4 ms·
"The truths of mathematics would be the same, because they're true by definition" means that "(x => y) AND x" means y is true based on the definition of => and
by jsbg 4y ago
"The truths of mathematics would be the same, because they're true by definition" means that "(x => y) AND x" means y is true based on the definition of => and AND. There's no "philosophy" behind this.
- lupire 4y agoWhy would aliens have the same definitions? Your AND maybe wouldn't exist to them. They could have a more statistical/global non-binary/discrete mathematics.
- vecter 4y agoI assume that PG was talking about "intelligent" aliens, which, for the sake of argument, let's say are those capable of interstellar communication (building radio telescopes and whatnot). I cannot fathom such a civilization not having discovered Boolean logic.
- wizofaus 4y agoI don't see why it's so absurd to think another alien species could develop interstellar communication without even being sentient in the way we understand it at all, or at least have anything like the level of abstract self-awareness that humans do. They may just experience something more equivalent to "emotional" reactions when attempting to manipulate the natural world to create technology in such a way that it guides them towards a successful outcome. Indeed comprehending Boolean logic seems no more necessary for that than it is for a dog in order to understand that when something in front of them is person 1 OR person 2, AND that certain sounds are coming from that person, they should sit.
- vecter 4y agoYou're right about dogs, but dogs cannot build radio telescopes so I don't understand the point. To be capable of interstellar communication, you have to be able to build machines, and doing so requires a systematic engineering culture and understanding of at least basic principles. To put it differently, do you think such an advanced civilization would not be able to do something as simple as calculus, which would be far more advanced than manipulating a basic truth table? They almost certainly won't do it in any language that we understand on Earth, but they'll be manipulating and reasoning about the same concepts.
- wizofaus 4y agoI honestly don't know, but I do think it's dangerous to assume an alien mind capable of interstellar communication would "think" sufficiently like human brains do for abstract concepts like calculus to be necessary or even make sense.
- vecter 4y agoThey would have to have developed calculus in order to build radio telescopes. We're not talking about how they think, we're talking about their understanding of concepts. These concepts are all hard prerequisites to being a species that can communicate across the stars.
- wizofaus 4y agoBut what does "understanding of a concept" mean if you have no idea how they think? And I disagree, I reckon even as humans we could come up with ways we might be able to build a device able to send radio signals interstellar distances without even having any real understanding of how it works. After all, beings as complex as ourselves came into existence via mechanisms that didn't involve, as far as we know, any sort of sentient understanding of the concepts of natural selection or basic laws of physics/chemistry/biology that you might think would be "hard prerequisites" for an ecosystem that can generate such an outcome. If there were a high selective pressure for the ability to transmit long-distance radio signals, do you really think natural selection could never have led to species natively capable of doing so?