Take judging as an example of A and judgment as an instance of B. Thus, judging (sądzenie) as an action produces judgment (sąd) as its product. Any classification of acts and products depends on their character. Consider mentality (being psychical) and physicality of A and P. Prima facie, we have the following possibilities:

  1. 4.

    (a) A, physical; P, physical

    (b) A, physical; P, psychical

    (c) A, psychical; P, physical

    (d) A, psychical; P, psychical

(4a) and (4c) is not relevant for Twardowski’s considerations of propositions, because judging is not physical according to his views. Consequently, (4b) and (4c) remain. The question is reducible to the nature of judgments. The position that they are mental products is equivalent to Twardowski’s early account. What about (4c)? It is possible by introducing (Twardowski did that) psychophysical products, that is, in the discussed case, sentences equipped with meaning (propositions in the logical sense, according to terminology explained in Sect. 2; see also the Sect. 3.5). Moreover, such items are enduring and exist after the end of related actions.

Enduring psychophysical products objectivize what is subjective, that is, the content of mental acts. Twardowski says ([40], p. 116, 122, 127):

[...] enduring psychophysical products confer on non-enduring mental products, the semblance of endurance by being the enduring effects of the latter, and their enduring partial causes as well. Consequently, mental products are bearing the relation to enduring psychophysical products may be termed preserved products, and we can accordingly speak of the “preservation” of non-enduring products. This preservation is not restricted to mental products, but perhaps also apply to non-enduring physical and psychophysical products. It will be always based on a relationship on an enduring product to a non enduring one, whereby the former, as an effect of the latter, becomes a partial cause which with conjunction of with other partial causes, will initiate the emergence of the same or a similar no-enduring products. [...].

[...]. Psychophysical products that signify certain mental products are also called signs of the latter, and the mental products themselves are termed the meanings of the psychophysical products. Therefore, a meaning is any mental product whose relation to a psychophysical product is that being signified by the latter. Accordingly, we speak of the meaning of a scream, the meaning of a drawing, the meaning of a movement, the meaning of a blush, etc. And linguistic “expressions” are also psychophysical products in which certain mental products – thoughts, judgments, etc. – find their expression [...].

Enduring products do indeed exist independently of the actions that produce them insofar as they continue to exist even though those actions have ceased to exist.

Psychophysical products that signify certain mental products are also called signs of the latter, and the mental products themselves are termed the meanings of the psychophysical products. Therefore, a meaning is any mental product whose relation to a psychophysical product is that being signified by the latter. Accordingly, we speak of the meaning of a scream, the meaning of a drawing, the meaning of a movement, the meaning of a blush, etc. And linguistic “expressions” are also psychophysical products in which certain mental products – thoughts, judgments, etc. – find their expression [...].

Thus, According to Twardowski, the significant connection or correlation between psychophysical product and a related action just forms the base of the relation (mentioned above) holding between psychophysical product deciding that non-enduring mental product can become preserved in an enduring psychophysical item. I do not enter into the problem whether Twardowski successfully overcame psychologism in his theory of language vs. related to the distinction of actions and products. Anyway, introducing enduring psychophysical products certainly goes beyond his earlier view, which is consistent in considering propositions as psychological items.

Still one point, related to the nature propositions, deserves an attention in Twardowski. Following Brentano, he divides theories of judgments into idiogenetic and allogenetic (idiogenic and allogenic, according to other terminology). Twardowski says in [39], p. 99:

The characteristic common to all the allogenetic theories is that they reduce every judgement of being synthetic or analytic, to some combination or interrelations of representations (i. e. intuitions or concepts). Moreover, they regard this synthesis or analysis, this combination or interrelation, as an essential constituent of the judgment. A further characteristic of representations allogenetic theories that follows this one is the tenet that at least two representations have to occur in every judgment. [...] According to the proponents of the of the allogenetic theory, this also implies that a “subject” and “predicate” belong to among the essential and indispensable constituent of every judgment. For those are names given to the two constituent representations. Idiogenetic theories differ from the allogenetic in the following respects: (1) they do not consider representations to be essential constituents of the judgment, but rather conditions for it; (2) they do not insist that two representations are necessary for making a judgment; (3) they see in the act of judging a mental phenomenon sui generis, and not some sort of synthesis, combination, or analysis of representation.

Twardowski adds that every judgment has an act, content, and object, that the first component (an act) consists either in affirmation (acceptance) or denial (rejection). Generalizing Twardowski’s remarks, the distinction of two theories of judgments can be applied to sentences as well. Grammarians usually consider sentences as combinations of words, particularly functioning as subjects and predicates, but logicians as basic logical items. My guess is that the idiogenetic theory is more suitable for the linguistic theory of propositions. Although Twardowski did not opt for reduction propositions to sentences, he accepted that propositions are correlated with sentences. Clearly, judging is a mental item for him, but producing a sentence expressing the judgment in question transforms the content of the act of judging in the meaning of the corresponding sentences.

4.2 Jan Łukasiewicz

Łukasiewicz began as a philosopher, but he concentrated later on formal (mathematical) logic. He distinguished (see [16], p. 13) propositions as a logical facts and judgments as a mental (psychological) appearance. He defines (according to him, he follows Aristotle) the former as (p. 14):

Proposition is a sentence, dressed in words – a sentence which means something. [...] a proposition is a sequence of words asserting that something is or is not.

This definition suggests that the terms “proposition” and “sentences” are equivalent for Łukasiewicz. He uses the former in [17], but replaced it by “sentence” in [18] (the latter paper is an extended version of [17]). The latter word is primary in Łukasiewicz’s later works (for instance, he consequently used the label “sentential calculus,” not “propositional calculus”), except [21], but this exception can be explained by the fact that this book is reconstruction of Aristotle’s syllogistic – yet Łukasiewicz repeats [16] and says ([21], p. 3) that proposition “is a sentence affirming or denying something of something.”

One philosophical problem, related not only to terminology but also to substantial issues, was discussed by Łukasiewicz, namely, the issue of realism/nominalism controversy. He wrote in [19], pp. 222–224;

Contemporary logic has a nominalistic guise. It refers not to concepts and judgments [in Polish original sądach – JW], but on names and sentences. [...]. If we treat propositions [in Polish original zdania – JW] as inscriptions and inscriptions as products of human activity, we must assume that the set of propositions is finite. No doubt that we are able to produce only a finite number of inscriptions. On the other hand, in any logical system we assume rules of inference which lead to an infinite set of theses, that is, propositions asserted in that system. [...].

How can we reconcile these facts with nominalism? We might simply disregard them and maintain that only those theses are exist which have been written someone. [...]. Such a point of view would be consisted, yet it seems that on such basis it would be difficult to engage in logistic , and in particular metalogistic research [...]. Further, following Dr. Tarski, we might consider as inscriptions not only products of human activity, but all physical bodies of definite size, and assume that there is infinitely many such bodies. [...]. But then we have to make logic depend on a hardly acceptable physical hypothesis, which is not desirable in any case.

Łukasiewicz rejected nominalism in [20], pp. 240/241:

I am not interests in ornaments and inscriptions. The whole difference between logistic and a game of chess consists precisely in this, that chessman do not mean anything, while logical symbols have meaning. We are concerned with with that meaning, with the thoughts and ideas expressed by signs, even if we do not know what that meaning are, and not with the signs as such. Through the intermediary of these signs we want to grasp some laws of thought that would be applicable to mathematics and philosophy and to all disciplines that make use of reasoning. [...]. Today I can no longer adopt a nominalist standpoint in logic.

The equivalence (or parity, if one prefers) of propositions and meaningful sentences sounds all the time in Łukasiewicz’s quoted remarks. One can also observe a problem in translation of Polish into English, because in some cases (see my bracketed additions) the term zdanie (sentence) is translated by “proposition.”

4.3 Stanisław Leśniewski

Leśniewski was a radical nominalist. Hence, he consequently used the term “sentence” in his all writings – he was speaking on propositions only polemically (see, e.g., [13]). Sentence is a concrete finite sequence of signs formed according to syntactic rule. However, and it is of the utmost importance, sentences have meanings. Leśniewski expressed this view in the following way ([14], p. 487):

Having no predilection for ‘various mathematical games’ that consist in writing out according to one or another conventional rule various more or less picturesque formulae which need not be meaningful or even – as some of the ‘mathematical gamers’ might prefer – which should necessarily be meaningless, I would not have taken the trouble to systematize and to often check quite scrupulously the directives of my system, had I not imputed to its theses a certain specific and completely determined sense, in virtue of which its axioms, definitions and final directives […] have for me an irresistible intuitive validity. I see no contradiction therefore, in saying that I advocate a rather radical ‘formalism’ in the construction of my system even though I am an obdurate ‘intuitionist’. Having endeavoured to express my thoughts on various particular topics by representing them as a series of propositions meaningful in various deductive theories, and to derive one proposition from others in a way that would harmonize with the way I finally considered intuitively binding, I know no method more effective for acquainting the reader with my logical intuitions than the method of formalizing any deductive theory to be set forth. By no means do theories under the influence of such formalizations cease to consists of genuinely meaningful propositions which for me are intuitively valid. But I always view the method of carrying out mathematical deduction on an ‘intuitionistic’ basis of various logical secrets as considerably less expedient method.

Leśniewski’s paper was originally published in German and contains the terms Satz, Sätze, and Sätzen translated, in the above quotation, as proposition and propositions, respectively. However, this translation should not suggest that Leśniewski had in his mind something similar to Bolzano’s Sätze an sich, but rather declarative sentences (see one of Carnap’s remarks quoted in Sect. 3). For Leśniewski, a deductive system consists of meaningful sentences. He termed this view on language as intuitionistic formalism (due to the meaning of “ituitionistic” in the foundations of mathematics, it is better to use the adjective “intuitive”).

Leśniewski was perfectly conscious that deductive systems in his understanding are always finite. Yet, they were formulated in such a way that their enlargement by new elements was prescribed by suitable syntactic directives of introducing additional expressions, for instance, via definitions. Although this aspect of constructing deductive systems was related to their formal shape, it can be used as a way of dispensing with propositions as abstract entities, because they are not needed to guarantee the infinity of theorems deduced for a set of axioms (I do not discuss whether this device is effective). Leśniewski also suggested (see [15], pp. 379–382) a method of dealing with sentences in which temporal coordinates occur. Omitting various details, I will concentrate on the expression “true at time t” (this context motivated Twardowski to distinguish sentences and propositions). According to Leśniewski, one should not say “A is true at t,” but “At is true.” Thus, the temporal parameter is to be attached to the content of A, not to truth-predicate. Consequently, we have not “It is sunny in Kraków” is true at March 3, 2021, but “It is sunny in Kraków at March 3, 2021” is true. Since this formulation eliminates indexicality, we do not need propositions as items with complete meanings vs. incomplete sentences.

4.4 Tadeusz Kotarbiński

Kotarbiński accepted in his mature works (see [12]), similarly as Leśniewski did, a radical nominalist. Additionally, he proposed reism, that is, the view that only material things exist – some of them are psychophysical. This ontological theory was supplemented by semantic reism dividing names into genuine and apparent (onomatoids). The former refer to individual objects (bodies), but the latter apparently to abstracts – apparently, because no abstract object exists. For instance, there are (exist) just people, but no justice as such. Common nouns function as genuine names, provided that they designate individual things – “horse,” “man,” etc. are examples. Using of onomatoids leads to hyposthazing that their references exist. In order to avoid hyposthases, we should be careful with employing apparent names and eliminate them from a reistically sound language. Here is an example. The term “redness” is an apparent name. Consider the sentence (a) redness characterizes some objects. The literal understanding of (a) suggests that there exists an entity called “redness,” which can be attributed to some things. The reist proposes to replace (a) by (b) some things are red – this replacement eliminates “redness” and produces a reistic translation of (a). Since reistic transformations of sentences frequently result in long and complicated expressions, non-reistic phrases can be tolerated, if their paraphrases into the reistic language are available.

Reistically speaking, every language, natural or specialized, consists of expressions understood as physical entities. Consequently, there is no room for propositions as abstract objects. The following fragment explains some details of Kotarbiński’s semantics ([12], pp. 100–104):

[...] the term “judgment” (equivalent of [...] the Latin iudicium, etc. is onomatoid, like the words “image” and “concept”. No judgments exist, since they would have to be psychic events. For a reist, only things exist. Hence there are only those who judge something. John imagines this or that, John conceives this or that, John judges that it is so and so. [...]. A sentence is the same as a statement of thought: strictly a statement, direct or indirect, by a person thinking that it is so and so, qua a thinking person. [...]. “Sentence” as interpreted in accordance with our intentions more or less corresponds to [...] Latin propositio (with its etymological derivatives in the various European languages, and the German Satz, but only in the external nominalist interpretation.

The word “sentence” is a genuine name, because sentences are concrete material entities. Since they are produced by human beings, they express something, for instance, judging. It is also the source of meaning. Although Kotarbiński does not mention Twardowski, the influence of the act/product distinction is obvious in views of the former. The end of the last quotation explains why the terms “proposition” and “sentence” can be used as equivalent.

4.5 Kazimierz Ajdukiewicz

Ajdukiewicz distinguished sentences as linguistic entities and propositions. The concept of meaning was his starting point (see [1], pp. 54–56):

Understanding of [...] an expression consists in a thought concerning of what this expression refers to [...]. The thought which grounds the understanding of an expression by a given person at a certain moment will call the psychological meaning of this expression. [...]. In any established (that is, not subjected to fluctuations) language, some contents are coordinated with its words and expressions. They are coordinated in the sense, that in order to use expressions of the language in question in the common manner, it is necessary and sufficient to connect thoughts with coordinated contents. These contents of thoughts which are coordinated (in the above sense) to a given expressions, we call the linguistic meaning possessed by this expression in the language in question. [...]. The distinction of psychological meaning and linguistic meaning enables us to distinguish two meanings of the term “proposition”. [...] some psychical phenomena [...] namely thoughts [...] expressible by a declarative sentence and consisting in inner belief that there is so and so or is not so and so. It is the meaning of the term “proposition” in psychology, playing the role of the name for a certain kind of psychical phenomena. The term “proposition” is also used in logic, but the meaning of the term in question is different than in psychology. Both these meanings of the term “proposition” [...] can be contrasted in the following way: we identify thoughts as psychological meanings of sentences with propositions in the psychological sense, and propositions in the logical sense – with contents of thoughts being linguistic meanings of sentences.

Both distinctions outlined in the above fragment were constantly elaborated in later works of Ajdukiewicz (see [3], Chapter II, for instance; the distinction of propositions in the logical sense and the psychological sense became crucial in Polish philosophy; see Sect. 2).

Ajdukiewicz never defined the concept of linguistic content basic for his theory of sentences and propositions. Generally speaking, he did not reduce contents to psychological phenomena and considered the former as something objective ([2], p. 349):

In this paper it is intended to give such a definition of of proposition which conceives as an objective, and not a linguistic or psychological entity, connected with the sentence by a semantic, and not a syntactic or a pragmatic relation, viz. relation of stating. This i why, with reference to sentences, besides the relation of denoting, another semantic relation, must be establish.

The semantic relation in question, different than that of denotation, is the relation of connotation of a sentence. Thus, Ajdukiewicz identified propositions with connotations of sentences. Omitting details of the entire “connotational” construction, I point out some ambiguity of the adjective “linguistic.” Clearly, propositions are closely related to sentences as their connotations, contents, or meaning. According to my previous remarks, it is a crucial aspect of the linguistic theory of propositions. On the other hand, Ajdukiewicz explicitly denies that propositions as connotations of sentences are linguistic items. Contradiction? Not, because it seems that the adjective “linguistic” refers to syntactic properties of sentences. Consequently, propositions cannot be defined in syntax, but semantic is the proper place for connotations. However, it should be noted that the identification of objectivity (in the context in question) with being defined by semantic properties does not solve the perennial controversy concerning the nature of propositions.

4.6 Alfred Tarski

Tarski consequently and deliberately used in his works, particularly concerning the concept of truth, words zdanie and Aussage, and “sentence” (I follow my considerations in [46], Chap. 4.2). It was a discussion between him and Karl Popper related to how the term Aussage should be translated into English. Tarski, in his letter to Popper of January, 2, 1955 (The Hoover Institute, box 27, folder 27), clearly preferred “sentence” over “statement” as far as truth-bearers are concerned. Popper (see [29], p. 333, note 1) remarked:

I understand that Tarski prefers to translate ‘Aussage’ and ‘Aussagefunktion’ [Tarski’s remark concerned translation from German – J.W.] by ‘sentence’ and ‘sentential function’ (while I am using here ‘statement’ and ‘statement function’ [...]).

Tarski was conscious of various problems associated with the sentential account of truth-bearers. How sentences should be understood – as token or type? As a nominalist (see [22, 23, 44] on Tarski and nominalism), he, at first, under Leśniewski’s influence, opted for the former alternative (see [31], p. 62), but later, he decided to prefer sentence types as the basic category. Tarski was aware that the sentential theory of truth-bearers has difficulties with infinite classes of sentences (it was pointed by Łukasiewicz; see Sect. 3.2). Tarski, probably influenced by Twardowski, wrote ([36], p. 174, note 2):

For example, the following truly subtle points are here raised. Normally expressions are regarded as the products of human activity (or as classes of such products). From this standpoint the supposition that there are infinitely many expressions appears to be obviously nonsensical. But another possible interpretation of the term ‘expression’ presents itself: we could consider all physical bodies of a particular form and size as expressions. The kernel of the problem is then transferred to the domain of physics. The assertion of the infinity of the number of expressions is then no longer senseless although it may not conform to modern physical and cosmological theories.

Independently whether the admission of infinite classes of sentences can be justified by such an appeal to physics, Tarski’s way of doing logic and the foundations of mathematics was strongly based on set theory. In particular, logical research cannot be limited by philosophical presumptions. Although it explains that Tarski could be a nominalist “privately” and a set theoretician professionally, the problem remains how to reconcile both positions.

The Polish title of Tarski’s study on truth is translated into English as The Concept of Truth in Languages of Deductive Sciences. He decided to use the phrase Der Wahrheitsbegriff in den formalisierten Sprachen in German edition (see [33], [45] for an analysis) – it was preserved in English translation. Omitting possible deliberations on esthetic reason of the change in question (the new title is shorter and perhaps more elegant), it seems that Tarski was motivated by the view, held by Carnap, that semantic investigations should be carried on in syntactically well-defined languages. Yet, Tarski decided to use not the adjective formale (favored by the Vienna Circle), but formalisierte. His choice can be illuminated by the following quotation ([36], pp. 166–167):

It remains perhaps to add that we are not interested here in ‘formal’ languages in one special sense of the word ‘formal’, namely sciences of the things and expressions to which no material sense is attached. For such sciences the problem here discussed [the problem of truth – JW] has no relevance, it is not even meaningful. We shall always ascribe quite concrete and, for us intelligible meanings to the signs we shall consider. The expressions which we call sentences still remain sentences after the things which occur in them have been translated into colloquial language. The sentences which are distinguished as axioms seem to us to be materially true, and in choosing rules of inference we are always guided by the principles that when such rules are applied to true sentences the sentences obtained by their use should also be true.

The expressions “material sense” (in Polish, intuicyjny sens; in German, inhaltliche Sinn) and “intelligible meaning” (in Polish zrozumiałe znaczenie; in German verständliche Bedeutung) are crucial in the above quotation. Roughly speaking, we can assume that the adjectives “material,” “intelligible,” and “intuitive” are close in meaning in Tarski’s usage as well as connected with his understanding of formalized languages. The intended meaning of “formalized” is that formalized languages arise as the product of formalization. Thus, formalized languages are always interpreted. This view was motivated by Leśniewski’s intuitive formalism (see Sect. 3.3). In other words, Tarski rejected formal languages as objects of semantic investigations. Although he abandoned intuitive formalism later (see [31], p. 62, a note to the 2nd ed. of the paper in question)), he kept his attitude toward language used in logic and the foundations of mathematics as formalized.

Tarski, due to his ant-Platonic tendencies (see [25]), was skeptical about the concept of meaning. Hence, he did not appeal to concepts or propositions as meanings of terms and sentences. Yet, meaning constitutes an attribute of linguistic expressions (see [34]). Perhaps, Tarski would agree with Greniewski (see Sect. 2) that expressions have formal (syntactic) side and material (semantic) side and with Ajdukiewicz (see Sect. 3.5) that the issue concerns the linguistic meaning of expressions. If we deal with formalized languages, meanings of expressions are associated with an interpretation, which must be assumed in the case of any semantic investigation. Consequently, a relativization to a language is automatically related to a given interpretation. The question of sources of interpretation in the case of formalized languages was not discussed by Tarski, but one might say that since interpretations are carried on in the metalanguage, its interaction with the object language at least partially determines meanings attributed to elements of the latter. Tarski’s remarks on languages, expressions, meanings, and interpretations, although incomplete at many points and inconclusive, allow to explain a frequent misinterpretation of the semantic definition of truth. Many authors claim that this theory is exclusively applicable to formal languages and conclude that it has no philosophical importance. However, the premise of this conclusion is obviously incorrect, because Tarski’s truth-definition is defined for formalized interpreted language. A more specific and perhaps a more philosophical observation was made by Arthut Pap (see [28]). He argued that since sentences are syntactic items, they cannot serve as truth-bearers – any semantic truth-theory requires propositions as units to which logical values are ascribed. Yet, nothing precludes considering sentences as directly meaningful or expressing propositions conceived as their meanings.

5 Final Remarks

Corcoran’s analysis reported in Introduction is inherently associated with English as lingua franca of philosophy. I tried to show that customs derived from Polish throw some light on traditional philosophical issues. All Polish authors mentioned in this paper distinguished sentences and propositions, but they did not follow Bolzano, Frege, or Meinong, that is, rejected Platonist account of the latter, independently whether they shared nominalism or not. Roughly speaking, propositions on “Polish” account are inherently associated with sentences as their meanings (Tarski was the most radical and rejected any talk about propositions). I consider this as the basic core of the linguistic (now, we can say semantic) approach to propositions. This fact justifies that sentences equipped with meaning suffice for logic. Still, one thing should be pointed out. Polish logicians and philosophers accepted that logic must be extensional and considered intensionality as a defect and invented various strategies to eliminate it (see [47], for a survey). Independently whether this position is right or not, it results in banishing one of the main arguments for propositions: intensional operators refer not to sentences but to timeless propositions. I do not claim that “Polish” approach to propositions solves all problems traditionally attached to this concept. Yet, I am inclined to maintain that it is more consistent with anti-Platonism than views based on considering sentences as items devoid of meanings, because if propositions are understood as independent of language, Platonism appears as a natural solution.