What is logic?
aeon.co
What is logic?
1–10 of 67 posts
Re: What is logic?
#2"The idea that ordinary language is expressively inadequate to account for mathematical (or even logical) reasoning became a recurring theme in the ensuing tradition of mathematical logic, so much so that the term ‘symbolic logic’ became synonymous with this tradition. Doing logic came to mean simply working with special symbols, not with ordinary words. In this respect, it is worth noting that the humanist authors had criticised the Latin of scholastic logicians precisely as ‘too artificial’, and even the Greek language that Aristotle relies on for syllogistic logic is regimented and removed from ordinary ways of speaking at the time. In a sense, perhaps a certain degree of ‘artificiality’ is at the core of logic throughout history, as it operates at levels of abstraction that are at odds with ordinary language usage."
True that, but were/are there alternatives? Difficult to say.
Re: What is logic?
#3From what I know, pure logic or even math are useless without assumptions. This is what reason and science give us: a standard set of axioms from which logic and math can lead us to useful conclusions.
Re: What is logic?
#4A set of general rules for not losing a connection to reality.
Could be used in reasoning or computer programming.
Re: What is logic?
#5From what I know, pure logic or even math are useless without assumptions. This is what reason and science give us: a standard set of axioms from which logic and math can lead us to useful conclusions.
Didn't it take some guy like 200 pages to prove logically that 2+2=4?
Re: What is logic?
#6From what I know, pure logic or even math are useless without assumptions. This is what reason and science give us: a standard set of axioms from which logic and math can lead us to useful conclusions.
But isn't reason is the result of logic? as in something is reasonable only when it is logically sound?
Re: What is logic?
#7"We just don't know"
Re: What is logic?
#8From what I know, pure logic or even math are useless without assumptions. This is what reason and science give us: a standard set of axioms from which logic and math can lead us to useful conclusions.
Where can I find this standard set of axioms?
Re: What is logic?
#9"The idea that ordinary language is expressively inadequate to account for mathematical (or even logical) reasoning became a recurring theme in the ensuing tradition of mathematical logic, so much so that the term ‘symbolic logic’ became synonymous with this tradition. Doing logic came to mean simply working with special symbols, not with ordinary words. In this respect, it is worth noting that the humanist authors h…
> In a sense, perhaps a certain degree of ‘artificiality’ is at the core of logic throughout history, as it operates at levels of abstraction that are at odds with ordinary language usage
Of course, you could say the exact same thing for programming languages (after all, what do programmers do if not "simply working with special symbols, not with ordinary words"? And isn't this the primary criticism of programming brought by people who find it distasteful -- that expressing their fuzzy intuitions in a precise enough manner for the computer feels like a pointless exercise in frustration?)
Really, the only difference between the proponents of mathematical logic over informal prose in the early 20th century and the proponents of programming languages over informal prose today is that computers obviate the problem with fuzzy thinking and fuzzier exposition. The philosopher or mathematician could hand-wave about their holes in their arguments, but the programmer can only hand-wave so much the uselessness of his unexecutable pseudo-code.
The golden standard would be a form of speech that is natural and ordinary, but also avoids misleading, omitting, and eliding essential details.
In other words, a language that is formal enough to be parsed, checked, and generated by a proof assistant program. But also natural enough to be read as if it's prose written by a native speaker of a natural language.
I'm of the opinion that such a golden standard does not exist, and so we're forever doomed to incremental improvement.
Re: What is logic?
#10From what I know, pure logic or even math are useless without assumptions. This is what reason and science give us: a standard set of axioms from which logic and math can lead us to useful conclusions.
Where can I find this standard set of axioms?
One widely-used system is Higher Order Logic (with various extensions sometimes), one core of which you can find here: http://sourceforge.net/projects/hol/files/hol/kananaskis-10/...
This is based on type theory (and has a model in set theory), but isn't as powerful as the logics used in Coq and similar theorem provers (the Calculus of (Inductive) Constructions).
You might be interested in metamath: http://us.metamath.org/, which lists the axioms used in its largest body of work: http://us.metamath.org/mpegif/mmset.html#axioms