Truth - defining true and false
Imagine that there is nothing around you. Nothing in the Universe. ( No point in logic, I just want to start from a point of no assumptions)
You have made no assumptions so far.
(Just asking you to imagine it, not stating that there is actually nothing or anything)
Now, to assign a property to any object that you might observe, you first start with giving it a first property. We need properties to discuss objects. You need to give this property a name. Let’s give this property the name “existence”. Could have been “pink”, but we gave it the name “existence”, for the sake of it.
(Any mapping can be seen as an observation). Let’s intuitively explain observation as “link between two points”. In this case all objects are mapped to existence. The links are observation.
For example,
The bottle in front of me , exists.
The bottle in front of me being 10 cm is true is equivalent to bottle exists at 10 cm and so on...
Now, I argue that truth can be mapped to this existence set or property. ( Set of all such properties of all objects)
Now, we need to define truth, and non truth or false, to distinguish between mappings you already have vs. mappings in the total set of mappings possible, because the latter set could be larger than the former set.
In order to define something, we need comparisons. Define A to be x transpose. A is compared to x, and so on..
So we can compare existence to other objects and other properties ( no other property than existence is given so far).
Now, if we were to form a question and an answer, or ask statements. Let’s first give the statement: “ Existence can be defined”. We have not yet defined a true and false, but let's assume as such that we will be able to do so in the future to talk about it first hand.
Is this statement true is the next question we must answer, because existence is the only mapping that “this”, statement has. We assigned this property to every sentence in observation or to any sentence possible, which we could make(The sentence would be an object).
Questions become a little more interesting. Any machine must be able to solve a problem, and hence we must be able to pose questions to it. Take for example, any command you give to the computer as a question. It must answer it in binary, 0 and 1. It’s almost the same here, but we will generalize it to yes or no. No if it cannot answer.
Let’s pose the question, “Can existence be defined?”. The answer to this question is no, because to define existence, we would need the set of all statements possible. (We cannot get this set completely because of limited observation)
Now, we argue that this question and answer statement is the point of maximum existence, or the point which captures the entire existence set. If we argue that “Can existence be defined to any links or mappings which we have?” Since the total number of mappings is unknown, we have to say No to this question, because if were to do so, we would miss the entire existence set. (since we would have substituted unknown number of mappings with a known number).
Since we cannot use all objects and all other properties to discuss existence, it cannot be defined.
So a machine, could possibly answer the question “ Can existence be defined”, as a No.
“Can existence be defined wrt sentence A, or B or C or…”, are also No. (Subsets of the question).
Note that this set of sentences has a one to one mapping with the entire existence set.
Now, we know not by definition, but by applying logic, that this Q&A set is the point of maximum of existence. It’s at least one set which has a one to one mapping. Any other set I might form, might have less mappings, but not more.
Now, let’s define a true and false set.
Truth is that which has a mapping to this Q&A set.
False is that which does not have a mapping to this Q&A set.
This true and false, is a different set compared to the existence set which we had earlier.
Anyone would be interested in a discussion ?
You have made no assumptions so far.
(Just asking you to imagine it, not stating that there is actually nothing or anything)
Now, to assign a property to any object that you might observe, you first start with giving it a first property. We need properties to discuss objects. You need to give this property a name. Let’s give this property the name “existence”. Could have been “pink”, but we gave it the name “existence”, for the sake of it.
(Any mapping can be seen as an observation). Let’s intuitively explain observation as “link between two points”. In this case all objects are mapped to existence. The links are observation.
For example,
The bottle in front of me , exists.
The bottle in front of me being 10 cm is true is equivalent to bottle exists at 10 cm and so on...
Now, I argue that truth can be mapped to this existence set or property. ( Set of all such properties of all objects)
Now, we need to define truth, and non truth or false, to distinguish between mappings you already have vs. mappings in the total set of mappings possible, because the latter set could be larger than the former set.
In order to define something, we need comparisons. Define A to be x transpose. A is compared to x, and so on..
So we can compare existence to other objects and other properties ( no other property than existence is given so far).
Now, if we were to form a question and an answer, or ask statements. Let’s first give the statement: “ Existence can be defined”. We have not yet defined a true and false, but let's assume as such that we will be able to do so in the future to talk about it first hand.
Is this statement true is the next question we must answer, because existence is the only mapping that “this”, statement has. We assigned this property to every sentence in observation or to any sentence possible, which we could make(The sentence would be an object).
Questions become a little more interesting. Any machine must be able to solve a problem, and hence we must be able to pose questions to it. Take for example, any command you give to the computer as a question. It must answer it in binary, 0 and 1. It’s almost the same here, but we will generalize it to yes or no. No if it cannot answer.
Let’s pose the question, “Can existence be defined?”. The answer to this question is no, because to define existence, we would need the set of all statements possible. (We cannot get this set completely because of limited observation)
Now, we argue that this question and answer statement is the point of maximum existence, or the point which captures the entire existence set. If we argue that “Can existence be defined to any links or mappings which we have?” Since the total number of mappings is unknown, we have to say No to this question, because if were to do so, we would miss the entire existence set. (since we would have substituted unknown number of mappings with a known number).
Since we cannot use all objects and all other properties to discuss existence, it cannot be defined.
So a machine, could possibly answer the question “ Can existence be defined”, as a No.
“Can existence be defined wrt sentence A, or B or C or…”, are also No. (Subsets of the question).
Note that this set of sentences has a one to one mapping with the entire existence set.
Now, we know not by definition, but by applying logic, that this Q&A set is the point of maximum of existence. It’s at least one set which has a one to one mapping. Any other set I might form, might have less mappings, but not more.
Now, let’s define a true and false set.
Truth is that which has a mapping to this Q&A set.
False is that which does not have a mapping to this Q&A set.
This true and false, is a different set compared to the existence set which we had earlier.
Anyone would be interested in a discussion ?
Comments (156)
Secondly, computers don't answer questions that they haven't been programmed to answer. They're not magic oracles. And Turing showed that there are some questions a computer can never answer. This result is in fact related to Gödel's result that sufficiently powerful formal systems can't resolve all propositions.
We can now assign this property to any sentence that we can make.
The bottle is in front of me is True.
The bottle is at some distance is True.
etc.
Computers answer questions nonetheless. This isn't a Turing machine, just giving an analogy. This is informal logic, I think, and not anything related to formal systems.
The answer to the question in the title doesn't use words shared with the question in the same sense as they are being used in the questions themselves.
Here's simple...
Statements are what's true/false. Correspondence to fact/reality is what makes them true. The lack thereof is what makes them false.
"That is a tree" is a true statement, if and only if, that is a tree. If that is not a tree, then "that is a tree" is a false statement.
Now, we need to be able to talk about objects that we can observe. So we need to give objects some properties, like length, breadth and height etc. But, first they must have a common property for comparison. So we try and give them the property of truth first.
I am trying to define a true and false set, based on points in reasoning or logic.
Existence is first.
Exactly, statements are what true and false.
Any object that you can observe, can be described by statements completely, by making an innumerable number of them about the object, with respect to all other objects and you.
Agree?
I agree that existence is first, but an object is true if it exists, it exists if it is true.
Be careful to not confuse giving with discovering.
The last statement... If being true requires only existing, then false statements are true.
A statement being false could be true.
1) A statement being true, could come from description of an observation (existence), or it could come from deduction. It's not that existence is the only criteria for truth.
2) False statements about observations cannot exist. You can only observe true statements, and then take their converse or complement to get false statements. (not this statement is false)
Names are abstractions. An abstraction is a proxy; a stand-in. Names stand in place of the named.
You may want to re-read that until epiphany.
Please do let me know if I made any more obvious or non obvious mistakes.
But the "false", cannot exist. That you bring existence into question is a little weird though. I only talk about mappings and any possible objects that you could have.
Eg:
The bottle will only be at a distance of 10m from me.
11 m is false, so is 9m and so on...
Strange thing about false statements, is that they can also be ascribed the property of truth, for example.
"The statement that the bottle is 9m in front of me is false," is also True
You can say even that reflects fact.
If you make the correct assumptions, whatever valid deduction you get has to be truth.
In my presentation, truth is decided by logical validity and the strength of assumptions.
It is subjective under the assumptions. Objective truth is one without any assumptions.
So the truth value of a sentence, depends on it's logical validity and the strength of the assumptions it is under.
As I said, under my proposition, truth is somewhat subjective as you say by preserving the truth of the premises.
Even observation is not without premise. You do need to presume that the world is real.
To say of what is that it is and of what is not that it is not is truth. To say of what is that it is not and of what is not that it is is falsity. Or something like that...
For example in mathematics, we say 2+ 2 = 4, is true, under a certain set of assumptions being held true.
Observations are not entirely so different, when you think about it.
At the very least, I already have a few pointers. Any thoughts about the idea itself?
Could be wrong, could be right, I'd really like to know.
I'd love to find out at the very least where I am inconsistent.
The initial term truth remains undefined.
I introduce another two terms true and false later on based on the undefined term truth earlier.
(Y)
Not sure if you are being sarcastic. Probably are.
Tarski is good. Lots of folk paved the way.
There are two truths in the statements I am making. I apologize for not pointing it out earlier.
I have made the edit now.
The truth which is defined eventually is not the same as the original truth.
Then you ought not use the same name.
Fine, I will change the names. Hopefully it comes out more poetic :P
Existence isn't generally considered a property - at least not a first-order one, which is what your scheme relies on.
You seem to be close to defining truth in terms of satisfaction. Not too bad an approximation.
True statements are accurate in relation to some universe, and completely logical.
False statements are statements that are inaccurate and/or illogical.
There are also statements (most) which are true in relation to some possible universes, but false in relation to others - ambiguously true or false statements.
Universe is undefined. Cannot be defined.
False as you say is in relation to true.
The problem with that universe thing again.
Existence just came close to what I wanted. Here, sets can exist, statements can exist, Questions can exist, No can exist, and maybe a few other elements, or uncertainty can also exist. But,k you will never know exactly what all can exist, so it's not possible to define this set.
It's the Universe, it will always be undefined.
Edit: The Universe is the set of all sets in existence.
But then existence is always undefined.
But the true set which I defined has a one to one correspondence with this undefined set, at least in one dimension, by definition, or construction through logic.
Trouble is, validity is defined in terms of truth. Circularity ensues.
I would certainly agree that truth has the property of certainty. Although it's relation to consciousness as mentioned in your post is slightly long worded, and complicated to understand in one try. I will read again.
"Trouble is, validity is defined in terms of truth. Circularity ensues."
I think I agree with you on this. If you were to define logical validity:
All m is P, is True
All S is m, is True
----
All S is P , is True.
How, do we know All S is P is valid? Because it is true, and other sentences which can be formed may not be.
I think that is a circularity we cannot do without, any definition of truth has to be based on some logical validity.
You guys are far to clever for me.
Sure. That's what happens when one holds false belief. Being called "true" doesn't make it so.
"That which makes individual true propositions true"...
Is the first "true" above necessary?
If that which makes a proposition true differs from true proposition to true proposition, then in what way does it differ?
I'm not following this. Why no truth?
I say it's that regardless of the interpretation you apply, it turns out true - ones all the way down the truth table.
What's your definition, such that truth is not involved?
So, it's not true by virtue of being the result of valid inference?
truth is a semantic notion - not just syntax; so it comes into the story along with the content.
Indeed that is a much harder question to answer.
Logic itself exists because intuitively we as human beings can differentiate between true and false.
I am just trying to define a true and false.
That particular circularity between logical validity and truth, I must argue is the minimum that has to be.
And there's your problem.
What could that mean?
The ultimate circularity of definitions should not be much of a surprise. I was thinking more in terms of ostension than imposition.
That particular circularity is impossible to avoid, even in Tarski's definition.
Any sentence he forms has to be logically valid, and what does logical validity eventually depend on? Truth.
There is more than one dimension to this circularity. One cannot avoid all of them.
For all x, True(x) if and only if ?(x)
?(s) if and only if ?
https://plato.stanford.edu/entries/tarski-truth/
He does assume logical validity after all.
Although, I must admit that I have not read him completely. Correct me please if you think I am wrong.
I find it odd to question the meaning of "by virtue of" and proceed to offer an answer like you did...
As a result of. Because of.
The important bit I was getting at was that being the result of valid inference does not make the conclusion true. Earlier you used the notion of what makes a true proposition true. I asked a question about that, but it has not been answered.
Quoting tim wood
I have no idea what you're trying to say with regard to all the concepts being a priori or a posteriori. Nor do I see how such talk helps to understand what truth is ans the role that it plays in everything ever thought, believed, spoken, and/or written. The talk of quality of truth is odd as well.
Quoting tim wood
Whether to attack at dawn is a matter of ought. 2+2=4 simply because we will not let it be any other way.
Regardless, it seems that we agree that validity and truth are not equivalent, and that being the result of a valid inference does not make the conclusion true(except in the cases you've mentioned where all the concepts are a priori).
Could you elaborate upon that? I mean what is the criterion which, when met by a candidate, make the candidate a priori?
The question was...
If that which makes a proposition true differs from true proposition to true proposition, then in what way does it differ? I take it that the answer was the a priori/a posteriori part?
Quoting tim wood
I find that the notion of a posteriori as used above conflates different kinds of talk. What should be done is a moral matter. You've contradicted yourself above regarding it. You first said it's a neither/nor matter, but then clearly said the truth of the claim was yet to be determined, but could be. Getting into whether or not an utterance of "should" is true, false, or neither isn't necessary here. It requires a baseline which has yet to have been established. That said, that particular example happens to also be one of prediction akin to saying the sun will rise tomorrow. On my view, it's neither true or false at the time it's uttered. Truth conditions matter.
"Peanut butter is good for you" is most certainly either true or false, depending upon the person. If it is true, then it is always true. If it is false then it is always false. The claim has different truth conditions depending upon the person being spoken to. If it is stated as a universal, as in it is good for everyone, then it is most certainly false.
Quoting tim wood
Learning the definitions of terms is determined by experience. A priori is 'true' by definition. I'm still wondering how this relates to a syllogism, because you earlier said that if all the concepts are a priori then a valid form will yield a true conclusion. Premisses are not concepts.
A different tack will help, I think. We are discussing logical truth, which involves an argument. We are talking about the different kinds of premisses that a syllogism can have, notably what makes them true. However...
A true statement does not require logic. Thus, either truth does not require logic, or true statements do not require truth.
Here's the thing. You're working from a framework of propositions being the things that can be true/false. I do not. I have worked through the question myself. The answer you've given is unacceptable. I'm asking how your framework accounts for the assertion you made. That's a perfectly acceptable thing to do given the situation. It's your claim, your justificatory burden.
Quoting tim wood
Poor wording on my part. I meant... notably what makes the different kinds of premisses true. You ought have known that, given the talk of a priori and a posteriori.
Quoting tim wood
Of course we presuppose the truth of the premisses. If they are true, and the argument valid, then the conclusion is true. Warrant is about belief, not truth. True premisses and valid argumentative form warrants belief that the conclusion is true. Belief is not truth.
Can you provide an example of such a proposition?
Sigh. Pots and kettles. Aren't you actively employing the term? You can replace the term "truth" with "correspondence" anywhere in my writing usually, although I do occasionally follow suit. I am quite cognizant of that.
I wonder if you have seen Kripke's idea:
But, how would you know if you are not assigning a false sentence the property of truth?
The barn is big is one sentence, the barn is small is another.
How would one know whether to club them together or not?
Plus we are assigning the property of truth here, not defining it.
If that which makes a proposition true differs from true proposition to true proposition, then in what way does it differ?
Perhaps it be better to ask... what, on your view, makes a proposition true?
I'm simply trying to understand what you're saying with regard to truth.
Defining true is calling something "true". Being true is not equivalent to being called "true". Exploring this difference(between being true and being called "true") can be interesting.
This look at truth should answer the question "can the universe be defined" to have an answer as it has truth value or it does not. However, as the observer here has literally mapped everything themself, the answer was always Yes, and the observer has quantified and defined the universe by observing it.
Even while the scope may be beyond our comprehension, what ' is' or that which 'exists' must indeed have an end as that is the simple nature of our universe.
My speculation is that truth is a comparison, a measure of equivalence or differentiation. This apple is red is a comparison of the apple's color to a predefined wavelength of light.
The binary bifurcation of true/false can be enhanced to true/not-true/false, where not-true and false are not identical sets. That increase in resolution also demonstrates that further increases could result in a gradient, perhaps what we call confidence.
Yes it does. That fact grounds my questions.
I've heard enough. Thanks for the exchange. I'm not interested.
I'm familiar with that article. I'm also cognizant of equivocation. I'm also up for it if you would like to compare the different conceptions of "truth". Other than that, I would still like for you to answer the question I asked earlier. Twice.
When I wrote "Yes it does", 'it' referenced the article. Maybe you should read the post; it's just above. Then compare what I wrote with what you quoted. Removing the context removes much of the meaning(or at least what is required for one to correctly attribute and/or share it).
If it was inadvertent, then my mistake and apologies. However, given the lack of commitment in your language to make any strong assertions, I'm cautious of both rhetoric and dialetheism(para-consistent logic).
Not sure what you're referring to. In the above question, replace the term "that" with what you're asking me about. That would let me know what you're asking hopefully.
Regarding beliefs that are never questioned...
Questioning one's own thought and belief is a metacognitive endeavor. Not everyone can, nor does. A crucial aspect of questioning one's own thought and belief is that one cannot effectively do it alone. It requires an other.
It could also be said that when one holds unshakable conviction in some belief or other, that that belief is unquestioned or unquestionable. However, that is not to say that it has never been.
Thought and belief without propositional content.. to me resembles instinct.
I had assumed that propositional content was exactly the methodology used to develop beliefs.
Maybe I am unclear on the idea?
Confidence in the mathematical sense used in probabilities and statistics. Roll a single six-sided die: Prior to the toss I am 5/6 confident (83%) that the result will not be a four.
Which wouldn't surprise me at all, given that my position is unconventional. They're catching up though. ;) Paradigm shift is a slow process. That post is underwritten by my own personal conception of thought and belief. One could say it's a theory of mind, however that would be misleading for I am not a mind/body dualist. I do not believe that disembodied cognition is even possible.
To be clear, the vast overwhelming majority of thought and belief could be said to have propositional content. It makes more sense, on my view at least, to say that most thought and belief are existentially contingent upon language, and as such the content therein can be - most times - adequately represented by virtue of statements thereof.
However, I do strongly argue for the notion that philosophy - on a whole - has gotten thought and belief wrong.
In order to achieve the relaxation that accompanies belief that something or other is true...
How many ways are there to convince another to believe something?
Truth - here - doesn't factor into the goal, except with regard to getting the answer correct. Otherwise... Ends justify the means.
Regarding another portion of your last reply...
What would count as conclusive with regard to truth?
"both propositions, both true. But what in their respective truths is the same? "
Since "strawberries taste good" is subjective I'm going to say perspective.
Willingness to be wrong is part of the equation. I can state with 100% certainty what the sum of the roll of a pair of dice will be before the toss: It will be a number in the range [2..12].
The value of 100% certainty is that it shows the full range of what is possible, but without a sense of what is probable. There is a trade-off that can be made where I can choose to be less certain of what is possible in exchange for what is probable.
For example, I can choose to narrow the outcome of that toss of dice to be a prediction in the range [5..9], with a confidence of (24/36 = 6/9 = 67%). I'll be right 2 times out of 3 and wrong 1 time out of three. If there's a financial gain/loss involved then that may be enough base a decision.
One might say the apple being red is true, and apple being red, and somewhat round is true.
The latter being more true etc.
In math for instance, sentences if true are equally true.
I am sorry, my way of looking at it is to define it(truth, or other things) one way, and then see what we can do with it. Does it cover everything or not?
Truth will depend upon the question being asked, that is certain, but everything in thought can be divided into questions and beliefs, even sensations, and emotions. The mind thinking of them as true.
What it actually is, is a matter of wide speculation, but I think the philosophical answer should depend on usefulness as well. How much can each viewpoint explain?
1+1 = 2; we say that is a true statement because the two sides match.
The apple is red; that statement could be true if the color of the apple matches the wavelength of red.
This is a fair pair of dice; that statement is classified as true if the observed results match a probability table for a pair of dice.
And there are degrees to which things may match, the most general being does/doesn't. Is this egg from a chicken or a goose? Weigh it, and we find the two ranges overlap.
The two egg-weight ranges aren't mutually exclusive, and so we can describe the egg as maybe 3/4 hen and 1/4 goose. That is a degree of match, a truth value for the comparison. That is not a proportion of ingredients within the sample egg.
Schroedinger's cat was merely modeled as alive and dead, with the statement that model is effective for any application needing that information.
So a statement can be true if it is logically valid, or assumed to be true(Putting definitions as assumptions as well, any rule too).
That's just plain wrong. Statements presuppose truth. There are no exceptions.
A statement can be the result of valid inference and either true or false. A statement can be the result of invalid inference and be either as well.
Verification/falsification?
Statements have the property of truth.
A statement either has the property of true, or true', which can be defined very easily as the set not true.
Neither the inferring nor the assuming make it so, however. Thats a crucial thing to note.
And then, everything can be modelled either as a statement or a question, or an assumption, all of which can have true or false value.
The Universe can be said to be generating true statements every moment.
The above puts it all on simple display. On the left is the belief statement. The truth conditions are set out by the rest. On the right, is what must be the case in order for the statement to be true.
If she receives no treats, her belief is false. Her expectation did not correspond with fact.
This one assumes an infinite tower of metalanguages. So, it assumes a concept of infinity.
Quoting guptanishank
Examples
An orange is a fruit -- true, matches
Your name is Amanda -- partially true, partial match to the readership
My name is Amanda -- not true, does not match birth certificate, driver's license
There is no left or right here. Orange is a fruit by definition.
Do you agree that the statement "an orange is a fruit" is a true statement?
Replace the word "is/was" with "matches" to see the left and right side of a match.
But there is no left or right there. You are thinking of an equation. No such thing is defined here.
It makes no sense at all, on my view, to talk in terms of "the truth in the meta-language". So, help me out here, if you would...
"That is a tree" is a true statement if, and only if, that is a tree.
Which part of that is meta-language, and what makes it so?
I'm not seeing a need for a meta-language; but the repetition of an identical perspective is somewhat less than revealing.
"That is a tree" is a true statement if the subject "that" matches the definition of "tree."
And the result of an intelligent system is feedback; her memory is updated to include that outcome. So her confidence in that outcome has gone down a bit, and the next time she hears rustling plastic in won't be as convincing to her that treats will ensue.
Indeed. That is precisely how it works.
Yes. That example could be rendered as such. It could also be an example of naming, for the first time, I mean. If it was a first time naming, the original coining, the definition would be in the process of being established, so the matching wouldn't have what it takes yet. A difference between truth and meaning.
The typical example uses cats and mats, which doesn't quite allow the same rendering.
To be clear...
I'm not claiming that all thought and belief is prior to language. Some clearly cannot be. Others clearly are. I've yet to read a proper account of this. Conventionally speaking...
If the content of thought and belief is propositional and propositions require language, then so too does thought and belief.
Of course that premiss is dead wrong. The content of all thought and belief is not propositional, it's correlation(s). All propositions consist of correlation(s). All is proposition is correlation. Not all correlation is proposition. Being propositional requires prior meaning. All meaning consists of correlation(s). So...