Simon blogs

[nin10doadict]

I mean, if there aren't any frogs in the box (whether they were there to begin with or not) then that's a null reference, right? It feels to me kind of like trying to divide by 0; it's something that just doesn't work. Yeah, all frogs in the box are green, but if there aren't any frogs, then how do we know that there isn't some non-existent purple frog? I feel that the sentence loses meaning if it references something that doesn't exist.

So is it automatically implied that "If the box contains a frog, then all frogs in the box are green?" More importantly, if there are no frogs, does that make the statement "All frogs in the box are green" true or false? It appears to have entered a third state, one of "irrelevance."

[Forestidia86]

I mean, if there aren't any frogs in the box (whether they were there to begin with or not) then that's a null reference, right? It feels to me kind of like trying to divide by 0; it's something that just doesn't work. Yeah, all frogs in the box are green, but if there aren't any frogs, then how do we know that there isn't some non-existent purple frog? I feel that the sentence loses meaning if it references something that doesn't exist.

So is it automatically implied that "If the box contains a frog, then all frogs in the box are green?" More importantly, if there are no frogs, does that make the statement "All frogs in the box are green" true or false? It appears to have entered a third state, one of "irrelevance."

So you see a presupposition of existence of frogs in the box in a statement like "All frogs in the box are green" (like the ancients)?
For reference in classical modern formal logic:
If there exist no frogs in the box then sentences of this form are always true: For all x (x is a frog in the box then A), whereby A is some other formula, e.g. For all x (x is a frog in the box then x is green) but as well For all x (x is a frog in the box then x is purple). This results roughly from following principle: non-P then (P then A) or as a rule of inference: You deduce (P then A) from non-P.
This principle/rule is sometimes critizised by non-classical logicians as unintuitive.

What do you mean with third state of irrelevance? Is it a real third value or gap beyond true and false or are we only not interested in the truth value of such statements? In other ways: Can't an irrelevant statement be still true or false?
It seems actually to be kind of a corner case.

[ccexplore]

Maybe a way to illuminate the situation is to consider a third logical value of "don't know" or "not sure", and also think about how people tend to arrive at rules like "A implies B" through an iterative process of evidence gathering.

In other words, there are 3 cases concerning a statement of the form "A implies B":

1) A is true and B is true.  This is an instance of evidence supporting the statement as true.  The more examples of this case someone experiences, the more the person will become convinced that the statement is true.

2) A is true and B is false.  This is an instance of counter-evidence disproving the statement.  A single counterexample is sufficient to demonstrate the falseness of the statement.

3) A is false. B may be true or false.  This is neither evidence for nor against the statement.  These irrelevant cases have no bearing on someone's confidence on the truthfulness of the statement.

The extreme is if A is always false, like talking about a purple frog in the box when no frogs are in the box.  Then by definition, there can never be any evidence supporting the statement, but also no evidence ever to disprove it.  In classical logic we still consider the statement true.  In most people's mind though, they intuitively want truth to correspond to a preponderance of evidence, and so when no evidence exists at all, they can't be comfortable considering it true.

[Forestidia86]

3) A is false. B may be true or false.  This is neither evidence for nor against the statement.  These irrelevant cases have no bearing on someone's confidence on the truthfulness of the statement.

It's an interesting point to see conditionals in a way of verification or falsification. The classical logical principle follows then the rule that if it can't be falsified it's true. Whereas intuition from your view (as I understand it) says that only what can be verified (or falsified) can be true. This is a very demanding view of truth which combines truth with the possibility of determining it.
It could be seen as problematic to mix up the logical conditional with natural language intuitions of "if-then" but since it's about formalization of natural language it's a valid point to question those formalizations. (The same applies maybe to the concept of truth.)

If you take the empty set that contains no elements: The fact that it contains no elements can be used with the logical principle discussed here:
E.g. You get to the conclusion that the empty set is a subset (or identical) of every other set.
This is because subset is defined in the following way:
Be x,y sets:
x is a subset (or identical) of y iff For all z (z € x then z € y). ('€' means "is element of")
Since z € empty set is always false, the whole universal sentence is (for x = the empty set) always true no matter which set y is.
Insofar I have a problem in calling such things irrelevant.

That leads to the question what is the consequence of the intuition that there is a "not sure"-value. Do we introduce this third value and how does our logic then look like? Does it have consequences for mathematics (in a very wide sense) as well or only for natural language?

[ccexplore]

If you take the empty set that contains no elements: The fact that it contains no elements can be used with the logical principle discussed here:
E.g. You get to the conclusion that the empty set is a subset (or identical) of every other set.
<snip>

Yes, that may well feel very natural in the context of mathematics and logic, you're used to this kind of thing.  But if you try to express this in natural language without making use of the word "set", I think you may find it a little tricky to come up with such a statement that sounds natural.  Like, I don't know, "nothing is always part of any group of things"?

I feel like the only natural way to talk about the conclusion to a layman is to maybe re-state in the negative form, ie., you can never find something in an empty set that doesn't belong to any set.  Even in this form it will feel a little strange, because the precise reason it is true is that nothing whatsoever ever can be found in the empty set anyway!  Like you said earlier, it is a corner case.

I'm certainly not advocating that there is any inherent weakness or flaw in how classical logic is formulated.  It has definitely served its domain (eg. mathematics) very well.  I'm just pointing out that the human mind seems not wired exactly like classical logic, and it's this mismatch between how our brains are wired vs how classical logic works, that I theorize is at the heart of the conflicting views here.

[Proxima]

I think you may find it a little tricky to come up with such a statement that sounds natural.  Like, I don't know, "nothing is always part of any group of things"?

"If you have some things to choose from and may take any number of them you wish, taking nothing is one of your options."

[Simon]

Thesis grind

I want to submit the PhD thesis by end of July, ideally by Friday, 27th. Every day is thesis day. Icho will be happy. Still must find extra profs for the defense comitee, time is running, I'm sending emails like a madman.

Until thesis submission, I'm supressing the urge to write colorful rants here (even the juiciest entertainment doesn't help finish thesis). Suppressing the urge to kill bugs in Lix, to improve level search or replay management in Lix, and even supressing urge to refactor. Supressing the implementation of girlfriend mode a.k.a. networked singleplayer.

Nap time now.

-- Simon

[Ryemanni]

(•_•)
( •_•)>⌐■-■
(⌐■_■)

Every day is thesis day.

[Simon]

This is how it looks in my room. I've handed in the thesis.

I've slept for 9 hours afterwards. I'm not in the mood to celebrate after the grind this week: It's still hard to realize that there is no immediate university work.

Defense is on September 10th. I have slides for a 30-minute talk from July 2017 in Stockholm, that gives me a head start to prepare the defense. Will take a few weeks of break.

-- Simon

[Colorful Arty]

Congrats on finishing the thesis, Simon!

[Akseli]

Breathtakingly splendid, Simon!

This makes me very happy for you.

[Simon]

Thanks for the kind words!

Heat

It's 30 degrees C in Germany and the sun shines all day.

Consequences

• Headaches, tiredness, dehydration
  
• Eyes hurt from bright environment (sunglasses as extra bloat to carry/wear/forget)
  
• Everybody becomes aggressive and unproductive
  

Benefits

• Simon rants more?

Solutions

• Freeze medical compresses, then wear one on the head. Buy 2-3 of these compresses to alternate: Whenever the current one thaws, re-freeze it and switch to a cold one. This works with headphones: Bend the phones' headband to the front and stick the compress behind the headphones, on the top of the head.
  
• Siesta. Take at least one longer nap during the day. Or work entirely at night, should that fit into your social life.
  
• Cover the outside of the windows with aluminum foil, or get proper window shades that block sunlight. Keep room dark at all times.
  
• Swim in a lake.
  
• Live in the US? Allegedly, more private houses in the US than here have air conditioning. Germans sure love their central heating.
  
• Fans? Noisy and they produce more heat, but you be the judge.
  

-- Simon

[Ryemanni]

Most of the houses in Finland are not prepared for the heat either, only for the cold. My only tips are to not go outside, drink a lot, and invest on an ASHP.

[nin10doadict]

So I'm not the only one who's sick of the summer heat.
Seriously, I really don't like the heat. Some people get seasonal depression in winter. I get it in summer.

[Colorful Arty]

I never, EVER complain about summer heat. I'd take heat over cold any day, partially because my skin shrivels up in the winter.