"cogito, ergo i erit"?

Throughout history there have been movements, and counter-movements. Eventually they settle down to a compromise. We see ample evidence of this all the way through from ancient Egypt to early 21st C western politics. Trump's presidency was self-evidently a disaster, so the Dems won control of the House at the mid-terms. Hegel's mistake was to imgine this kind of development as a mystical metaphysical progression, when it's really just human psychology.

But I accidentally posted the previous before I was ready. I was going to add that the pre-occupation with english-style prepositions may be questionable. Chinese, for example, has a different set of linguistic conventions for dealing with the prepositional context. "Dao wo zher lai" means "come to me", but does not actually contain any word which would translate directly as a preposition in English.

I'm not familiar with this context, but perhaps the fact that it was in the background, evidently unopened (since the cover was visible), implies that he was sufficiently open-minded to have read the book, rejected its ideas, and placed it behind him.

I don't think any of the comments quite addresses ucarr's point. It's true that he says "If I can say it, then I can think it". But this is not the first step in logical thinking. I think he would agree that the perception of logical connection is essentially non-verbal, and language follows later as an attempt to communicate the logical connection to others. Five million years ago, proto-humans understood that they were wet because it was raining. The ability to express this thought more or less accurately in language must have followed much later.

invizzy, I'm afraid you are really re-inventing too many wheels. Please read up on what Aristotle has to say about cause, and what subsequent philosophy (Russell and Hume, for example) has had to say on the subject.

Aristotle was great on trivial detail, hopeless on the big moral or metaphysical questions. Like Descartes, a philosophical impostor.

I think this is the issue of moral relativism versus moral absolutism. Are there any absolute, indisputable standards of morality, or is morality relative to the place and time? According to the Old Testament, if my wife is unfaithful, I should bury her up to her neck in sand, gather all my friends together with the largest rocks they can carry, and collectvely turn her head into strawberry jam. How would society deal with me, if I did that today?

I don't personally subscribe to any of the traditional systems of superstitious belief, and I follow Bertrand Russell: the good life is the life enlightened by knowledge, and guided by love.

On the other hand, irony may be defined as critical thought which rejects the tramlines of De Leuzean orthodoxy and remorselessly challenges us to reframe our ambitions and expectations in terms of a survivable compromise between social fitness and personal self-actualisation. How do you see this paradox being resolved?

Interesting idea, but can you give an example of the sort of thing you have in mind? It's fairly obvious how such an approach could be useful in a mathematical philosphy forum, for example, but how do you see it applying to areas like metaphysics or epistemology? In what way would it be superior to a simple verbal reply?

"I am studying Hegel and am struggling to understand Hegel's dialectic and his claims of objectivity"

Take heart, Bertrand Russell had the same problem.

I'm not sure that your distinction between "listening to people" and "listening to arguments" will withstand critical analysis. There is certainly a valid distinction between "listening to opinions" and "listening to reasoned arguments". Is this what you are referring to?

I'm recalling a British comedy movie of the 1950's called "The Man Who Liked Funerals". One of the characters says: "Remember the family motto: first we act, then we think!"

Your mistake is to confuse "deductive" and "inductive". Modus Ponens is a deductive argument; if A and B are indisputably true, then C follows necessarily. But if you introduce probabilities ("65% likely to be true"), it is no longer Modus Ponens; it is an argument in inductive reasoning, which is something entirely different and much more complicated!

"Thou" sayest that your post is unnecessarily confusing... this is, of course, a classic question in religious and moral philosophy: is a thing good because God likes it, or does God like it because is is good? Either answer is unacceptable.

If God likes a thing because it is good, this is tantamount to saying that the criterion of goodness is independent of God's will; consequently, God is irrelevant to the definition of moral goodness. On the other hand, if a thing is good because God likes it, then there is no fixed criterion of goodness, since God has the power to change His mind at any time; and so the criterion of goodness may change from day to day. If the good is what God likes, and God decides to "like" the massacre of infidels, then the Talibaan will become the guardians of goodness, and we should all live by their rule.

Erratum: in the opening sentence, for "science", read "scientific philosophy".

“The foundation for knowledge must be something from which we can go about doing inquiry with agreement on some propositions.”

Pure gold, but it is not clear why you think this approach is primarily "practical", and does not form the basis of ALL knowledge?

I think there is no better introductory text to the foundations of knowledge than the first half-dozen pages of Euclid's "Elements of Geometry". There you will find the whole of the Socratic/Platonic/Cartesian enterprise set out in all of its clinical purity. Definition > axiom > theorem. All else is commentary.

A big subject, indeed the biggest. I would like to advise against taking the Cartesian "Universal Doubt" as a criterion for anything. You'll have noticed that there are all sorts of things which it never occurs to Decartes to doubt; that knowledge is possible, that "truth" and "error" are absolute categories, and that other beings exist, for example. He applies his own criterion in a very partial and disingenuous way.

The Cartesian "Universal Doubt" is the Classical approach on stilts; reduce everything to the smallest possible number of indubitable propositions, and see what can be built from that. Lacking the intellectual honesty and impartial rigour of a Socrates or a Euclid, however, Descartes quickly digs himself into a hole from which only an appeal to God's goodness can rescue him. Of all the most famous and influential of philosophers, Descartes is undoubtedly the least honest and least competent.

Not sure I quite got the gist of this, but ≈137 is not guaranteed to be a rational number, because it is an approximation. The absolute value might be a real number, to which 1/137 is just the nearest rational.

I don't want to rain on a parade, but I think you would be extremely courageous to build a philosophical arguement on Cartesian Scepticism nowadays. The most destructive criticism I have come across was written by a Jesuit priest who was a lecturer at the University of Sydney (unfortunately, I'm ashamed to admit, I can't remember his name). Cartersian Scepticism appears to work only on condition you stop halfway. Descartes never doubted that truth exists, reason exists, criteria to distinguish truth from falsehood exist, and that the nature of existence is basically rational and follows logical rules, and finally - and this most telling - never doubted for a moment that God exists. Even to the lacklustre extent that he applied his "universal doubt", he relies upon God to pull him out of the logical hole he digs for himself.

What a jewel in the mud this thread is. Only three posts; an intelligent question, which attracts two intelligent answers, and no further comment really needed. If only the rest of the forum could be like this.

But not much use in proving mathematical propositions, I'm afraid.

Sorry, please wait while I gather my wool and my needles!
Although I suppose there is a mathematical aspect to the question: should justice be reducible to a strict logical formula, in the same way that all of mathematics can be reduced to a system of formal logic? And how might such a system be defined so as to allow justice to be tempered with mercy (essentially, extenuating circumstances)? Could that, in its turn, be reduced to a system of formal logic?

I think there should be more lemonics in cookery programs. Speaking for myself, I love the flavour

"If true equilibrium is reached then “push” and “shove” (the equals and opposites) are equally matched and therefore nothing actually happens."

You need to develop this point because it embodies an obvious contradiction. It cannot be the case that "nothing actually happens" if there is an interplay of opposing forces, even though the outcome might be representable as zero on some scale.

Oedipus, schmoedipus. What's it matter so long as a boy loves his mother?

Ouch!

I wish I could think of an intelligent response. Of course, there are logical similarities with Russell's Paradox and the Cretan Liar. But right now I can't think of a knock-down philosophical analysis (memo to self: ease up on the Semillon when browsing philosophy forums!)

... contributor whose intelligence is equal to my own?

Ma foi! Tamade! Oi vei! this is the second time this evening that Agent Smith has anticipated my own comment... could it be that there is another

I think Agent Smith has made the most intelligent comment in this whole dialogue. "Logic" describes a deductive or inductive system of evidence-based reasoning which leads to a definite conclusion. In the case of deductive logic, at least, the conclusion is necessary or unavoidable.

Fer chrissakes, Timothy, enrol in a Phil 100 course.

"If its any help, the "number" of points inside a cube is the same as found on one of its defining edges (lines)."

Can you develop that a bit further? Points in any continuum are infinitely many.

"If there were a finite number of things on 3 axises, could that same information be represented in a single line?"

Yes indeed. You might read up on Georg Cantor, who did a lot of work in this area.

"It wasn't until they shifted their perspective of mathematics from "truthbearer" to "useful tool" (roughly) that negative numbers started to become accepted. And for good reason, they clearly work and make mathematics more pleasant to work with."

I think this answers your own question, Jerry. What is the square root of -1? We haven't a bloody clue, so we call it "i" to disguise our ignorance. Funny thing is, engineers use "i" all the time to build suspension bridges and skyscrapers which safely carry thousands of us every day. It's just our way of recognising that the universe is cleverer than we are. We are relatively stupid beings, but (paradoxically) we are intelligent enough to discover interesting things we can't understand.

"Being able to reason in exactly the right way may be useful for some people, but not all."

Tobias, can you even hear the words which are coming out of your mouth? In what way could "wrong reasoning" possibly be useful to any human being?

I'm sorry, but isn't this supposed to be a mathematical philosophy page?

Ok,,, I am familiar with expressions like btw and imho and fyi, but I would never have guessed that "grok" means "get the picture"...!

But Sam26: it is always a tactical mistake to ask members to watch a video. Much better to summarise the argument of the video in 100-200 words, and include a link to it in your post, for those who want to pursue it in more detail. Nobody is going to invest 1.5 hours in watching a video which may or may not be relevant to their philosophical interests.

Can I take this opportunity to remind contributors that this is a mathematical page, and we are discussing polarity in the purely mathematical sense?

To return to mathematics for a moment, polarity first becomes significant when we develop the relational number line out of the natural number line. The relational number line, the line of the negative and positive numbers, is sometimes (confusingly) referred to as the "integer" line; I prefer the term "relational", because it more accurately captures what is important and interesting about this particular number line.

Whereas a natural number is the name of a set, by adding a polarity to the number, we transform it into a quantitive relation. In the context of the "relational" number line, the relation is obviously to 0; -2 points to the value which is 2 less than 0. In any other arithmetical operation, the relation -2 points to the number which is 2 less than the preceding number; so, 0 - 2 = -2, but 5 - 2 = 3.

I remember that Winifred Atwell was a wonderful piano player... or am I thinking of a different Atwell?