are you saying that the main reason we construct logical theories is because they are useful and relevant to our lives? — khaled

That's why I construct them, and I suspect it's the reason for most other people as well. In the end though, I can only speak for myself.

Arbitrary premise -> arbitrary logic
No it's
Arbitrary "life impact" -> arbitrary premise -> arbitrary logic

I don't know what role the word 'arbitrary' is playing here. It doesn't seem to fit. I either take premises that are observations or beliefs that are relevant to an actual situation I care about, or that are hypotheses and beliefs about a hypothetical situation I am interested in. I don't see how arbitrariness has anything to do with this, unless one were to say that what I care about, am interested in, observe or believe is arbitrary, in which case I'd say 'I don't see that as arbitrary but I don't mind if somebody else wants to say it is'.

P1: arithmetic is correct
P2: 2+2=7
3+3 = (2+1) + (2+1) = 2+2+2= 7+2=9
Therefore the premise: 3+3=6 is false — khaled

Two ways. 1) 2+2 does not equal 7.

2) you can have the proposition, "if (2+2=7) then (3+3=6)
and, "If (2+2=7) then (3+3 does not equal 6).
Both these hypothetical propositions are "true," per truth table. But neither is an argument with a conclusion. If you also have a premise that 2+2=7, then by modus ponens you have both 3+3=6 and 3+3 does not equal 6

It isn't consistent because from P1 we can prove that 3+3=6, which contradicts the deduction that ~(3+3=6).

Actually, there are many premises that cannot be "validated" by any premise. And it's time for you to define "validate."

I define arbitrary as: Accepted without logical proof in which case interests are arbitrary. I don't mean random or meaningless

restate P1 as:
3 = 2+1
And add P3: (a+b) + (c+d) = a+b+c+d
And add P4: 1+1=2
And now it's consistent

then by modus ponens you have both 3+3=6 and 3+3 does not equal 6 — tim wood

How? By modus ponens if 2+2=7 and you replace the premises as I did accordingly in my last comment then it can be inferred that 3+3 does not equal 6

Actually, there are many premises that cannot be "validated" by any premise. And it's time for you to define "validate." — tim wood

Validate: for premise A to validate premise B means that premise B logically follows from premise A

I agree. There are apriori premises. However there is no reason to pick apriori premise A over apriori premise B by definition. Apriori premises have no validation and thus nothing to use in judging between apriori premise A and B

The entire point of this post is that there are multiple possible apriori premises to pick from and to use in validation of other premises and that there is nothing to distinguish these without relying on other apriori premises but then THOSE have no validation. The point is that human belief must start from an arbitrary pivot

The entire point of this post is that there are multiple possible apriori premises to pick from and to use in validation of other premises and that there is nothing to distinguish these without relying on other apriori premises but then THOSE have no validation. The point is that human belief must start from an arbitrary pivot — khaled

The solution is to give up trying to render ultimate validation via apriori premises or fundamental axioms, and to instead rely on the empirically accessible; we can't touch the bottom. Once we pass a certain depth of substantiation, we get decreasing returns on the utility and additional strength that more actually gives to our conclusions. For example, if we try to assess the prevalence of something by statistical survey, there is a practical limit to the number of samples (or sample size) required to get a well resolved prediction. Additional data can always increase precision, but unless we have practical reason to do so, why bother?

There is no ultimate certainty, and some would accuse me of therefore embracing some form relativism and/or by extension, nihilism. I disagree. Despite there being no ultimate certainty, there are indeed degrees of greater and lesser certainty; degrees of reliability and substantiation. Instead of expecting to arrive at ultimate certainty, I expect that I will forever approach it. It's not easy to know what's ahead of us on the road of approaching certainty, but it is generally easy to know what's behind us. It seems true that we're stuck with our own relative beliefs and perceptions, but some beliefs and perceptions are better - more accurate - than others.

p3 is false

how so?

Verification/falsification

falsification is much easier. Show me a premise that can be known to be true without referring to any other premises

The solution is to give up trying to render ultimate validation via apriori premises or fundamental axioms, and to instead rely on the empirically accessible — VagabondSpectre

To choose to accept emperically accessible information rather than apriori "knowledge" is an apriori ought. It doesn't solve the issue, it's one of an infinity of possible solutions. What you're describing is not degrees of certainty but degrees of practical reliability. To emphasize practical reliability is axiomatic and invalidated just like all it's alternatives

Show me a premise that can be known to be true without referring to any other premises — khaled

Does understanding how to use the English language count as referring to another premiss?

All premisses are statements. Some statements are true. Some true statements can be verified.

Where's the need to refer to another premiss?

Does understanding how to use the English language count as referring to another premiss? — creativesoul

Yes. You'd have to accept premises such as "Humans are capable of storing memories", "Auditory input is reliable", etc. If Auditory input is not reliable you can't learn English

Does understanding how to use the English language count as referring to another premiss?
— creativesoul

Yes. You'd have to accept premises such as "Humans are capable of storing memories", "Auditory input is reliable", etc. If Auditory input is not reliable you can't learn English — khaled

No. This is confused.

One can know that the statement "there is a cup on the table" is true by virtue of looking. There is no need for one to refer to another premiss. Referring to another premiss requires thinking about one's own thought and belief. That's a metacognitive endeavor.

One can know that some statements are true, and they can know how to tell if they are long before one is able to use them as a premiss.

Thought/belief and statements thereof are long prior to logic. Logic is meant to take account of them. Your argument neglects these facts and suffers as a result.

A child amidst language acquisition doesn't need to accept any premiss such as "auditory input is reliable" in order to know that that thing over there is a cup.

I don't think what an eighteen-month old knows is anything like as philosophical as that. My guess is that what they know is that you make the 'cup' noise when you want to draw attention to a thing that looks like what's over there. It's a game, a language game.

We need more additional premises than those two, to deduce ~(3+3=6). For a start we need 6<>9 and 7+2=9. We will also probably need some commutative and associative rules. So there'll be quite a few premises. But yes, given any false arithmetical statement that is not self-contradictory in the underlying language, one can make up a consistent little logical theory, not including all of arithmetic, of which that statement is a theorem.

I've lost track of what that example was intended to demonstrate though.

I don't think what an eighteen-month old knows is anything like as philosophical as that. My guess is that what they know is that you make the 'cup' noise when you want to draw attention to a thing that looks like what's over there. It's a game, a language game. — andrewk

Yeah, you're probably right. I mean I wouldn't argue against that. It wasn't the best supportive reasoning...

I was more applying the consequences of drawing the distinction between thought and belief and thinking about thought and belief. All premisses are statements used for a specific purpose. All statements are belief statements(assuming sincerity). One can know that a statement is true long before ever knowing why and/or how they've come to believe it.

How? By modus ponens if 2+2=7 and you replace the premises as I did accordingly in my last comment then it can be inferred that 3+3 does not equal 6 — khaled

Try reading the post again.

Validate: for premise A to validate premise B means that premise B logically follows from premise A — khaled

Logically follows?

One can know that a statement is true long before ever knowing why and/or how they've come to believe it. — creativesoul

I think so too

One can know that the statement "there is a cup on the table" is true by virtue of looking. There is no need for one to refer to another premiss — creativesoul

Incorrect. One would have to accept the premise "Visual input is reliable"

it was intended to demonstrate P6

Logically follows — tim wood

Syllogisms that do not commit logical fallacies

Try reading the post again — tim wood

restate P1 as:
3 = 2+1
And add P3: (a+b) + (c+d) = a+b+c+d
And add P4: 1+1=2
And now it's consistent

it was intended to demonstrate P6 — khaled

I don't know what P6 means.

P6 means that, since you need a premise A by which to determine the truth value of premise B (P3) (for example, "Visual perception is reliable" -> "Visual perception tells me "There is a cat"" -> "There is a cat") and since there is an infinite number of possible premises (P5) (almost any sentence can work as a premise including this one), There is an infinite number of possible premises A by which to determine the truth value of premise B

A demonstration:
"Visual perception is reliable" (PA)-> "Visual perception tells me "There is a cat"" -> "There is a cat" (PB)
OR (in the following example the guy also sees a cat)
"My wishes are a better representation of reality than visual perception" (PA) -> "I wish there was a waterfall" -> "There is a waterfall, not a cat" (PB)

Both examples are consistent but "There is a cat" is true in the first and false in the second

P6 is saying that, since there is infinite PAs for each PB, that it is possible to determine the truth value of PB either way depending on which PA you choose. (Essentially postmodernism)


The only way to refute this would be to find a premise B that does not need any premise A by which to determine its truth value which is just refuting P4. This is why I said I expected people to try to refute P4, it is the central premise of the whole thing.

Incorrect. One would have to accept the premise "Visual input is reliable" — khaled

So, if an average 8 year old child is asked if "there is a cup on the table" is true and s/he answers "yes" while pointing at the cup, you're saying that they do not know that the statement is true or that in order to know that they must also know what "visual input is reliable" means and believe it too?

As if knowing that that statement is true requires knowing how to do logic?

:yikes:

It's a reductio. Don't deny it. Fix it.

What a hypothetical 8-year-old believes about the existence or lack thereof of a cup on a table does not stand as proof neither for nor against the premise: "Visual input is reliable". Giving me an example of someone accepting said premise and using that as proof of the premise's truth value is absurd and logically flawed. It's like me saying: "The premise "The earth is flat" has no proof" and then you rebutting by saying "So you're telling me that if a flat-earther says the earth is flat, that he does not know that statement is true?"

I said that the premise "Visual input is reliable" is based on nothing and so, upon further examination, anyone would see that it is not necessarily a true premise. Also, the fact that you had to include "average" 8-year-old suggests that this isn't even that absurd. Ask the kid later "Do you KNOW that to be true?" once or twice and they'll start to doubt. If you want to tie truth to the beliefs of 8-year-olds then go ahead but I wouldn't do that.

As if knowing that that statement is true requires knowing how to do logic? — creativesoul

It is not known if it is not reasoned, which is why it doesn't take that long to convince a kid that external reality is fake if you're the parent you could do that. I mean, people can convince their kids that there is a giant bearded man in the sky that knows and sees everything they're doing so....

What's wrong with this argument? — khaled

It didn't mention me even once. :smile: