In Popper's book Assumptions and Refutations, the entire 14th chapter is devoted to this question and proves that the meaningfulness of a statement is not related to the possibility of being true or false.
Of course they can. There are modal logics in which your question is, for example, a perfectly meaningful proposition, but neither true nor false. There are multi-valued logics, in which judgments can be far from only true and false, but, for example, probabilistic and so on.
What is a judgment? This is a sign of the situation in reality. What is the situation? This is a state of affairs that connects real-world objects with their properties or relationships to each other.
The objects themselves are designated by names and interpreted through concepts. Properties and relationships get predictor signs. A sentence as a sign is a combination of names, predictors, functors, etc., which in natural languages are called parts of speech or members of the sentence (not the same thing).
The name and its semantic formulation (concept) is a sign of an object. The sentence and the judgment that interprets it (more precisely, the sentence is a sign of the situation, and the judgment is the meaning of the sentence, just as the concept is the meaning of the name).
How do we arrive at situations? By analyzing phenomena. We distinguish in reality the parts that we understand as objects (they get names that are defined in concepts), properties and relations (they are expressed by predictors, defined through signs), mental transitions from one to the other are fixed in functors.
A situation is a synthesis of a phenomenon from its individual parts-objects, properties, and relationships. But if you separate a phenomenon, you can glue it together correctly or incorrectly. Something happens in reality, but something does not happen. Sometimes something appears and then disappears again. Therefore, propositions and the judgments that interpret them can be true or false. A true judgment refers us to a real situation. And a false judgment doesn't have an existing one (probably at the moment) situations. It's like the name of a nonexistent object. In this sense, we can say that names can also be true or false if they mean what is or what is not.
So meaningful judgments are true or false, depending on the presence or absence of the specified situation. And the situation is either there or it is not. You are either at home or not at home. This means that meaningful judgments are either true or false.
But what does meaningful judgment mean? The same as certain concepts. That is, every judgment, like a concept, must first be defined. The definition refers to the relationship of the new, unknown with the old, known. It is through this connection that we understand concepts and judgments, otherwise they would be empty phrases.
This is, for example, the phrase “I'm lying” or “I'm telling the truth.” If we change these phrases into the language of logic, we get: A: = “not A” (lsu); B: = ” B ” (I'm telling the truth). Thus, the meaning of the first” phrase ” is that it is false, and the second – that it is true. But what is false? what is true? In the definition of phrases, they occur themselves, that is, there is a vicious circle of thought. This means that the definition is incorrect, the phrases are incorrect and, therefore, meaningless, and therefore do not have truth. That is, these are not judgments at all.
On the contrary, the phrase In := “this phrase is written in Russian” does not speak about itself, but about the language (the same applies to handwriting, font, volume, etc.). That is, there is no circle here. The phrase makes sense. Its truth is verified by experience.
Every sentence (meaningful!) indicates a situation, such as sentence B. And phrases A and B are infinitely looped on themselves, with A turning over, due to internal negation,and B without turning over, because there is no negation. But neither one nor the other points to situations, and therefore again are not judgments (meaningful sentences).
The question is not a judgment. This is part of it. A question with an answer is already a judgment. “Where did Peter go? “(not all information) – “to the theater”. As a result, we have a judgment: “Peter went to the theater.”
As for estimates, I think that these are subjective sentences, and they also have a subjective truth. Petya will say, “It's cold here,” and Vasya will say, ” it's warm here.” Both are right subjectively. Objectively, Petya is cold, but Vasya is warm. Now this is true or false (they can communicate their feelings honestly or deceive). So the phrase “cold” is similar to the question”who is cold?” – Petya. The phrase “heat” refers to Vasya. “Vasya is warm.” Without this connection, they, like questions, are not judgments, but only subjective phrases. And with a connection – these are judgments that, like all others, are either true or false.
If we answer the question technically, here we meet with another aspect, something like necessity in connection with the question of true and false. These things are literally made for each other. One might wonder if what you mean belongs to something general, or if you can put something particular under the category of general. But this is not the same as asking the question of true and false. Therefore, judgment, the fact of judgment, which is the core of Kantian criticism, belongs rather to the field of aesthetics.
As you know, everyday philosophical wisdom says that there is no such judgment that is only true or only false. That is, on the other hand, we can conclude that there is no false or true proposition. Because, on the other hand, it can be deductive or correctly deduced, or it can be a mathematical result. Judgment implies something like candor. This leads us to the fact that the judgment resists, does not allow itself to be placed under the category of true or false.
On the one hand, the judgment itself defines some relation that connects other judgments or facts. This means that the truth of this judgment, even if it is meaningful and true for some logic, will depend on the truth of the initial premises on which it is based. And the truth of the premises, in turn, will depend on the truth of the judgments on which they are based. To overcome this infinite recursion, some initial assumptions are simply assumed to be true axioms.
On the other hand, any fact is theoretically loaded, that is, it depends on the theory in which it is considered, because any theory is based on dogmatism of axioms and relations based on the doctrine of their truth.
I conclude that the truth and falsity of a meaningful judgment in a particular theory or logic is accepted at your discretion or at the discretion of the logic accepted by you and at your discretion.
My understanding of this question is as follows: the division of propositions into true and false is finding an unambiguous comparison of the set of propositions under consideration and the set (0, 1). How this unambiguous comparison is achieved in the general case is not so important for formal logic. Therefore, the question should be clarified in one of two ways::
1) For any set of “meaningful” statements, it is always possible to find an unambiguous comparison with the set (0, 1) within the framework of any variant of formal logic. Answer: no. There are types of statements that “don't fit” into certain types of logic.
2) For any set of “meaningful” statements, you can always find some algorithm for establishing an unambiguous correspondence with the set (0, 1). Answer: yes. Because whatever types of statements we take, modal, fuzzy, etc. After ordering them in the system in which they were formulated, you can come up with a certain algorithm for unambiguously matching them all with (0, 1).
(Here I have some doubts about the possibility of” ordering”, which I somehow associate with the” meaningfulness ” of the statement. It's a pity there aren't any draft answers, I'll think about it later, but I have to get on the bus right now. If someone comes and scolds me for being wrong, then, well, what should I do?)
In Popper's book Assumptions and Refutations, the entire 14th chapter is devoted to this question and proves that the meaningfulness of a statement is not related to the possibility of being true or false.
Of course they can. There are modal logics in which your question is, for example, a perfectly meaningful proposition, but neither true nor false. There are multi-valued logics, in which judgments can be far from only true and false, but, for example, probabilistic and so on.
Hello, Karina.
What is a judgment? This is a sign of the situation in reality. What is the situation? This is a state of affairs that connects real-world objects with their properties or relationships to each other.
The objects themselves are designated by names and interpreted through concepts. Properties and relationships get predictor signs. A sentence as a sign is a combination of names, predictors, functors, etc., which in natural languages are called parts of speech or members of the sentence (not the same thing).
The name and its semantic formulation (concept) is a sign of an object. The sentence and the judgment that interprets it (more precisely, the sentence is a sign of the situation, and the judgment is the meaning of the sentence, just as the concept is the meaning of the name).
How do we arrive at situations? By analyzing phenomena. We distinguish in reality the parts that we understand as objects (they get names that are defined in concepts), properties and relations (they are expressed by predictors, defined through signs), mental transitions from one to the other are fixed in functors.
A situation is a synthesis of a phenomenon from its individual parts-objects, properties, and relationships. But if you separate a phenomenon, you can glue it together correctly or incorrectly. Something happens in reality, but something does not happen. Sometimes something appears and then disappears again. Therefore, propositions and the judgments that interpret them can be true or false. A true judgment refers us to a real situation. And a false judgment doesn't have an existing one (probably at the moment) situations. It's like the name of a nonexistent object. In this sense, we can say that names can also be true or false if they mean what is or what is not.
So meaningful judgments are true or false, depending on the presence or absence of the specified situation. And the situation is either there or it is not. You are either at home or not at home. This means that meaningful judgments are either true or false.
But what does meaningful judgment mean? The same as certain concepts. That is, every judgment, like a concept, must first be defined. The definition refers to the relationship of the new, unknown with the old, known. It is through this connection that we understand concepts and judgments, otherwise they would be empty phrases.
This is, for example, the phrase “I'm lying” or “I'm telling the truth.” If we change these phrases into the language of logic, we get: A: = “not A” (lsu); B: = ” B ” (I'm telling the truth). Thus, the meaning of the first” phrase ” is that it is false, and the second – that it is true. But what is false? what is true? In the definition of phrases, they occur themselves, that is, there is a vicious circle of thought. This means that the definition is incorrect, the phrases are incorrect and, therefore, meaningless, and therefore do not have truth. That is, these are not judgments at all.
On the contrary, the phrase In := “this phrase is written in Russian” does not speak about itself, but about the language (the same applies to handwriting, font, volume, etc.). That is, there is no circle here. The phrase makes sense. Its truth is verified by experience.
Every sentence (meaningful!) indicates a situation, such as sentence B. And phrases A and B are infinitely looped on themselves, with A turning over, due to internal negation,and B without turning over, because there is no negation. But neither one nor the other points to situations, and therefore again are not judgments (meaningful sentences).
The question is not a judgment. This is part of it. A question with an answer is already a judgment. “Where did Peter go? “(not all information) – “to the theater”. As a result, we have a judgment: “Peter went to the theater.”
As for estimates, I think that these are subjective sentences, and they also have a subjective truth. Petya will say, “It's cold here,” and Vasya will say, ” it's warm here.” Both are right subjectively. Objectively, Petya is cold, but Vasya is warm. Now this is true or false (they can communicate their feelings honestly or deceive). So the phrase “cold” is similar to the question”who is cold?” – Petya. The phrase “heat” refers to Vasya. “Vasya is warm.” Without this connection, they, like questions, are not judgments, but only subjective phrases. And with a connection – these are judgments that, like all others, are either true or false.
Good luck to you!
If we answer the question technically, here we meet with another aspect, something like necessity in connection with the question of true and false. These things are literally made for each other. One might wonder if what you mean belongs to something general, or if you can put something particular under the category of general. But this is not the same as asking the question of true and false. Therefore, judgment, the fact of judgment, which is the core of Kantian criticism, belongs rather to the field of aesthetics.
As you know, everyday philosophical wisdom says that there is no such judgment that is only true or only false. That is, on the other hand, we can conclude that there is no false or true proposition. Because, on the other hand, it can be deductive or correctly deduced, or it can be a mathematical result. Judgment implies something like candor. This leads us to the fact that the judgment resists, does not allow itself to be placed under the category of true or false.
On the one hand, the judgment itself defines some relation that connects other judgments or facts. This means that the truth of this judgment, even if it is meaningful and true for some logic, will depend on the truth of the initial premises on which it is based. And the truth of the premises, in turn, will depend on the truth of the judgments on which they are based. To overcome this infinite recursion, some initial assumptions are simply assumed to be true axioms.
On the other hand, any fact is theoretically loaded, that is, it depends on the theory in which it is considered, because any theory is based on dogmatism of axioms and relations based on the doctrine of their truth.
I conclude that the truth and falsity of a meaningful judgment in a particular theory or logic is accepted at your discretion or at the discretion of the logic accepted by you and at your discretion.
My understanding of this question is as follows: the division of propositions into true and false is finding an unambiguous comparison of the set of propositions under consideration and the set (0, 1). How this unambiguous comparison is achieved in the general case is not so important for formal logic. Therefore, the question should be clarified in one of two ways::
1) For any set of “meaningful” statements, it is always possible to find an unambiguous comparison with the set (0, 1) within the framework of any variant of formal logic. Answer: no. There are types of statements that “don't fit” into certain types of logic.
2) For any set of “meaningful” statements, you can always find some algorithm for establishing an unambiguous correspondence with the set (0, 1). Answer: yes. Because whatever types of statements we take, modal, fuzzy, etc. After ordering them in the system in which they were formulated, you can come up with a certain algorithm for unambiguously matching them all with (0, 1).
(Here I have some doubts about the possibility of” ordering”, which I somehow associate with the” meaningfulness ” of the statement. It's a pity there aren't any draft answers, I'll think about it later, but I have to get on the bus right now. If someone comes and scolds me for being wrong, then, well, what should I do?)
In the framework of formal (Aristotelian) logic-no. There, any statement is either true or false.
And within the framework of our imperfect language, yes. For example, “this statement is false” is neither true nor false.