What are the limits to the capability of the logical process?

[geordief]

Can it reasonably  be said that the  main limit is that logic can only show a negative and never a positive?

If so are there any other limits?(computing capacity for one?)

[Genady]

I need a clarification. I can logically show that for any prime number there exists a greater prime number. Is it a negative or a positive?

Edited December 29, 2021 by Genady

[studiot]

51 minutes ago, geordief said:

Can it reasonably  be said that the  main limit is that logic can only show a negative and never a positive?

If so are there any other limits?(computing capacity for one?)

You are actually asking about two different things.

'Computability' and 'Logic'.

In the UK the definitive books is

https://www.amazon.co.uk/Computability-Logic-Fifth-George-Boolos/dp/0521701465

(Boolos is the principal author)

Earlier editions can be had for a few quid.

[geordief]

3 hours ago, studiot said:

You are actually asking about two different things.

'Computability' and 'Logic'.

In the UK the definitive books is

https://www.amazon.co.uk/Computability-Logic-Fifth-George-Boolos/dp/0521701465

(Boolos is the principal author)

Earlier editions can be had for a few quid.

Thanks ,but I have an aversion to computer studies

 

I only mentioned computing because it seems to be joined at the hip with the concept of logic.

 

I have come across the idea that there are some questions (or problems)that could only be answered if the universe was converted into a giant computer 

[exchemist]

4 hours ago, geordief said:

Can it reasonably  be said that the  main limit is that logic can only show a negative and never a positive?

If so are there any other limits?(computing capacity for one?)

I thought logic mainly returned values of "true" or "false" rather than +ve or -ve. But then there is fuzzy logic............. 

[geordief]

20 minutes ago, exchemist said:

I thought logic mainly returned values of "true" or "false" rather than +ve or -ve. But then there is fuzzy logic............. 

Oh ,I see positive could be false and negative could be true(that it?)

Or would positive/negative be neither true nor false?

Already out of my depth  ,but (perhaps off topic) is there any relationship I wonder between fuzzy logic and quantum  computing?

 

Fuzzy logic sounds to me like software and quantum computing like hardware.

Would they be well suited if so?

Edited December 29, 2021 by geordief

[Genady]

5 minutes ago, geordief said:

is there any relationship I wonder between fuzzy logic and quantum  computing?

No.

[exchemist]

11 hours ago, geordief said:

Oh ,I see positive could be false and negative could be true(that it?)

Or would positive/negative be neither true nor false?

Already out of my depth  ,but (perhaps off topic) is there any relationship I wonder between fuzzy logic and quantum  computing?

 

Fuzzy logic sounds to me like software and quantum computing like hardware.

Would they be well suited if so?

No. True and false conclusions derive from testing a proposition against given information. There is nothing necessarily  +ve or -ve about that.

As for fuzzy computing, I know essentially nothing about this but my very limited understanding is that it is designed for situations in which the information supplied is not definitive, or is expressed in terms of a range, e.g. of probability, and returns an answer that is similarly expressed as a range e.g of probability, rather than a "black or white", true or false result. 

Quantum computing is something else entirely. I gather it is to do with faster speeds and miniaturisation (hence greater computing "power"), rather than any different logic.  

[Genady]

1 hour ago, exchemist said:

Quantum computing is ... to do with faster speeds and miniaturisation (hence greater computing "power"), rather than any different logic.  

Yes, quantum computation is based on a different logic. The foundation for it is quantum entanglement, which cannot be implemented using usual logic in principle. Thus, it allows to run completely different kind of algorithms. For some problems these algorithms are orders of magnitude shorter than the ones based on usual logic. This is where the quantum computing advantages come from rather than just speed and miniaturization.

[swansont]

2 hours ago, exchemist said:

Quantum computing is something else entirely. I gather it is to do with faster speeds and miniaturisation (hence greater computing "power"), rather than any different logic.  

Not based on miniaturization, either. While we’re not quite retracing the “computer the size of a room” steps, the devices, the size of early devices is big compared to the number of qubits. Size reduction is ongoing, but these aren’t at the “chips on a board” stage.

18 hours ago, geordief said:

Can it reasonably  be said that the  main limit is that logic can only show a negative and never a positive?

What kind of logic? Formal logic? Informal? Boolean?

[geordief]

34 minutes ago, swansont said:

 

What kind of logic? Formal logic? Informal? Boolean?

I had ,,hopefully a layman's idea of formal logic

Can it be viewed as there being one kind of logic that begets other kinds?

One logic "to rule them all" so to speak or are you perhaps going to say that all we have is models?

[dimreepr]

54 minutes ago, geordief said:

Can it be viewed as there being one kind of logic that begets other kinds?

Not if you want to be logical.

3 minutes ago, dimreepr said:

Not if you want to be logical.

Fuzzy logic, is just a third choice...

[studiot]

16 hours ago, geordief said:

Thanks ,but I have an aversion to computer studies

Computability is a branch of Mathematics, it is not about IT in general or any sort of 'Computer Engineering'

Note that not all computing technology is based on 'logical systems', there are for instance such things as analogue computers which work on entirely different principles.
 

Swansont has probably the most relevant comment

1 hour ago, swansont said:

What kind of logic? Formal logic? Informal? Boolean?

There is a heirarchy of systems of logic, known as First Order, Second Order and so on.

The most commonly referred to is First Order Logic which basically corresponds to the popular idea of systems based on black and white, one or zero, high voltage or low voltage, True or False... etc.

Associated with FOL is something called 'The Law of the Excluded Middle'

This declares that every possible result is either  a 1 or a zero or whatever.
Or as the name suggests there is no middle or third option.

This works very well for logical systems that can be broken down into simple enough parts.
But many systems have compound situations and FOL can fial in these cases leading to such paradoxes as

"Nick the Greek says that all Greeks are liars"

Second Order Logic dispenses with the Law and can overcome these paradoxes.

But there are many other variatios of the theme, both in the 'hardware' (physical implementation) and the 'software' (rules) of logical systems.

[Agent Smith]

As pertains to logic/rationality

Positives

1. Explosion of knowledge (most prominent in the sciences).

2. Systematization, generally, leading to more productivity in anything we do.

Negatives

1. Wars still prevalent (failure of rationality, assuming to take up arms is always illogical)

2. The correlation coefficient between logic/rationality and goodness is zeroish. There are as many intelligent people who are good as there are intelligent people who are bad. 

[Phi for All]

3 hours ago, Agent Smith said:

As pertains to logic/rationality

On 12/30/2021 at 5:59 AM, geordief said:

I had ,,hopefully a layman's idea of formal logic

The OP wants to discuss formal logic. What you're commenting on is more like "reasonableness", or "things that make sense to me". 

[Agent Smith]

2 minutes ago, Phi for All said:

The OP wants to discuss formal logic. What you're commenting on is more like "reasonableness", or "things that make sense to me". 

Reasonableness, things that make sense (to me/you), are endpoints of (formal) logic (applied). That's what I think anyway. I could be wrong though. Point noted nevertheless. Thank you. 🙂

Edited February 16, 2022 by Agent Smith

[Phi for All]

1 minute ago, Agent Smith said:

I could be wrong though.

You are, but I blame Mr Spock from Star Trek. He never used formal logic, but he became synonymous with the word "logical", and now whole generations are using a bad definition.

[Agent Smith]

On 12/29/2021 at 11:22 PM, geordief said:

Can it reasonably  be said that the  main limit is that logic can only show a negative and never a positive?

Yes, if you're talking about abductive reasoning/argument to the best explanation.

Given some info in re a particular situation/circumstance, one generates multiple hypothesis that fit with the info.

However, one can't know which hypothesis is the correct one since all square with the info.

That said, the hypotheses in question may entail certain observables. When these are not found, the set of hypotheses that entail these observables is considered falsified. 

2 minutes ago, Phi for All said:

You are, but I blame Mr Spock from Star Trek. He never used formal logic, but he became synonymous with the word "logical", and now whole generations are using a bad definition.

Sorry then for the poor quality post. I hope it isn't a big deal.

When I make mistakes or when others do, I comfort myself/others by saying "Even Aristotle (the father of logic) made mistakes."

I like Mr. Spock! I read up on him and it seems Leonard Nimoy became so deeply involved in the character of Spock that, on many occasions where he had to make (tough) decisions, he used to ask himself "what would Spock do?" 😁