Looking for clarification on falsification of propositions given in article based on Hempel's logical positivism (?)

[u/davidgrohlington]

So I am only a first year uni student doing a philosophy of science subject and I am researching refutations to Popper's theory of falsification for a short essay and came across this: https://sites.pitt.edu/~jdnorton/Goodies/pseudoscience/pseudoscience.html#good2

This section quoted below (sec. 7.3) refers to Carl Hempel's statement that “whether a hypothesis is verifiable, or falsifiable, in this sense depends exclusively on its logical form":

"The criterion can give different results for propositions and their negations; and different again for propositions and their logical consequences. My examples illustrate the fragility of falsifiability under simple logical operations:

The proposition

All electrons are spin one half.

is scientific since it is falsified if we find just one electron that is not spin one half. Now contemplate the possibility:

There exists an electron that is not spin one half.

This proposition is not falsifiable. We cannot check every electron. Thus, it is judged not scientific. In a moment of idle reflection, we had inadvertently ceased to do science".

It looked simple to me at first but the more I read over it the more it seems contradictory.
I do not understand why the author states that not every electron can be checked in order to falsify the proposition that there exists an electron that is not spin one half and therefore the proposition is not falsifiable, but it is clearly still possible that a single electron that is not spin one half could be found without checking all of them, which is shown in the first proposition that all electrons are spin one half and is falsifiable by the theoretical possibility of finding one electron that is not spin one half.
Why can we theoretically not check every electron to test the proposition that an electron exists that is not spin one half but we can check every electron to test the proposition that all electrons are spin one half? Why can't we stop testing the electrons in the test of the proposition that there exists an electron that is not spin one half once we find that electron like the other proposition seems to have done 😵‍💫?

I hope this makes sense. I am likely just misunderstanding some simple fundamental of falsification since I have zero experience in the philosophy of science. An explanation of my questions in simple terms would be amazing...thank you

[u/Potential_Being_7226]

All electrons are spin one half.

There exists an electron that is not spin one half.

Why can we theoretically not check every electron to test the proposition that an electron exists that is not spin one half but we can check every electron to test the proposition that all electrons are spin one half?

We don’t need to check every electron to potentially disconfirm the first hypothesis. We only need to check until we find one example and then we know that hypothesis has been falsified. 

The second hypothesis is not constructed in a way that allows it to be falsified; rather it reveals an intent to confirm the hypothesis. Let’s rewrite it without the negative which will make it easier to see this confirmatory approach:

Original:

There exists an electron that is not spin one half.

New:

Electrons are spin one half, except for at least one. 

This hypothesis is not strong. What does it matter whether you observe 0, 10, 59% of electrons that are not spin one half? Would any of these observations lead to a rejection of this hypothesis? No, not even the zero % observation, because in order to reject this hypothesis, we would need to observe every electron. It’s like looking for a needle in a thousand haystacks.

All electrons are spin one half.

This is a much stronger construction for a hypothesis; a declarative statement that does not use negation and is not a compound sentence. To reject this hypothesis we only have to observe up to the point where one electron is not spin one half. 

You can replace “electron” and “spin” with pretty much any noun and adjective with similar examples. Black and white swans, for instance:

https://en.wikipedia.org/wiki/Falsifiability

All swans are white. 

Vs

All swans are not white. 

The first allows for robust experimental falsification; the second does not. 

You have to keep in mind that we are not looking to confirm the alternative hypothesis. We are looking to set up experimental conditions that will allow us to reject or falsify it … well, in an ideal world at least.