First principles is when you reason from fundamental axioms, everytime. It's a cognitive model that's designed to not remember a multitude of facts/observations.
Think of it as a logical framework of understanding: If you understand the essential logic of a system, you can reason from those principles. I see the cognitive model as being a true form of understanding because many people will blurt out facts that aren't based on first principles but rather inherited from others, akin to a record player repeating the same track.
We were taught to do maths from first principles.
First principles means reasoning from fundamental axioms, as you explained, which means you have to forget about the last 2500 years of maths and science, and start re-discovering everything from scratch. Not very practical.
However, if you have learned to prove things from first principles in maths, which can be done, as you are always taught the proof in maths, then if you are in an exam and you forget a formula, or a formula doesn't quite apply to an exam question, you can work it out from scratch. So it's useful, but mainly when you don't have a formula or theory.
Reasoning from first principles is longer because you have to reason every single time, however you understand the topic better and are less prone to illogical statements,
You still have to prove things from first principles. So your conclusions are dependent on the quality of your proofs, which is dependent on the level effort you make to ensure that you carefully check everything you write down for errors. Great logicians understand things better. Poor logicians understand things worse.
like hearing a doctor say "SSRIs are good" and extrapolating that point in a different context. If you understood the function of SSRIs from first principles, the function of serotonin in the body/brain and how serotonin is inhibited from being reuptaked through the body such as the heart and muscles and staying inside the brain, you can understand from principles how that would effect brain chemistry.
True. But so little was understood, and is still not understood, about the way serotonin worked in the first place, that SSRIs were notorious for having a hit & miss effect. The other issue was that the reuptake process wasn't really understood completely in terms of its indirect consequences, leading to unpredictable side-effects that differed from subject to subject, but without much being observed as similar with patients with the same side-effects. It was usually a case of being prescribed SSRI after SSRI until the patient found one worked with few side effects.
First principles isn't essentially the way an INTJ would learn, they operate like a mastermind in the few subjects they're interested in. They compound knowledge, first principles isn't compounding knowledge in layers, it's abstracting from first principles every single time.
I'm pretty sure INTJs reason from analogy, like any other person.
INTJs tend to be generalists. They like to be the "go-to guy", the guy a client will go to for ANY problem. To put it another way, INTJs describe their Ni as something that generates an answer to (almost) every question and a solution to (almost) every problem.
An INTJ once gave an example that illustrates the way INTJs think: You want a slushie. It's 2am, and all of the slushy places are closed. What do you do?
An INTJ would say "What techniques do I have for solving the problem?"
- See what you have available: There's some ice in the freezer and a blender in the kitchen.
- Think about how things are designed to work: a slushie is essentially finely crushed ice. The blender chops vegetables finely until they reach liquid consistency.
- Now think about repurposing them to achieve your goal: Now see Put the ice in the blender instead of vegetables, and you can chop up the ice finely, until it's almost crushed. Stop the blender before the slush turns into liquid, and you have a slushie.
INTPs tend to pick a subject they are interested in, and then study it to death. Then when they encounter a situation in that subject, they can pretty much do anything they want with it, as if they were an expert in the subjects they are interested in, but novices on other subjects. It can take quite a while until an INTP has built up mastery on enough subjects that they can pretty much answer how to handle most subjects.
INTPs are good disassembling logical fallacies in people's point, so they too would also be able to detect logical principalities.
Ti tends to be very good at analysing things and seeing their consequences, and their consequences' consequences, and so on. It also works incredibly fast. That makes Ti very good at proving indirect consequences of first principles.
It also means INTPs are good at applying an analogy quite consistently, and thus quite plausibly.
The standard model in particle physics is a good example where you can calculate physical interactions between atoms (with the exception of gravity) based on 32 different variables, instead of remembering 30,000 different equations for rocket propulsion, light emission and whatever have you.
First Principles isn't useful in physics, because that would require doing all 2500 years of physics, which includes millennia of scientific experiments and lots of interpretations (called theories) and interpretations of interpretations.
It's useful when you take some existing laws of physics and use mathematics to unify them, such as Maxwell's unification of the 4 laws of electricity & magnetism which predicted the existence of radio waves, and Dirac's unification of quantum mechanics and special relativity which predicted the possibility of anti-matter.
If you understand both operating systems at a fundamental level, you can reason on what is actually true.
This tends to be a problem, because most Linux programmers don't like to do much programming for Windows.
Linux is open source based on the GNU library, you can modify cfg files, different desktop environments, powerful terminal commands and create your own distro if you are so inclined
Linux was a distro of Unix made by Linus Torvalds. It was horribly difficult to operate using the GUI. You really needed the command line to do most things, which was really powerful in Unix. So you really needed to be a programmer to use Linux. But at the same time, there was extensive documentation on everything. It also came with some built-in lockouts that meant that your worst nightmare was that your user account was corrupted, in which case, you simply made a new user account. It was an OS for programmers to learn on and play with.
which you can't do in windows because it's proprietary software.
Windows was based on DOS which was based on CP/M, which provided a really basic set of instructions for loading programs for the Intel 8080, one of the early CPUs for PCs. Windows added the Windows API, a set of routines to do GUIs and other OS functions, but which again needed to be run from a program. So you could run Windows without being a programmer, but only if a programmer who knew what he was doing, set Windows up for you.
Because of that overly simplistic design, a programmer who knew what he was doing could do a ridiculous amount of things with it, but only by writing a proper program with a lot of error handling. The documentation was also incomplete, and the routines could be glitchy. So it wasn't the sort of OS you could just knock a shell script up in 20 minutes to do a backup. It was an OS where you had to write a proper program that took time, and was really only worth the effort if you were going to then distribute that backup program to a series of business machines for a fair bit of money. For the same reason, it wasn't a great machine to learn how to code on. With Windows, you learned by experience.
So Windows wasn't wasn't an OS for people learning programming. Windows was an OS that was for experienced programmers to develop on, and for clients to use.
Again, the difference is Open source vs proprietary. It is actually far more secure if you understand how to implement security features. All packages are installed from the GNU Library, compared to people writing random programs to run on windows 10 with viruses. You have to login to get root permission everytime you install an application, as soon as you leave terminal you're logged out so viruses can't execute continuously while you're using your computer. Linux isn't just one OS it's a family of OSs, classified as rolling releases (ARCH, I think Gentu is too), stability (Mint, Ubuntu LTS), Moshka Desktop (Bohdi) and of course, cornerstone debian. You can get OSs like Tails which are security driven, completely keeping all memory inside of RAM so there is no read/write function to SSD/HDD.
In Unix systems, there's a lot of built-in security functions with lots of documentation. So it's a great place to start learning about security, and quite easy to set up once you've learned how.
In Windows, the security was that you'd developed the boot routines and programmed the locks yourself, for your clients. Again, Windows was pretty good at what you did, if you'd taken the time to look through all the nooks and crannies to understand its strengths and its flaws, which would be a lot of work for one person, but not that much if you were studying it so you could figure out how to program it for an entire department.