PHIL 4150: Analytic Philosophy
Dr. Robert Lane
Lecture Notes: Thursday September 13, 2012


[2.8.] The “Laws of Truth.”


“Thought” (1918) is one of three papers Frege wrote late in his life. Collectively, the papers are known as Logical Investigations.[1] These papers were the beginning of Frege’s attempt to write a non-technical introduction to his system of logic.


“Thought” opens as follows:


Just as ‘beautiful’ points the way for aesthetics and ‘good’ for ethics, so do words like ‘true’ for logic. All sciences have truth as their goal; but logic is also concerned with it in a quite different way: logic has much the same relation to truth as physics has to weight or heat. To discover truths is the task of all sciences; it falls to logic to discern the laws of truth. (22)


Here Frege makes the following claims:

·         All sciences aim to discover truths, i.e., they all engage in inquiry, truth-seeking.

·         But logic is different, in that it aims to discover the laws of truth; i.e., logic investigates truth itself.


He goes on to explain this claim by distinguishing two types of law:

1.      laws that ought to be obeyed but which sometimes are not, e.g., “moral or civil laws” (22) (these are known as normative or prescriptive laws); and

2.      laws that are always conformed to, e.g. laws of nature, which are very broad descriptions of things as they actually occur in the natural world (these are known as descriptive laws).


The “laws of truth” that are investigated by logic are descriptive. They do not prescribe how anything should be, but instead describe how something actually is. But what is it that they describe?


Frege’s answer seems to be that they describe what truth itself is: “The Bedeutung [reference] of the word ‘true’ is spelled out in the laws of truth.” (23)[2]


Frege notes that the word “true” is used in many different ways, and he wants to make it clear what he means when he uses that word.


He notes that he is interested in “the sort of truth which it is the aim of science to discern.” (23) So he is concerned with “truth” in the sense in which ordinary scientific or factual claims can be true.


So the question is: what is it for an ordinary scientific or factual claim to be true? This is the question that the “laws of truth,” once identified, will answer. Those laws will explain this sense of the word “true.”



[2.9.] The Correspondence Theory.


Frege rejects a theory of truth that has been around since at least the time of Plato:


the correspondence theory of truth (df.): truth is a relation of correspondence between propositions (or sentences, or beliefs), on one hand, and the world, on the other; for a proposition (etc.) to be true is for it to correspond to the way things are. [This way of thinking about truth was held by Russell and the early Wittgenstein.][3]


Frege says a number of critical things about this theory. One of them is as follows:


[C]ould we not maintain that there is truth when there is correspondence in a certain respect? But which respect? For in that case what ought we to do so as to decide whether something is true? We should have to inquire whether it is true that an idea and a reality, say, correspond in the specified respect. And then we should be confronted by a question of the same kind, and the game could begin again. So the attempted explanation of truth as correspondence breaks down. (23)


Frege’s reasoning here can be expressed as follows...


Frege’s Argument Against the Correspondence Theory


1.      Assume that truth is a relation of correspondence with the world. Then...

2.      In order to discover whether “p” is true, we would need to discover whether “‘p’ corresponds to the world” is true.

3.      In order to discover whether “‘p’ corresponds to the world” is true, we would need to discover whether “‘“p” corresponds to the world’ is true” is true... and so on, without end.

4.      So, if we assume that truth is a relation of correspondence with the world, we can never discover whether a given proposition is true.

5.      [implicit] But we can in fact discover whether a given proposition is true.

6.      So, truth is not a relation of correspondence.



[2.9.1.] A Defense, and a Rejoinder.


A defender of the Correspondence Theory (CT) might respond as follows: Frege is wrong to say that the Correspondence Theory leads us into an infinite regress whenever we attempt to discover whether a sentence is true. For example, if we want to know whether the sentence “The mug contains water” is true, all we have to do is check to see whether the mug contains water. We don’t have to check whether there is a relation between that sentence and the world. So lines 2 and 3 do not follow from assumption 1.


But Frege might answer this objection as follows:

·         The defender of correspondence is right: we can check to see whether “p” is true without checking whether there is a relation between “p” and the world.

·         But in saying this, she is denying the Correspondence Theory. If we can check whether “p” is true without checking whether “p” stands in a certain relation to the world, then the truth of “p” must not be a relation to the world.

·         Furthermore, the fact that we can check that “p” is true simply by checking whether or not p (e.g., we can check that “The mug contains water” is true simply by checking whether or not the mug contains water) suggests that truth is not a property at all.


This conclusion suggests a different theory about truth, the Redundancy Theory. We will return to this shortly.



[2.10.] Thoughts as Immaterial, Imperceptible Truth-Bearers.


Contemporary philosophers use the term “truth-bearer” to refer to anything that can be true or false, be it a sentence, proposition, statement, belief, or anything else.


Frege’s position is that thoughts (i.e., propositions, the senses expressed by sentences) are truth-bearers:


…when we call a sentence true we really mean [meinen] that its sense is true. And hence the only thing that raises the question of truth at all is the sense of sentences. …

                Without offering this as a definition, I call a ‘thought’ something for which the question of truth can arise at all. So I count what is false among thoughts no less than what is true. So I can say: thoughts are senses of sentences, without wishing to assert that the sense of every sentence is a thought. The thought, in itself imperceptible by the senses, gets clothed in the perceptible garb of a sentence, and thereby we are enabled to grasp it. We say a sentence expresses a thought. (23-23, bold added)


So for Frege, sentences are not truth-bearers.


Rather, it is the sense expressed by a sentence that is a truth-bearer, i.e., that is capable of being true or false.


He goes on to make a few more negative claims about thoughts and truth:


A thought is something imperceptible: anything the senses can perceive is excluded from the realm of things for which the question of truth arises. Truth is not a quality that answers to a particular kind of sense impressions. So it is sharply distinguished from the qualities we call by the names ‘red’, ‘bitter’, ‘lilac-smelling’.” (24)


·         Thoughts are immaterial (non-physical).

·         Thoughts are imperceptible (cannot be seen, heard, etc.).

·         Truth, if it is a quality at all, is very much unlike perceptible qualities (colors, tastes, smells, etc.)


But now he considers an objection to that last claim, and a response to that objection:


[Objection:] But do we not see that the sun has risen? And do we not then also see that this is true? [Response:] That the sun has risen is not an object emitting rays that reach my eyes; it is not a visible thing like the sun itself. That the sun has risen is recognized to be true on the basis of sense impressions. But being true is not a sensible, perceptible property. (24)


And finally, he points out that


·         We recognize some thoughts (propositions) to be true on the basis of sense impressions (e.g., the thought that the sun has risen), but not all (e.g., the thought that I do not smell anything right now).



[2.11.] The Redundancy Theory.


Frege does say something positive about truth:


It is also worth noticing that the sentence ‘I smell the scent of violets’ has just the same content as the sentence ‘It is true that I smell the scent of violets.’ So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth. (24)


·         When we say that the thought that p is true, we are saying nothing more than had we simply said that p.


He made the same point about a different true sentence in “On Sense and Reference”:


                One might be tempted to regard the relation of the thought to the True not as that of sense to reference, but rather as that of subject to predicate. One can, indeed, say: ‘The thought, that 5 is a prime number, is true.’ But closer examination shows that nothing more has been said than in the simple sentence ‘5 is a prime number.’ (13)


What Frege says here resembles the


redundancy theory of truth (a.k.a. deflationism) (df.): the word “true” (as well as the word “false”) can always be eliminated from a linguistic context without loss of meaning.

·         For example, the sentence “It is true that Obama is President” means exactly the same thing as “Obama is President.” Other sentences require more complicated “translations” to eliminate the word “true”, e.g. “Everything Obama says is true” might mean the same as, “For any proposition p, if Obama says that p, then p.”

·         This theory derives primarily from 20th c. British philosopher Frank Ramsey and has appeared in numerous different versions throughout the 20th century.[4]


According to this theory, truth is not a relation between a proposition (or sentence, or belief) and the world; in fact, truth is not a property at all.


Frege’s example about the smell of violets clearly anticipates this theory: “It is true that I smell the scent of violets” means exactly the same as “I smell the scent of violets.” The phrase “it is true that” can be eliminated without changing the meaning of the sentence at all.


But note that he goes on to say some things that indicate he is not completely satisfied with the redundancy theory:


And yet is it not a great result when the scientist after much hesitation and laborious researches can finally say ‘My conjecture is true’? The Bedeutung [reference] of the word ‘true’ seems to be altogether sui generis. May we not be dealing here with something which cannot be called a property in the ordinary sense at all? (24)


Which theory of truth is correct (if in fact any of them is) is still a matter of controversy.[5]



[2.12.] Thought, Force, Connotation.


Not all meaningful sentences express or contain thoughts.


·         Imperative sentences (commands) have senses, but these senses are not thoughts, since “the question of truth could [not] arise for” them. (95) For example, “Shut the door!” does express a sense, but it is not a thought, since there is no question whether it is true.


On the other hand,


·         Interrogative sentences (questions) have senses, and these senses are thoughts[6]—the question of truth does arise for the thought contained in “Is the door closed?” The difference between this sentence and the indicative sentence “The door is closed” is that the indicative sentence contains something else that is missing in an interrogative question: assertive force.[7]


Frege points out that there is a third aspect of a sentence’s meaning that goes beyond its thought and its force: its connotation (he doesn’t use this English-language term; in fact he does not use any specific technical term for it at all; but this is what this aspect of language is usually called). This is the aspect of the sentence which affects the feelings or mood of the hearer.


For example, the difference between “The door is open” and “The damned door is open!” has nothing to do with the thought being expressed or the fact that the thought is being asserted rather than being asked about.


Connotation matters a great deal in poetry, but not at all in scientific and mathematical writing.



indicative sentences

(e.g., “The door is closed.”)

interrogative sentences

(e.g., “Is the door closed?)

imperative sentences (e.g., “Close the door.”)














yes: assertion


yes: request


[he doesn’t say, but presumably yes: command]






(less common in scientific and mathematical writing)



[he doesn’t say, but presumably usually]


[he doesn’t say, but presumably usually]




[2.13.] The Three Realms.


What sort of thing are the senses expressed by indicative sentences? In other words, what sort of thing are thoughts?


You should remember from “On Sense and Reference” that senses (be they senses of words or sentences) are not in the mind. They are public, accessible by more than one person.


But Frege has also told us earlier in “The Thought” that they are immaterial and imperceptible; they are not part of the sensible material world.


So what are they?


Frege comes closer to a full answer to this question when he distinguishes among three different “realms.”



The First Realm


A person who is still untouched by philosophy knows first of all things which he can see and touch, in short, perceive with the senses, such as trees, stones and houses, and he is convinced that another person equally can see and touch the same tree and the same stone which he himself sees and touches. Obviously, no thought belongs to these things. (97-98)


·         This is the outer world, the world of material, perceptible things.

·         Things in this world can exist without being perceived or thought about by anyone.

·         Thoughts (propositions, the senses of indicative sentences) do not belong to this realm.



The Second Realm


                Even an unphilosophical person soon finds it necessary to recognize an inner world distinct from the outer world, a world of sense-impressions, of creations of his imagination, of sensations, of feelings and moods, a world of inclinations, wishes and decisions. For brevity I want to collect all these, with the exception of decisions, under the word “idea.” (98)


·         This is the inner world, the world of ideas, including sensations, feelings, moods, inclinations, wishes, etc. [Frege is using “idea” more broadly here than in “On Sense and Reference” – in that earlier paper, he limited ideas to mental images].


He goes on to list explain the following points about ideas (98):


·         “Firstly: Ideas cannot be seen or touched, cannot be smelled, nor tasted, nor heard.” You do not see your mental image of a tree; you see the tree, and that’s what it is to have a mental image of a tree.


·         “Secondly: Ideas are had. One has sensations, feelings, moods, inclinations, wishes. An idea which someone has belongs to the content of his consciousness.”


·         “Thirdly: Ideas need a bearer.” “An experience is impossible without an experient. The inner world presupposes the person whose inner world it is.” In this way ideas are unlike objects in the First Realm, which are independent of anyone.



·         “Fourthly: Every idea has only one bearer; no two men have the same idea.”



The fact that a given idea can be “had” by only one bearer indicates to Frege that thoughts are not ideas.

·         If thoughts were ideas, then there would not be a single Pythagorean Theorem (a2  + b2 = c2) about which we all can communicate. Instead, there would be my Pythagorean Theorem, your Pythagorean Theorem, her Pythagorean Theorem, etc. etc.

·         More generally, if thoughts were ideas, then “there would be no science common to many, on which many could work.” (99) Frege imagines what truth would be like if truth-bearers (thoughts, propositions) were ideas and thus limited to one person:


But I, perhaps, have my science, namely, a whole of thought whose bearer I am and another person has his. Each of us occupies himself with the contents of his own consciousness. No contradiction between the two sciences would then be possible and it would really be idle to dispute about truth, as idle, indeed almost ludicrous, as it would be for two people to dispute whether a hundred-mark note were genuine, where each meant the one he himself had in his pocket and understood the word genuine” in his own particular sense. If someone takes thoughts to be ideas, what he then recognizes to be true is, on his own view, the content of his consciousness and does not properly concern other people at all. If he were to hear from me the opinion that a thought is not an idea he could not dispute it, for, indeed, it would not now concern him. (99)


·         In that last sentence, Frege is suggesting an argument against the view that thoughts are ideas (and therefore mental, and therefore specific to one and only one person)... If thoughts are actually ideas, then it is impossible for a critic to object to Frege’s claim that thoughts are not ideas... since then, Frege’s claim would express an idea/thought that belongs only to Frege and that a critic could never grasp, or understand, or come to know.



So Frege concludes that there must a third realm...


The Third Realm


A third realm must be recognized. What belongs to this corresponds with ideas, in that it cannot be perceived by the senses, but with things, in that it needs no bearer to the contents of whose consciousness to belong. Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer. It is not true for the first time when it is discovered, but is like a planet which, already before anyone has seen it, has been in interaction with other planets. (99)


·         The Third Realm is the world of thoughts (i.e., propositions).


·         Like ideas, thoughts cannot be seen, heard, etc.


·         But like things in the First Realm, they do not need a bearer.


·         They are true (or false) whether or not anyone thinks they are.


·         A given thought can be apprehended by more than one person.




Stopping point for Thursday September 13. For next time, read Russell, “On Denoting,” pp.35-38 (to the end of the first complete paragraph on p.38). Note the following:

·         Russell translates Frege’s term “Sinn” not as “sense” but as “meaning.”

·         And he translates Frege’s term “Bedeutung” not as “reference” but as “denotation.” What Russell says is that some terms denote; this is what Frege means when he says (in translation) that some terms refer.

·         So when Russell is talking about Frege’s distinction between sense and reference, he uses the terms “meaning” and “denotation.”

Come to class prepared to answer the question:

·         According to Russell, is the sentence “The King of France is bald” true, false, or neither?




[1] The three papers are: “Der Gedanke. Eine Logische Untersuchung” [“Thought: A Logical Enquiry”], 1918; “Die Verneinung. Eine Logische Untersuchung” [“Negation: A Logical Investigation”], 1918; and “Logische Untersuchungen. Dritter Teil: Gedankengefüge” [“Logical Investigations. Third Part: Compound Thoughts”], 1923.


[2] In Frege’s view, the laws of truth are not psychological laws; in particular, they do not describe the ways that people always in fact think. People can think in accordance with the laws of truth, and they frequently do; but they do not have to. “Laws of truth” are not the same things as “laws of thought” or “laws of assertion.” Here Frege is rejecting psychologism, the view that the purpose of logic is to describe the laws or principles by which people actually think.


[3] For more on the correspondence theory, see “The Correspondence Theory of Truth” in the Stanford Encyclopedia of Philosophy: .

[4] For more on this account of truth, see Daniel Stoljar and Nic Damnjanovic, “The Deflationary Theory of Truth,” The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = < >.


[5] For further reading on this issue, see the article “Truth” in the Routledge Encyclopedia of Philosophy [B51.R68 1998, in Ingram Library REFERENCE stacks], as well as Michael Glanzberg, “Truth,” The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), forthcoming URL = < >.


[6] This is something about which Frege changed his mind. Earlier, in “On Sense and Reference,” he had maintained that interrogative sentences do not express thoughts/propositions, but instead express questions, which are different than thoughts/propositions.


[7] The German phrase that Frege used and that gets translated as “assertive force” is “behauptende Kraft.” “Kraft” means force, power, strength; “behaupten” means to assert, to claim, to aver, to allege.

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