It seems that investigations of language and logic have focused on truth as the assumed designated value (the value preserved by valid entailments). It is only in later, non-classical logic that non-truth based designated values were introduced to govern the inferential steps from sentences bearing other semantic values; the value of correctness is one I have in mind.

Why is Truth the default designated value in logic and language? When, and by who, if by anyone at all determined it as such? Are there any philosophers who take other semantic values as more fundamental and/or more basic that truth (which?)

From what I've read in non-classical logic, logic can merely be used to maintain the designated value within the system, which is why correctness-functional entailment can produce correct conclusions from correct premises. The preservation of any semantic value can be termed valid inference depending on which semantic value is chosen. It is simply not the case that logic only deals with truth, as can be seen in Ian Rumfitt's "Truth and Meaning", which uses correctness-functional entailment, with correctness as the designated value in the deductive system, to govern the inferential steps of three-valued logic (as an intended solution to problems for truth like the Liar Paraodox).

I have seen no arguments to support the notion that the system is fundamentally truth-functional. Certainly no more than that a decimal mathematics is more fundamental than a duodecimal one. If there were some argument that indicated that truth is not only fundamental in logic, but also necessarily fundamental, I would be very interested in this. I doubt that I have identified a lack of literature, as it seems most philosophical topics have been covered with at least some depth.

Any comments and recommendations on this topic will be much appreciated.

  • Because people that tell the turth are appreciated while people that tell the false are e.g. convicted to prison. Commented Apr 22, 2018 at 17:04
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    You might have missed what I'm getting at. My intentions with this question concern the nature of language and logic, rather than the nature of our legal system. Furthermore, can we not conceive of another possible world where one must tell only what is correct in court? Though, I should reiterate, I'm not concerned with the applied use of semantic values in the world, but with their place within the structure of logic. Many semantic values play important roles within logic which, in some systems, take the place of the designated value. Why and when was this decision made/by who? Commented Apr 22, 2018 at 17:12
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    A prime example is that in a deductive system with truth as the designated value, it can only express the assertion of the truth of a sentence or the assertion of that sentence's negation. In a deductive system with three-values, the mere assertion of truth is insufficient to express the range of values in the deductive system. Some introduce operators and then use a designated value of correctness to govern the inferential steps in this sort of deductive system. Commented Apr 22, 2018 at 17:29
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    I will agree that logic bears a relation to truth, but it is not the case that logic=the theory of truth. Logic can merely be used to maintain the designated value within the system, which is why correctness-functional entailment (C-Validity) can produce correct conclusions from correct premises. It is simply not the case that logic only deals with truth. Although this is certainly classical logic. But I have seen no arguments to support the notion that the system is fundamentally truth-functional. Certainly no more that a decimal mathematics is more fundamental than a duodecimal one. Commented Apr 22, 2018 at 20:56
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    Propositional logic always comes equipped with canonical semantics, where the truth values are the propositions themselves (modulo whatever relevant form of equivalence). E.g. with classical propositional logic, this algebra of truth values really is a Boolean algebra.
    – user6559
    Commented Apr 23, 2018 at 2:01

2 Answers 2


I wish I could give a comprehensive answer to your question, but my knowledge is limited. I'm moved to reply because I think the comments to the question are giving the OP a hard time; I think the question makes excellent sense. Unusually, I disagree with Mauro: logic is not fundamentally about truth, it is about consequence, or deducibility. One of the striking things about the relation of logical consequence is that it is not confined to statements with truth values. Many, perhaps most, speech acts possess their own logic. Obligations can entail other obligations, commands can entail commands, necessities can entail necessities, etc. Validity is not exclusively about preservation of truth. A valid argument in a deontic logic is one that preserves obligation from premises to conclusion. An intuitionistically valid argument is one that preserves constructive provability from premises to conclusion.

Typically, it is a standard move when dealing with such modalities to introduce box/diamond notation and to replace "A is necessary" with "□A is true", for example. We commonly wrap up semantic properties and put them in the box in order to reduce everything down to truth. This tendency towards a semantic monism in which only truth is considered important is fairly pervasive, but I share the OP's desire for it to be justified. After all, many theories of meta-ethics do not assign truth values to moral judgements, so why should we assume that a logic governing moral obligations should be expressed in a truth-theoretic way?

An initial observation might be that since we already have a calculus that expresses the implicational behaviour of propositions that are connected by 'and', 'or', 'not', etc, it might be a duplication of effort to create new rules to show how these connectives behave when they connect things other than propositions. The axiomatization of a modal logic has the effect of demonstrating how to reduce sentences involving connectives between modalities to sentences involving only propositional connectives. For example, the K axiom of modal logic effectively reduces strict implication to material implication. If we can axiomatize a modal logic and perform this reduction correctly, then this suggests that the logics of modalities other than truth are eliminable.

Another point is that we desire our logical operations to be computable. We might argue on the basis of the Curry-Howard correspondence that our best understanding of computability corresponds to the concept of provability afforded by classical logic. And classical logic has the natural semantics of truth and falsehood. This suggests that any logic worthy of the name is ultimately either about truths and falsehoods or about something that looks just like them.

Another consideration is that logic has epistemological consequences. We use logic because we want to come to know things by inference from other things we know. But we usually conceive epistemology as being concerned with knowing things that are true. Think of all those theories of knowledge that are taught in epistemology classes: "X knows that P iff..." and typically one of the conditions is that P is true. Maybe such accounts are too limited and we can have knowledge that is not of things that are true or false, but detractors might claim that we would be describing mere sensibilities and not real knowledge.

But all this still leaves the question that if the logic of modalities is reducible to that of truths, what are modal claims true of, exactly? Are there really necessary truths, moral truths, even aesthetic truths, etc? Modal logic is commonly expressed using Kripkean possible world semantics, but does this mean that if we judge a modal claim to be true, we are committed to the existence of PWs? David Lewis thought so and embraced modal realism, but his position has not proved popular. Others have adopted anti-realist or quasi-realist positions. I suspect that in the last analysis a full answer to your question can only be given on the basis of a comprehensive account of truth and realism and the relationship between them.

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    I appreciate your reply. I particularly like your argument from epistemology. It seems like the primacy of truth in most uses of logic might be derived from its apparent nature of claiming "correspondence" between the world and language. From what I read at the beginning of your response, it seems like in some cases, the crucial value is partly dependent on the mode/use of the logic at hand. Which would make sense, using other semantic values as preserved when conducting the study of language and logic. Many thanks! Commented Apr 23, 2018 at 11:44

I recommend you take a look at Joseph Heath's discussion of the later work of Jurgen Habermas. Habermas attempts to establish precisely what you are proposing. Specifically, in the case of normative inference he proposes 'right' rather that rather than 'truth' as the designated value. Heath convincingly shows that whilst appealing it is in fact impossible to preserve valid inference with such a designated value.

See Following the Rules and Communicative Action and Rational Choice

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