u/confusus_animus

If for an single object A the implication that all ravens are black (∀R(x) -> B(x)) is true, that doesn't support that implication - as Hume brought forward.
However Popper now claims that if the implication is true in one case it can at least falsify the opposite implication: in this example it would falsify the hypothesis that all ravens are non black (∀R(x) -> !B(x)).
However, couldn't you now falsify the opposite hypothesis by observing an object B, for which the complementary hypothesis (∀!B(x) -> !R(x)) is true? In this case: for a non black object that is non raven, the hypothesis that all raven are black is also true. But because the one time validation of this hypothesis also falsifies the opposite hypothesis, a non black object that is non raven falsifies the hypothesis that all ravens are non black.
Here's the summary:

1. ∀R(x) -> B(x) The one time observation of (1.) doesn't validate or support it but falsifies this implication:
2. ∀R(x) -> !B(x) But that means that an observation of the complementary implication of (1.) looking like this:
3. ∀!B(x) -> !R(x) falsifies 2., which is counterintuitive.

Am I missing something, and/or are there articles on the application of the raven paradox on falsificationism?

I'd love to visit UNAM for one or two semesters as an exchange student, but unfortunately my uni doesn't have an agreement with UNAM. Is it still possible to go to UNAM as a "freemover"? If you yourself or someone you know went to UNAM as an exchange student, I would love to know how that went out! Is it a lot of hassle to organize? How hard is it to get accepted? Are there any other important points to consider?

Thanks for your insights :)

The idea is to search for the highest number of the unsorted array, and then to create an 2d-Array, whose length equals the highest number. Afterwards all items of the unsorted array are placed in the sorted array into the place with the index that equals their number.

So every 0 is placed into the first array of the sorted array, every 2 is placed in the third array of the sorted array, every highest number is placed in the last array of the sorted array.

In the end an array, that may look like this: [[0,0],[],[1],[],[2], [4,4,4]], will be compiled into a proper 1-d array (in this case: [0,0,1,2,4,4,4]).

Therefore the sorting algorithm has a time complexity of O(n).

Here’s the python code:

import time
import numpy as np

start = time.time()

def proto_sort(arr):
    highest_value = 0
    for item in arr:
        if item > highest_value:
            highest_value = item
    sorted_arr = [[]] * (highest_value + 1)
    for num in arr:
        sorted_arr[num] = sorted_arr[num] + [num]

    output_arr = [None] * len(arr)
    num = 0
    for item in sorted_arr:
        for j in item:
            if j != None:
                output_arr[num] = j
                num += 1


arr = []
for i in range(100):
    arr.append(np.random.randint(0, 100))
sorted_arr = proto_sort(arr)
end = time.time()
print(end - start)

However at least in my tests, counting sort is always better - the space complexity just isn't good (I just wanted to share the idea) (Edits for clarification)

Do you know per chance an algorithm with a similar approach?

Goodman claims that induction cannot be justified, as the observation of a given object at a specific point in time (t0) leads to the confirmation of contradicting hypotheses.
To support his claim, he brings the following statements forward:

• Hypothesis 0: an object is green when it's observed at t0 (and afterwards stays green).
• Hypothesis 1: an object is grue when it's observed at t0 (meaning that it's green during observation, but afterwards will change its colour to red). If we now observe an object at t0, both H0 and H1 are supported, even though they exclude each other in their predictions about the future. So, he essentially says that we can't predict the future by observing the present.

However, I argue that that's exactly what Hume meant when he said that the sun rising tomorrow doesn't allow for any prediction about what will happen afterwards. It could be that the sun will rise blinking, fading, or not at all. So the only difference between Goodman and Hume's argument is that Goodman gives these predictions their own adjectives.
To illustrate that, one could describe Hume's problem with sunrises in a Goodman way of giving the different hypotheses words:

• Hypothesis 0: the sun is a reliable object when it rises tomorrow (and will rise the next day).
• Hypothesis 1: the sun is an unreliable object when it rises tomorrow, but won't rise the next day. Now, observing the sun rising tomorrow will confirm the sun as a reliable and as an unreliable object at the same time. Therefore, Goodmans argument seems to me as a complicated way of explaining Hume.

That's why I don't consider Goodmans New Riddle of Induction as new, or am I missing something? And do you know, per chance, an article that argues in this way?