What is the connection between Logic and Certainty?

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Reply Sat 10 Apr, 2010 03:35 pm
I am new to Logic, but I am a fan. I took an introductory Logic course and I remember my professor saying two things are certain, Logic and Mathematics even more than Science. He said something about it being a complete system. I should of paid more attention. Does anyone know the connection between Logic and certainty? Is Logic certain?
 
kennethamy
 
Reply Sat 10 Apr, 2010 03:46 pm
@Blackphilo-relig,
Blackphilo-relig;150352 wrote:
I am new to Logic, but I am a fan. I took an introductory Logic course and I remember my professor saying two things are certain, Logic and Mathematics even more than Science. He said something about it being a complete system. I should of paid more attention. Does anyone know the connection between Logic and certainty? Is Logic certain?


Only in this sense: if the premises of a (deductive) argument are true, and the argument is valid (the conclusion follows from the premises) then it is certain that the conclusion is true. That is because validity is defined as such a relation between the premises and conclusion of an argument that it is impossible for a valid argument to have true premises and a false conclusion.
 
Fil Albuquerque
 
Reply Sat 10 Apr, 2010 03:52 pm
@Blackphilo-relig,
Blackphilo-relig;150352 wrote:
I am new to Logic, but I am a fan. I took an introductory Logic course and I remember my professor saying two things are certain, Logic and Mathematics even more than Science. He said something about it being a complete system. I should of paid more attention. Does anyone know the connection between Logic and certainty? Is Logic certain?


Faith in the premisses and faith in the conclusion when it comes to put it in practical terms...
I wish you teacher knew more on the foundations on mathematics, he would probably be disenchanted with it...

YouTube - BBC-Dangerous Knowledge (Part 1-10)
 
Reconstructo
 
Reply Sat 10 Apr, 2010 04:00 pm
@Blackphilo-relig,
Blackphilo-relig;150352 wrote:
I am new to Logic, but I am a fan. I took an introductory Logic course and I remember my professor saying two things are certain, Logic and Mathematics even more than Science. He said something about it being a complete system. I should of paid more attention. Does anyone know the connection between Logic and certainty? Is Logic certain?



Logic is certain, but that's because logic is tautology, or truism. The problem is connecting the closed tautological aspect to living language/experience, which is not similarly closed. You would probably love this book. I know I do. It tackles exactly such issues, and issues like the self and causality as well.

This is a free download of one of the great philosophical books of the 20th century. I hope you check it out.
Tractatus Logico-Philosophicus by Ludwig Wittgenstein - Project Gutenberg
 
kennethamy
 
Reply Sat 10 Apr, 2010 04:05 pm
@Reconstructo,
Reconstructo;150360 wrote:
Logic is certain, but that's because logic is tautology, or truism. The problem is connecting the closed tautological aspect to living language/experience, which is not similarly closed. You would probably love this book. I know I do. It tackles exactly such issues, and issues like the self and causality as well.

This is a free download of one of the great philosophical books of the 20th century. I hope you check it out.
Tractatus Logico-Philosophicus by Ludwig Wittgenstein - Project Gutenberg


"Logic is a tautology" is false, if it makes any sense at all. That is because only propositions are tautologies, and logic is not a proposition. Therefore, logic cannot be a tautology. It might be that you want to say that the propositions of logic are tautologies, and that is a different matter. But I think that is what Wittgenstein said. He certainly did not say that logic is a tautology, since that is nonsense.

It is not clear what it means to say that anything but persons are certain about something. Tautologies are necessary truths, but what does it mean to say that all necessary truths are certain? I don't know. Do you? Did Wittgenstein say that all tautologies are certain. I bet he did not.
 
Fil Albuquerque
 
Reply Sat 10 Apr, 2010 04:08 pm
@kennethamy,
kennethamy;150362 wrote:
"Logic is a tautology" is false, if it makes any sense at all. That is because only propositions are tautologies, and logic is not a proposition. Therefore, logic cannot be a tautology.

It is not clear what it means to say that anything but persons are certain about something. Tautologies are necessary truths, but what does it mean to say that all necessary truths are certain? I don't know. Do you?


Logic without propositions is like time without space or movement, empty !
 
Owen phil
 
Reply Sun 11 Apr, 2010 07:51 am
@kennethamy,
kennethamy;150362 wrote:
"Logic is a tautology" is false, if it makes any sense at all. That is because only propositions are tautologies, and logic is not a proposition. Therefore, logic cannot be a tautology. It might be that you want to say that the propositions of logic are tautologies, and that is a different matter. But I think that is what Wittgenstein said. He certainly did not say that logic is a tautology, since that is nonsense.

It is not clear what it means to say that anything but persons are certain about something. Tautologies are necessary truths, but what does it mean to say that all necessary truths are certain? I don't know. Do you? Did Wittgenstein say that all tautologies are certain. I bet he did not.


Tractatus:
4.464 A tautology's truth is certain, a proposition's possible, a contradiction's impossible. ...

5.525 ...The certainty, possibility, or impossibility of a situation is not expressed by a proposition, but by an expression's being a tautology, a proposition with sense, or a contradiction. ...
 
kennethamy
 
Reply Sun 11 Apr, 2010 08:52 am
@Owen phil,
Owen;150524 wrote:
Tractatus:
4.464 A tautology's truth is certain, a proposition's possible, a contradiction's impossible. ...

5.525 ...The certainty, possibility, or impossibility of a situation is not expressed by a proposition, but by an expression's being a tautology, a proposition with sense, or a contradiction. ...


Yes, I agree he wrote it. But what he must have meant is not that tautologies are certain, but that people can be certain that tautologies are true. The former makes no sense. At least, I hope he meant that. Tautologies are necessary truths, of course, and I suppose that we can be certain the necessary truths are true.
 
Owen phil
 
Reply Sun 11 Apr, 2010 09:25 am
@kennethamy,
kennethamy;150530 wrote:
Yes, I agree he wrote it. But what he must have meant is not that tautologies are certain, but that people can be certain that tautologies are true. The former makes no sense. At least, I hope he meant that. Tautologies are necessary truths, of course, and I suppose that we can be certain the necessary truths are true.


imo,
Within classical logic...
Necessary truths are true, is necessary.
Necessary truths are true, is tautologous.
Necessary truths are true, is certain.
I can be certain that tautologies are true, within the system of classical logic.
All of truth is relative to the system that decides it.
What is tautologous for one system of decision may well be false in another system.

There is no absolute certainty.
Relative to classical logic, certainty is tautology.
eg. It is certainly true that (p v ~p) is tautologous.
It is certainly true that (p v ~p) is necessary
It is certainly true that (p v ~p) is certain.
 
kennethamy
 
Reply Sun 11 Apr, 2010 09:36 am
@Owen phil,
Owen;150537 wrote:
imo,
Within classical logic...
Necessary truths are true, is necessary.
Necessary truths are true, is tautologous.
Necessary truths are true, is certain.
I can be certain that tautologies are true, within the system of classical logic.
All of truth is relative to the system that decides it.
What is tautologous for one system of decision may well be false in another system.

There is no absolute certainty.
Relative to classical logic, certainty is tautology.
eg. It is certainly true that (p v ~p) is tautologous.
It is certainly true that (p v ~p) is necessary
It is certainly true that (p v ~p) is certain.


Yes. Of course the terms, "necessary" and "certain" are often confused with one another in ordinary talk. But philosophers should avoid that confusion. For example, although it is necessarily true that, (p v ~p) is tautologous, that means that we can be certain that, (p v ~p) is tautologous (given that we are always certain of necessary truths-another topic) but that does not mean that necessary truths are certain. I fact, that seems to be a category mistake.
 
metacristi
 
Reply Sun 11 Apr, 2010 10:09 am
@Reconstructo,
Reconstructo;150360 wrote:


This is a free download of one of the great philosophical books of the 20th century. I hope you check it out.
Tractatus Logico-Philosophicus by Ludwig Wittgenstein - Project Gutenberg



Is it? Some would argue (on very good reasons) that the Tractatus is not at all great and verificationism a resounding failure. I certainly prefer Wittgenstein's later theory of meaning...Anyway I agree that in the past there were many who argued in that direction (and that Wittgenstein was a genius): in 1929 G.E. Moore (who conducted the examination of Wittgenstein when he applied for his Ph.D in Cambridge with Tractatus) it is reported to have said that 'it is my personal opinion that Mr. Wittgenstein's thesis is a work of genius; but, be that as it may it is certainly well up to the standards required for the Cambridge Degree of Doctor in Philosophy'...Even if his Tractatus was finally demolished his fellow intellectuals still regarded him as a genius (well not all): indeed his later theory of meaning is very influential even today (though it is said that Russell did not derive any enlightenment from reading 'Philosophical Investigations').
 
kennethamy
 
Reply Sun 11 Apr, 2010 10:22 am
@metacristi,
metacristi;150544 wrote:
Is it? Some would argue (on very good reasons) that the Tractatus is not at all great and verificationism a resounding failure. I certainly prefer Wittgenstein's later theory of meaning...Anyway I agree that in the past there were many who argued in that direction (and that Wittgenstein was a genius): in 1929 G.E. Moore (who conducted the examination of Wittgenstein when he applied for his Ph.D in Cambridge with Tractatus) it is reported to have said that 'it is my personal opinion that Mr. Wittgenstein's thesis is a work of genius; but, be that as it may it is certainly well up to the standards required for the Cambridge Degree of Doctor in Philosophy'...Even if his Tractatus was finally demolished his fellow intellectuals still regarded him as a genius (well not all): indeed his later theory of meaning is very influential even today (though it is said that Russell did not derive any enlightenment from reading 'Philosophical Investigations').


Many philosophical works are wrong through and through, but are great for other reasons than their truth. Descartes' Meditations, Plato's Republic, Aquinas's Summas, all immediately spring to mind. I am sure we can think of many more.
 
jack phil
 
Reply Sun 11 Apr, 2010 01:37 pm
@Blackphilo-relig,
I have been thinking about Kennethamy's point: namely, I said tautologies were certain, and he rather prefers what W said, that the truth of tautologies is certain.

1. The truth of tautologies is certain
2. Tautologies are certain (of their truth)

Maybe I am too detached from logic. Is it plain to see that these props say different things?

That damn "is"...

> & =
 
kennethamy
 
Reply Sun 11 Apr, 2010 02:04 pm
@jack phil,
jack;150572 wrote:
I have been thinking about Kennethamy's point: namely, I said tautologies were certain, and he rather prefers what W said, that the truth of tautologies is certain.

1. The truth of tautologies is certain
2. Tautologies are certain (of their truth)

Maybe I am too detached from logic. Is it plain to see that these props say different things?

That damn "is"...

> & =


What I said was that it is people who can be certain or not certain. To say that tautologies are certain is just short of saying that people are certain about tautologies. 2. above, really makes no sense, since tautologies are propositions, and how can proposition be certain of anything? It would be like saying that a chair was certain. It hasn't anything to do with "is".
 
Reconstructo
 
Reply Sun 11 Apr, 2010 03:15 pm
@metacristi,
metacristi;150544 wrote:
Is it? Some would argue (on very good reasons) that the Tractatus is not at all great and verificationism a resounding failure. I certainly prefer Wittgenstein's later theory of meaning...Anyway I agree that in the past there were many who argued in that direction (and that Wittgenstein was a genius): in 1929 G.E. Moore (who conducted the examination of Wittgenstein when he applied for his Ph.D in Cambridge with Tractatus) it is reported to have said that 'it is my personal opinion that Mr. Wittgenstein's thesis is a work of genius; but, be that as it may it is certainly well up to the standards required for the Cambridge Degree of Doctor in Philosophy'...Even if his Tractatus was finally demolished his fellow intellectuals still regarded him as a genius (well not all): indeed his later theory of meaning is very influential even today (though it is said that Russell did not derive any enlightenment from reading 'Philosophical Investigations').


Did you read it? And did you like it? I know of certain opinions this way and that way, but I also think it has largely been misunderstood. I'm a fan of Rorty, and I think Rorty, for all his wit, missed much of its genius. Wittgenstein is a master of understatement and implication.

Please tell me you have read it, and are not just repeating hearsay. Smile
 
metacristi
 
Reply Mon 12 Apr, 2010 05:42 am
@Reconstructo,
Reconstructo;150596 wrote:
Did you read it? And did you like it? I know of certain opinions this way and that way, but I also think it has largely been misunderstood. I'm a fan of Rorty, and I think Rorty, for all his wit, missed much of its genius. Wittgenstein is a master of understatement and implication.

Please tell me you have read it, and are not just repeating hearsay. Smile



What makes you believe that I have to read it all? I assure you that I've read enough much philosophy of science to realize that an integral reading of Tractatus is pointless (I understand quite well its message* and why it - and its legacy, the positivist philosophy of the Vienna Circle which I know well - is untenable in many respects). My point was that philosophers should always tell people about the problems of such works as well (especially when important criticism exist).


*including Wittgenstein's defense of fideism in the Tractatus
 
kennethamy
 
Reply Mon 12 Apr, 2010 07:08 am
@metacristi,
metacristi;150783 wrote:
What makes you believe that I have to read it all? I assure you that I've read enough much philosophy of science to realize that an integral reading of Tractatus is pointless (I understand quite well its message* and why it - and its legacy, the positivist philosophy of the Vienna Circle which I know well - is untenable in many respects). My point was that philosophers should always tell people about the problems of such works as well (especially when important criticism exist).


*including Wittgenstein's defense of fideism in the Tractatus


I agree with you, but still, in the case of philosophy (as contrasted with science) a great word can be thoroughly wrong, through and through (as is the Tractatus) because it teaches us what is a mistake in philosophy, and enables us to avoid those mistakes in the future. And only the greatest philosophers make the greatest mistakes. (Descartes is another case in point, and so is Hume).

Some like the Tractatus because it is written aphoristically and sounds profound, and some think that is so cool. They value style over substance.
 
Emil
 
Reply Mon 12 Apr, 2010 07:52 am
@kennethamy,
kennethamy;150809 wrote:
I agree with you, but still, in the case of philosophy (as contrasted with science) a great word can be thoroughly wrong, through and through (as is the Tractatus) because it teaches us what is a mistake in philosophy, and enables us to avoid those mistakes in the future. And only the greatest philosophers make the greatest mistakes. (Descartes is another case in point, and so is Hume).

Some like the Tractatus because it is written aphoristically and sounds profound, and some think that is so cool. They value style over substance.


I think it is really cool. :bigsmile:
 
kennethamy
 
Reply Mon 12 Apr, 2010 08:03 am
@Emil,
Emil;150816 wrote:
I think it is really cool. :bigsmile:


But it doesn't follow that it is true. Nor, does it not matter whether or not it is true because it is cool.
 
Emil
 
Reply Mon 12 Apr, 2010 08:13 am
@kennethamy,
kennethamy;150818 wrote:
But it doesn't follow that it is true. Nor, does it not matter whether or not it is true because it is cool.


Right. (12 characters)
 
 

 
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