Statements are true or false?

What is the basis for reason? And mathematics?

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A_Seagull
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Statements are true or false?

Post by A_Seagull »

Is the assertion that statements are either true or false itself true? If so by what criteria?

And if it is true what methods can be used to determine whether a statement is true or false?

And what is meant by 'true' and 'false' in this scenario?
'
And what are the specifications for a 'statement'?

(As you may have inferred I am very sceptical about the whole assertion.)
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Greta
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Re: Statements are true or false?

Post by Greta »

A_Seagull wrote:Is the assertion that statements are either true or false itself true? If so by what criteria?

And if it is true what methods can be used to determine whether a statement is true or false?

And what is meant by 'true' and 'false' in this scenario?
'
And what are the specifications for a 'statement'?

(As you may have inferred I am very sceptical about the whole assertion.)
I don't have the theoretical tools, only an example:

"You are alive" is obviously true. I expect the "why" would pertain to the fact that those things that exist (true?) are those things that can exist - at least at this time.
Walker
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Re: Statements are true or false?

Post by Walker »

Truth is what accords with reality.
So, just figure out what’s real and compare the sentence to that.
If the sentence accords with reality, the sentence is true.

I am is true, all else is inference.

In reality, a machine can compose sentences.
In reality, “you” may be a sentence composing machine, and not alive.
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Terrapin Station
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Re: Statements are true or false?

Post by Terrapin Station »

A_Seagull wrote:Is the assertion that statements are either true or false itself true?
On a correspondence view, it's only true if it's implied that you're referring to the conventional definition, qua the conventional definition, of what statements are. It's not true or false outside of that context. It's a stipulation by convention.
And what are the specifications for a 'statement'?
It's simply (the meaning of) a sentence that has a truth value. By correspondence, it has a truth value by virtue of a judgment about the relation of (the meaning of) the sentence and states of affairs in the world.
Skip
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Re: Statements are true or false?

Post by Skip »

A_Seagull wrote:Is the assertion that [all]statements are either true or false itself true? If so by what criteria?
Yes - this is true of a class of statements: factual claims; simple direct responses to simple questions; statements regarding verifiable reality: scientific observation, measurements, states of matter and physical entities or processes.
No - if you include the inserted qualifier, or if you infer its presence. In that case, several classes of statement would be exempt: self-contradictory statements, such as "The water is boiling cold.", compound statements wherein there is both truth and falsehood: "I saw you yesterday shedding a snakeskin."; statements out of context: "The Scarlet Pimpernel rescued French aristocrats."; nonsense statements: "Twas brillig, and the slithy toves Did gyre and gimble in the wabe"; complex statements that include facts but are largely conjecture "When he climbed out out onto the roof, he must have expected to catch a pigeon but caught a cold instead." and unverifiable statements: "I believe unreservedly in the resurrection." or "The universe began as a singularity with no size or duration."
And if it is true what methods can be used to determine whether a statement is true or false?
Class 1 statements can be verified with more or less effort; class 2 statements can be divided into their components and some parts verified, or relegated to their proper context.
And what is meant by 'true' and 'false' in this scenario?
Depends on which scenario.
And what are the specifications for a 'statement'?
There are several. I think what you're looking for is : a declaratory sentence (has subject and predicate; ends with a period)
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

Skip wrote:
A_Seagull wrote:Is the assertion that [all]statements are either true or false itself true? If so by what criteria?
Yes - this is true of a class of statements: factual claims; simple direct responses to simple questions; statements regarding verifiable reality: scientific observation, measurements, states of matter and physical entities or processes.
No - if you include the inserted qualifier, or if you infer its presence. In that case, several classes of statement would be exempt: self-contradictory statements, such as "The water is boiling cold.", compound statements wherein there is both truth and falsehood: "I saw you yesterday shedding a snakeskin."; statements out of context: "The Scarlet Pimpernel rescued French aristocrats."; nonsense statements: "Twas brillig, and the slithy toves Did gyre and gimble in the wabe"; complex statements that include facts but are largely conjecture "When he climbed out out onto the roof, he must have expected to catch a pigeon but caught a cold instead." and unverifiable statements: "I believe unreservedly in the resurrection." or "The universe began as a singularity with no size or duration."...
I'm failing to understand how it makes sense to call many of those statements. Doesn't 'X''s being a statement require it's saying something sensible about the world and/or ourselves? It seems like not all of those examples do that.
Skip
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Re: Statements are true or false?

Post by Skip »

creativesoul wrote:
Doesn't 'X''s being a statement require it's saying something sensible about the world and/or ourselves? It seems like not all of those examples do that.
No. They are all statements. They are not all reality-claims.
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

I'm asking for the criterion, which when met, counts as being a statement. Surely, that includes saying something, right?

:?
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

A_Seagull wrote:Is the assertion that statements are either true or false itself true? If so by what criteria?
Yes. Statements say something. Saying something requires saying something about the world; the universe; reality; the case at hand; the way things are; etc. What a statement proposes to be the case is either true or false, per the principle('law') of bivalence.

...what methods can be used to determine whether a statement is true or false?
Verification/falsification methods.

And what is meant by 'true' and 'false' in this scenario?


When a statement is "true" it corresponds to fact/reality(the way things are; the case at hand; the world; etc.), and when "false" it lacks such correspondence.
'
And what are the specifications for a 'statement'?
Saying something.

(As you may have inferred I am very sceptical about the whole assertion.)
Nothing wrong with well placed skepticism...
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A_Seagull
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Re: Statements are true or false?

Post by A_Seagull »

It seems that there is confusion (or perhaps it is just me that is confused) over what constitutes a statement. On the one hand it is something that someone says (presumably as a communication) about the state of the world. And this statement can then be analysed to see whether it has an accurate correspondence with the world, and if it does it is labelled 'true' and if not it is labelled 'false'.

And then there are the statements which can be considered to be logical units and which can possess the property of being true or false and which can be analysed using logical methods.

Is this a reasonable distinction? Because it seems to me that too often the two types are conflated and there is confusion.
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

A_Seagull wrote:It seems that there is confusion (or perhaps it is just me that is confused) over what constitutes a statement. On the one hand it is something that someone says (presumably as a communication) about the state of the world. And this statement can then be analysed to see whether it has an accurate correspondence with the world, and if it does it is labelled 'true' and if not it is labelled 'false'.

And then there are the statements which can be considered to be logical units and which can possess the property of being true or false and which can be analysed using logical methods.

Is this a reasonable distinction? Because it seems to me that too often the two types are conflated and there is confusion.
Yup. Nothing at all unreasonable in that account. Two different kinds of statements. It is well worth noting, in addition to what you've written, that logical methods presuppose correspondence(truth) of premisses, and attribute truth to conclusions based upon coherency/validity. The property which warrants/justifies being called "true" is coherency/validity. It's about the argumentative form.
wtf
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Re: Statements are true or false?

Post by wtf »

A_Seagull wrote: Is this a reasonable distinction? Because it seems to me that too often the two types are conflated and there is confusion.
I believe there is a distinction that is sometimes made between a statement and a proposition. Statements don't have truth values. Propositions do. In fact the very definition of a proposition is that it is a statement that has a truth value. It's a "truth bearer," a philosophical phrase I've come across.

Here's another way to think of it. It's the difference between syntax and semantics.

This being the philosophy of math section, I'll give a mathematical example.

Consider the statement: "(∃x) x + 2 = 1". Is it true? Is it false? I have no idea until you tell me the universe over which x may vary, and what the symbols mean. If the universe is the natural numbers 0, 1, 2, 3, 4, ... then the statement is false. But if the universe is the integers, which are all the positive and negative natural numbers, the statement is true, it's satisfied by x = -1.

Seen this way, a statement is a string of symbols formed according to formal rules of syntax. "(∃x) x + 2 = 1". It is completely meaningless. It has no truth value. However it a well-formed formula of first-order predicate logic. By definition it's a statement.

A statement becomes a proposition when you choose a domain of interpretation, and map the symbols to objects in your domain. For example we might say that the domain is the natural numbers, and the symbol '2' refers to the number 2, and the symbol '+' refers to the addition of natural numbers, and so forth. Or perhaps the symbol '2' refers to the number we usually call 47. The mapping of symbols to objects in the domain is arbitrary. 2 + 2 = 4 isn't true till we say what '2', '4', '+', and '=' are.

So: A proposition = a statement + a domain + a mapping of symbols to objects in the domain.

This is my understanding of the difference between a statement and a proposition. Only propositions have truth values.

To answer your original question: Propositions have truth values because we define them that way. Statements that don't have truth values are not propositions.
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

wtf wrote:I believe there is a distinction that is sometimes made between a statement and a proposition. Statements don't have truth values. Propositions do. In fact the very definition of a proposition is that it is a statement that has a truth value. It's a "truth bearer," a philosophical phrase I've come across.
Indeed. Many, if not most academic philosophers like/use this framework. I'm not sold on the idea that it makes sense to call a meaningless string of symbols a statement. The notion of truth-bearers has it's fair share of problems as well, although I'm not sure unpacking them is germane as of now. If a proposition is a statement that is capable of being true, then I've no apparent reason to disagree and could roll with such a framework in order to see it's consequences. However, having a "truth value" is a 'measure' of coherency/validity. An argument can have a valid and false conclusion. Such an argument would qualify as being "logically true". We could call it a "logical truth". It's 'truth' value, as determined by the rules of correct inference, would be "true". Truth cannot be false.
Here's another way to think of it. It's the difference between syntax and semantics.

This being the philosophy of math section, I'll give a mathematical example.

Consider the statement: "(∃x) x + 2 = 1". Is it true? Is it false? I have no idea until you tell me the universe over which x may vary. If the universe is the natural numbers 0, 1, 2, 3, 4, ... then the statement is false. But if the universe is the integers, which are all the positive and negative natural numbers, the statement is true, it's satisfied by x = -1.

Seen this way, a statement is a string of symbols formed according to formal rules of syntax. "(∃x) x + 2 = 1". It is completely meaningless. It has no truth value. However it a well-formed formula of first-order predicate logic. By definition it's a statement.

A statement becomes a proposition when you choose a domain of interpretation, and map the symbols to objects in your domain. For example we might say that the domain is the natural numbers, and the symbol '2' refers to the number 2, and the symbol '+' refers to the addition of natural numbers, and so forth. Or perhaps the symbol '2' refers to the number we usually call 47. The mapping of symbols to objects in the domain is arbitrary. 2 + 2 = 4 isn't true till we say what '2', '4', '+', and '=' are.

So: A proposition = a statement + a domain + a mapping of symbols to objects in the domain.

This is my understanding of the difference between a statement and a proposition. Only propositions have truth values.

To answer your original question: Propositions have truth values because we define them that way. Statements that don't have truth values are not propositions.
That sounds about right, if by that I mean this seems to be an accurate account of current convention.
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A_Seagull
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Re: Statements are true or false?

Post by A_Seagull »

RE Propositions vs Statements
I think there is a similar distinction between pure maths and applied maths. And typically philosophers conflate the two and claim that " two sheep + two sheep = four sheep " is a necessarily true statement. When really what is required is a mapping between the domain of arithmetic and the domain of sheep.

Also I think there are two types of truth. There are the abstract truths where, for example, the string of symbols "2+2=4" is true, but only within the abstract system of pure mathematics. And it is true because either it is an axiom of the system or it can be proven from the axioms using deductive inferences which are defined by the axioms.
Then there are the truths of facts whereby a statement is labelled as true if it is considered that it corresponds with the facts.

And it seems to me that logicians conflate the two and consider that logical identities will apply as of right with facts about the world with out being aware that a mapping is required.
creativesoul
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Re: Statements are true or false?

Post by creativesoul »

Yup. Sounds about right, if by that I mean sounds like current conventional wisdom. More importantly however, it sounds exactly like talking about talk; thinking about thought; metacognition at work.

Correspondence precedes mapping. Coherency cannot.
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