Post by Eugene 2.0 on Oct 31, 2020 15:04:11 GMT
1. I guess that people had been noticing many things. They could watch while an event #n was occurring, it had been causing by the cause #n. Some people saw different causes as the event reasons; some saw the events from different angles. Anyway, people could keep in mind or they could draw (e.g. all those ancient tablets we can see engraved on the pyramids or some tombs which haven't been raid yet) some tablets in which some events were matching some causes.
As you can see, these statements might be even less sane, and there could be no logic behind all that. Some probably saw the lightening when it was raining, and they could thought about a god of thunder, or kinda.
Such notifications could imply on their conclusions. So, each time e#2 and e#3 are happening together, some flames light the sky.
2. The same table can be rewrite into some induction-type mode. For these we need to count some events, or more precisely, just count all the events in some manner. And following Mr. Mill, John Stewart Mill the famous philosopher from British Empire, we may do it like this:
I. FrequencyInductive(x,y,z) = A iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, A occurs too.
II. OmitInductive(x,y,z) = B iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, B never occurs.
III. ChangingInductive(x,y,z) = Cj iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, Cj occurs too, and i = j.
IV. AnalogyInductive(x,y,z) = D1E2F3G4 ... Xn-1Yn most likely has Zn+1 iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi-1, yi occur, ζi occurs too, and the higher is n, the closer ζn+1 to Zn+1.
As you can see this method is more formalized. But we don't need to rely on this as long as there are enough of semantics. We can get rid of it for some purposes - to make it be even clearer. The Truth Tables is what can be used here.
3. Briefly, it's something like this:
Where we can see that f(x,y,z) is true iff y&z are both false. So, the answer is f(x,y,z) = ~y & ~z.
The truth tablets are more useful, because of its plainness, however, the form of just casual compareness was the first form. And induction was something that continued those comparative tablets.
| event #1 | event #2 | event #3 | consequences | consequences | consequences |
| 1 | 1 | 1 | something was happening | some saw the light | - |
| 1 | 1 | 0 | - | some said they had seen something | - |
| 1 | 0 | 1 | - | - | it was raining |
| 1 | 0 | 0 | something was happening | >> had seen something | it was raining |
| 0 | 1 | 1 | - | some saw flames | it was raining |
| 0 | 1 | 0 | something was happening | some saw a man walking backwards | - |
| 0 | 0 | 1 | - | - | it was nothing |
| 0 | 0 | 0 | something was happening | some saw a man walking forwards | - |
As you can see, these statements might be even less sane, and there could be no logic behind all that. Some probably saw the lightening when it was raining, and they could thought about a god of thunder, or kinda.
Such notifications could imply on their conclusions. So, each time e#2 and e#3 are happening together, some flames light the sky.
2. The same table can be rewrite into some induction-type mode. For these we need to count some events, or more precisely, just count all the events in some manner. And following Mr. Mill, John Stewart Mill the famous philosopher from British Empire, we may do it like this:
I. FrequencyInductive(x,y,z) = A iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, A occurs too.
II. OmitInductive(x,y,z) = B iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, B never occurs.
III. ChangingInductive(x,y,z) = Cj iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi, yi, and zi occur, Cj occurs too, and i = j.
IV. AnalogyInductive(x,y,z) = D1E2F3G4 ... Xn-1Yn most likely has Zn+1 iff in {x1, y1, z1, ...xi, yi, zi,... xn, yn, zn} each time when xi-1, yi occur, ζi occurs too, and the higher is n, the closer ζn+1 to Zn+1.
As you can see this method is more formalized. But we don't need to rely on this as long as there are enough of semantics. We can get rid of it for some purposes - to make it be even clearer. The Truth Tables is what can be used here.
3. Briefly, it's something like this:
| x | y | z | f(x,y,z) |
| T | T | T | F |
| T | T | F | F |
| T | F | T | F |
| T | F | F | T |
| F | T | T | F |
| F | T | F | F |
| F | F | T | F |
| F | F | F | T |
Where we can see that f(x,y,z) is true iff y&z are both false. So, the answer is f(x,y,z) = ~y & ~z.
The truth tablets are more useful, because of its plainness, however, the form of just casual compareness was the first form. And induction was something that continued those comparative tablets.