Where debating everything under the sun is only the beginning

Quote from: Belfrager on 2014-07-01, 15:33:49

But no one pays attention to the pre socratics these days.

Not quite true: Among other things, some pre-Socratic Greek Stoics did creditable work on what we now call the sentential calculus; that the logic of the syllogism eclipsed it is a fact of history that I think retarded both science and logic/mathematics…

(Yes, I do think that the "modern" first-order predicate calculus should have been recognized and formalized in the Middle Ages. Instead, we had to wait until 1879… )(Popper himself said this.*)

Do numbers "exist" before they are constructed? Was the square root of two (or negative one) an entity before someone considered them?
Consider π: We do really know that it is an irrational and transcendental number. (Don't we?) And that it is merely the ratio of a circle's circumference to its diameter… (Not an unusual nor certainly bizarre notion!) Why is it thus?

Have you recanted your belief in Platonic ideas, and accepted the Nominalism of common sense?

what makes the syllogism inferior and the propositional calculus superior? Specifically and at length please. And in your own words, no links to external writers thankyouverymuch.

You've tasked me severely, ersi! And insulted me and my intelligence a few times along the way, all in one post…

To begin with: Did you never wonder why I rejected the work of Algazel you steered me to?

All his arguments stopped at his dogmatic Islam, and -for him- to question or contradict Islam was proof of error.
Not much there, for me, unless I was willing to join up! I wasn't. I'm still not.
I don't accept that kind of Authority…

So, here we go:

Quote from: ersi on 2014-07-01, 20:31:10

what makes the syllogism inferior and the propositional calculus superior? Specifically and at length please. And in your own words, no links to external writers thankyouverymuch.

A combinatorial formulation of generality with the sentence connectives was unnecessary: The few (valid) modes of the syllogism were idolized as the epitome of logic…suitable for doctrinal squabbles, from received dogma; but not much else.
The focus on the terms of the syllogistic culminated in what I'd call "the logical suppositories"… But the silliness of existential import was already enough to beg for a better formalism!

(I suspect you'll dislike "my own words" but, then, you asked for them… )

The predicate calculus was that better formalism.

Donc, Il doit existre!!
Respondez, Monsieur!

To begin with: Did you never wonder why I rejected the work of Algazel you steered me to? All his arguments stopped at his dogmatic Islam, and -for him- to question or contradict Islam was proof of error.

Just a little busy work for you, ersi: Kindly recast Gödel's incompleteness theorems in your preferred formalism…

I'll wait.

I long ago gave up the search for unassailable warrants.
Those who still want (! both senses !: lack and desire…) unassailable warrants mystify me! (That is, I don't understand what they want (ask) of me. Is nodding my head whenever they speak sufficient? Repeating their particular verbal formulations? Giving them access to my bank accounts? )

Why are my personal, eccentric pronouncements not given the primacy and potency of -say- Gautama? Because no statues of me exist?

Quote from: Belfrager on 2014-07-02, 14:10:36

The Mystical experience is another form of discovering

Or as Sparta so eloquently puts it: BS!

Any thinker of your age, if he can be called a thinker, has thought things through deeply enough to be able to give, at any moment, the answers to the little baby questions I asked.

   
• Never fail to give empirical data its due.

   
• Use the best analytical tools available.

   
• Take the arguments of others at face value, and

   
• Seek the best interpretation of them.

So, you hope no one will notice that you made no attempt to recast Gödel's theorems in syllogistic logic? Okay.

What answers I've thought I had seldom stay bright! Upon further reflection, I usually feel I've failed to express my thoughts well enough or that I've let go unnoticed difficulties in their formulation that no better rendering will fix.

which seems to be yet another thing that interests you more than me

Now Gödel. To understand how to solve the seeming dilemma arising from Gödel's incompleteness theorem, [and on and on, to missing the point...]

What do you think of Pascal's Wager? I'll give my (almost) off-the-cuff: It's a futile gesture. Belief isn't a matter of choice… And sincerity can't be faked, if one's audience is God!

Structuralism is not, as I understand it, a formalism of logic. I don't consider it such, and -besides you- I doubt anyone else would.

Gödel's incompleteness theorem is itself a mathematical object!

And the logistic thesis was, prior to its (the theorem's) derivation*, considered a real(izable) possibility.

In a few summarising sentences, what did Popper say as per you?

Okay, so it used to be a problem somehow in historical literature. Whatever. It doesn't matter. I solved it

Quote from: ersi on 2014-07-01, 20:31:10

In a few summarising sentences, what did Popper say as per you?

Yes, this is fairly easy: He credited the Ionian Schools with two innovations. One, cosmological theorizing; and, two, a disputational method -- as opposed to exegesis. And he believed (well, he said he did...) that these two innovations were necessary for what we now call science.

Quote from: ersi on 2014-07-03, 10:15:08

Okay, so it used to be a problem somehow in historical literature. Whatever. It doesn't matter. I solved it

Your "proof" requires a Medieval mind-set... If it doesn't fit with "approved" texts, its details and import are negligible! Except that I think you go a bit farther: If you don't "like" it, it's unimportant...
Am I entirely wrong?

Quote from: OakdaleFTL on 2014-07-03, 16:51:51

Gödel's incompleteness theorem is itself a mathematical object!

This is exactly what I concluded in my analysis, unless you misread something again.

And the logistic thesis was, prior to its (the theorem's) derivation*, considered a real(izable) possibility.
[...]
* I chose 'derivation' so as not offend anyone with opinions about the create/discover issue...

The results that Gödel proved have been important to computer science.

OakdaleFTL said "I chose 'derivation' so as not offend anyone with opinions about the create/discover issue..."
Except that you didn't manage to circumvent the create/discover issue.

I have been thinking how this could be, and came up with this:

Being a nominalist, you probably assume that mathematical objects come into existence as someone writes about them. Similarly, you assume that prior to Gödel nobody had any clue of the coherence problem, i.e. the mathematically provable systemic incompleteness of axiomatics as demonstrated by Gödel. As per you, this issue became known only after Gödel had written about it and others had read his texts.

Let me explain again how the distinction works. There are facts, such as mathematical objects, on one side, and statements about them on the other. Gödel's theorem is a mathematical object alright […]*, but Gödel's formulation about it is a statement about the object. The object exists no matter if Gödel wrote about it or not, but Gödel's formulation is how we know what we are talking about. Got it?

Another example: When I say "dog", my word is ABOUT some dog, but the word itself is not the dog. The dog does not come into existence when I talk about it. Rather, when I mention the dog, you find out that I have discovered the dog, whereas you may have discovered the dog independently without mention. For non-nominalists, this analogy applies in case of mathematical objects equally well.

why should the first-order predicate calculus have been invented in the middle ages? What seemed to be leading up to it? What necessitated it? Or what would have been the benefits, had it been invented?

A proof of Fermat's Last Theorem exists, before anyone has created it, and -on your tack- the theorem was always true, even though it might have been false?

Wouldn't you have to say that it couldn't have been false? In that case, of what matter are mathematical proofs? Are they all-but pointless exercises, only meant to convince the recalcitrant mind of that which could and should have been merely apprehended?

You seem to conflate musings and (un-warranted) beliefs with proofs… Let's try a thought-experiment:
Can you know something that isn't true?

So, which is it? Is the theorem more like a dog or more like a "dog"? I'd want to argue, the latter…

Indeed, wouldn't you have to say that 2 + 2 = 5 is a mathematical object no less than 2 + 2 = 4 is, rather than simply saying that it is false?

Is then this mysterious realm of existence filled with objects each individually and indistinguishably privileged? In other words, the Is of predication is, indeed, the Is of existence…?

To elaborate (rather than just refer you to my shelf at the Universal Library…), we'd likely agree that "2 + 2 = 5" is false, and that "'2 + 2 = 5' is false" is true.
What we mean by the former is that 2 + 2 does not equal 5; by the latter, the same. No? How, then, to explain the discovery of "2 + 2 = 5"?

I only require that one's premises require one's conclusion; from there, we can talk about the reasons for accepting or rejecting those premises. From numerous examples, I've determined that you require others to accept your premises…

Didn't De Saussure argue that the meaning of particular words in particular languages were essentially arbitrary?

Which is to say, your "in my native language it's a strict impossibility to use 'invent' in this way. Logic and its glory can only be a discovery, not invention" is mere ignorance or subterfuge on your part: You can't claim that the distinction is not permitted, because "your" language -so far as you know- doesn't have a ready-to-hand expression for it!

How would you gain an un-impeded access [to knowledge]? Who or what were you impeded by? And why…?

Or are you content to say your language is best, mine inferior;

hence, you don't need to understand what I'm saying to refute it?

There's a reason why most mystics are hermits…

Alternatively, "because you don't know a word for it, the idea expressed is nonsense or wrong?" How is that explained, in terms of eternal, ideal objects that pre-exist linguistic expression?

Nobody's a tabula rasa. There's always something pre-existing in the image of the mind, and the new concept looks for its place somewhere and it can fit appropriately, making the mind with its images a better navigation tool in reality - or it can be proven inappropriate.

You've done an admirable job of explaining -to yourself- why and how your system is consistent, using the tools of ambiguity and unwarranted reification... That is, the terms you accept into your premises are necessary to your system but their justification is precisely and only such necessity: Coherence. But because of how you'd use them their meanings shift about, will-he, nil-he: So, your system's coherence is an illusion.