As a child I decided to do a philosophy course as an extracurricular activity. In it the teacher explained to us the notion of schools of philosophical thought. According to him classifying philosophers as adhering either to school A or school B, is typical for Anglo thought.
It deeply annoys me when Americans talk about Democrat and Republican political thought and suggest that you are either a Democrat or a Republican. The notion that allegiance to one political camp is supposed to dictate your political beliefs feels deeply wrong.
A lot of Anglo high schools do policy debating. The British do it a bit differently than the American but in both cases it boils down to students having to defend a certain side. Traditionally there's nearly no debating at German high schools.
When writing political essays in German school there’s a section where it's important to present your own view. Your own view isn't supposed to be one that you simply copy from another person. Good thinking is supposed to provide a sophisticated perspective on the topic that is the synthesis of arguments from different sources instead of following a single source.
That's part of the German intellectual thought has the ideal of 'Bildung'. In Anna Wierzbicka tells me that 'Bildung' is a particularly German construct and the word isn't easily translatable into other languages. The nearest English word is 'education'. 'Bildung' can also be translated as 'creation'. It's about creating a sophisticated person, that's more developed than the average person on the street who doesn't have 'Bildung'. Having 'Bildung' signals having a high status.
According to this ideal you learn about different viewpoints and then you develop a sophisticated opinion. Not having a sophisticated opinion is low class. In liberal social circles in the US a person who agrees with what the Democratic party does at every point in time would have a respectable political opinion. In German intellectual life that person would be seen as a credulous low status idiot that failed to develop a sophisticated opinion. A low status person isn't supposed to be able to fake being high status by memorizing the teacher's password.
If you ask me the political question "Do you support A or B?", my response is: "Well, I neither want A or B. There are these reasons for A, there are those reasons for B. My opinion is that we should do C which solves those problems better and takes more concerns into account." A isn’t the high status option so that I can signal status by saying that I'm in favour of A.
How does this relate to non-political opinions? In Anglo thought philosophic positions belong to different schools of thought. Members belonging to one school are supposed to fight for their school being right and being better than the other schools.
If we take the perspective of hardcore materialism, a statement like: "One of the functions of the heart is to pump blood" wouldn't be a statement that can be objectively true because it's teleology. The notion of function isn't made up of atoms.
From my perspective as a German there's little to be gained in subscribing to the hardcore materialist perspective. It makes a lot of practical sense to say that such as statement can be objectively true. I have gotten the more sophisticated view of the world, that I want to have. Not only statements that are about arrangements of atoms can be objectively true but also statements about the functions of organs. That move is high status in German intellectual discourse but it might be low status in Anglo-discourse because it can be seen as being a traitor to the school of materialism.
Of course that doesn't mean that no Anglo accepts that the above statement can be objectively true. On the margin German intellectual norms make it easier to accept the statement as being objectively true. After Hegel you might say that thesis and antithesis come together to a synthesis instead of thesis or antithesis winning the argument.
The German Wikipedia page for "continental philosophy" tells me that the term is commonly used in English philosophy. According to the German Wikipedia it's mostly used derogatorily. From the German perspective the battle between "analytic philosophy" and "continental philosophy" is not a focus of the debate. The goal isn't to decide which school is right but to develop sophisticated positions that describe the truth better than answers that you could get by memorizing the teacher's password.
One classic example of an unsophisticated position that's common in analytic philosophy is the idea that all intellectual discourse is supposed to be based on logic. In Is semiotics bullshit? PhilGoetz stumbles about a professor of semiotics who claims: "People have an extra-computational ability to make correct judgements at better-than-random probability that have no logical basis."
That's seen as a strong violation of how reasoning based on logical positivism is supposed to work. It violates the memorized teachers password. But is it true? To answer that we have to ask what 'logical basis' means. David Chapman analysis the notion of logic in Probability theory does not extend logic. In it he claims that in academic philosophical discourse the phrase logic means predicate logic.
Predicate logic can make claims such:
(a) All men are mortal.
(b) Socrates is a man.
Therefore:
(c) Socrates is mortal.
According to Chapman the key trick of predicate logic is logical quantification. That means every claim has to be able to be evaluated as true or false without looking at the context.
We want to know whether a chemical substance is safe for human use. Unfortunately our ethical review board doesn't let us test the substance on humans. Fortunately they allow us to test the substance on rats. Hurray, the rats survive.
(a) The substance is safe for rats.
(b) Rats are like humans
Therefore:
(c) The substance is safe for humans.
The problem with `Rats are like humans` is that it isn’t a claim that’s simply true or false.
The truth value of the claim depends on what conclusions you want to draw from it. Propositional calculus can only evaluate the statement as true or false and can’t judge whether it’s an appropriate analogy because that requires looking at the deeper meaning of the statement `Rats are like humans` to decide whether `Rats are like humans` in the context we care about.
Do humans sometimes make mistakes when they try to reason by analogy? Yes, they do. At the same time they also come to true conclusions by reasoning through analogy. Saying "People have an extra-computational ability to make correct judgements at better-than-random probability that have no logical basis." sounds fancy, but if we reasonably define the term logical basis as being about propositional calculus, it's true.
Does that mean that you should switch from the analytic school to the school of semiotics? No, that's not what I'm arguing. I argue that just as you shouldn't let tribalism influence yourself in politics and identify as Democrat or Republican you should keep in mind that philosophical debates, just as policy debates, are seldom one-sided.
Daring to slay another sacred cow, maybe we also shouldn't go around thinking of ourselves as Bayesian. If you are on the fence on that question, I encourage you to read David Chapman's splendid article I referenced above: Probability theory does not extend logic
I'm going to risk going down a meaningless rabbit hole here of semantic nothingness --
But I still disagree with your distinction, although I do appreciate the point you're making. I view, and think the correct way to view, the human brain as simply a special case of any other computer. You're correct that we have, as a collective species, proven and defined these abstract patterns. Yet even all these patterns are based on observations and rules of reasoning between our mind and the empirical reality. We can use our neurons to generate more sequences in a pattern, but the idea of an infinite set of numbers is only an abstraction or an appeal to something that could exist.
Similarly, a silicon computer can hold functions and mappings, but can never create an array of all numbers. They reduce down to electrical on-off switches, no matter how complex the functions are.
There is also no rule that says natural numbers or any category can't change tomorrow. Or that right outside of the farthest information set in the horizon of space available to humans, the gravitational and laws of mathematics all shift by 0.1. It is sort of nonsensical, but it's part of the view that the only difference between things that feel real and inherently distinguishable is our perception of how certain they are to continue based on prior information.
In my experience talking about this with people before, it's not the type of thing people change their mind on (not implying your view is necessarily wrong). It's a view of reality that we develop pretty foundationally, but I figured I'd write out my thoughts anyway for fun. It's also sort of a self-indulgent argument about how we perceive reality. But, hey, it's late and I'm relaxing.
I don't understand what point you're making with the computer, as we seem to be in complete agreement there. Nothing about the notion of ideals and definitions suggests that computers can't have them or their equivalent. It's obvious enough that computers can represent them, as you demonstrated with your example of natural numbers. It's obvious enough that neurons and synapses can encode these things, and that they can fire in patterned ways based on them because... well that's what neurons do, and neurons seem to be doing to bulk of the heavy lifting as f... (read more)