Results [Issue 50] The Logic Challenge #1

[GoldRock 6,165]

The results are here!

 

And, without further ado...

 

In 1st place and winning 30,000 crystals: firebolt55439, scoring 9/12!

 

Whilst the initial 'cut off' set for the doubled prize fund was 10/12 or higher, I felt this entrant scored highly enough to deserve the doubled prize fund, especially in comparison to other scores and considering the difficulty of the questions. Excellent responses. Got caught out on the last question though (hehe), but apart from that, extremely well done! 

 

In 2nd place with a 10,000 crystal reward: @MegaPeg, scoring 6/12!

 

First 4 questions completely right, a correct approach to explaining the fallacy in question 2 that I actually hadn't spotted was identified. One or two of the responses could've been clearer however, and the answer to q5 hinged upon a fallacy which was not correct thanks to a technicality (@MegaPeg: Vulcan users not necessary having more skills --> they still could, in theory, all have all skills). Question 6 was also unfortunately wrong, but good effort overall!

 

And in 3rd place with a 5,000 crystal reward: @rock_extreme1, scoring 5/12!

A very good answer to question 5 was put forward with strong reasoning evident; however, other answers were not so strong, unfortunately. Still, a relatively good showing, and one of the earlier entries made, too!

4th-6th place (2,500 crystals each):

- @beaku - 5/12 - well structured, some good points made and answers effectively addressed the questions asked - but held back by other logically incorrect answers, unfortunately

- - 4/12 - another early entry, nicely done especially at first, but doubted truth of premises towards the end (particularly the IF/THEN statements) instead of answering the questions, with the odd error in reasoning.

- @HUGHIY - 4/12 - some good points, however other answers were either logically incorrect or also tended to doubt the truth of premises rather than directly addressing the questions asked (e.g. answer to q6).

 

Correct solutions:

Warm up questions (worth 1 point each):

 

Foreword: One of the most common mistakes in answering these questions was a tendency to doubt the truth of premises (statements) given as part of the arguments, when the questions asked what the logical problem was. In other words, if a question asks what is logically wrong about the argument A → B, not-B ∴ not-A (A implies B, so not-B means that not-A - this contains a logical fallacy present in one of the arguments below), it will not do to argue that A or B are wrong in terms of them not being true statements. That just doesn't address the question, which is about how the links used between A and B are illogical. Apart from that, it seems almost everyone understood how to approach the contest and the questions, and answers were generally fairly relevant.

 

1. What logical fallacy invalidates this argument?

The Ultimate Argument for the Noob-ness of A Vulcan User (What do you Mean it's Logically Fallacious No it Isn't Pls):

All noobs are human,
Vulcan users are human,
∴ Vulcan users are noobs.

 

Solution: Fallacy of the undistributed middle. Whilst all noobs are human, not all humans are noobs and so Vulcan users being human does not make them noobs. Thus, as per the premises, Vulcan users may be human without being noobs.

 

2. What makes this argument inconclusive?

The All-New Ultimate Non-Fallacious Non-Animalist Non-Inanimate-Objectist Argument for the Noob-ness of Vulcan Users:

All noobs can be correctly described as 'noob',

Vulcan users are 'noob',

∴ Vulcan users are noobs.

 

Two approaches were possible here.
Solution 1: The second premise may not be true - it could be true or false. It is merely an assertion made without any evidence or reasoning as to its truth put forth, and thus the conclusion drawn from it (that Vulcan users are noobs) is unsubstantiated.

Solution 2: The first premise does not state that all those described as 'noob' are noobs, which technically means that those described as 'noob' do not necessarily have to be noobs. For example, the fallacy is similar to that in arguing: "All cardinals can be correctly described as 'red.' Robins are red. Therefore, robins are cardinals." (thanks @MegaPeg!) This is basically another example of the fallacy of the undistributed middle, but more subtle.

 

More challenging questions (worth 2 points each):

 

3. What logical fallacy is present in the structure of this argument?
The Argument from GoldRock's Pro Emotions for the Noob-ness of Vulcan Users:

Night-Sisters denies that Vulcan users are noobs,

GoldRock has chosen to 'cri' in response to this assertion,
If Vulcan users are noobs, then GoldRock will always choose to 'cri' (he will 'cri everytiem') at Night-Sisters' ignorance,
Not knowing the true extent of Vulcan users' noob-ness, Night-Sisters possesses ignorance on the matter,

∴ Vulcan users are noobs.

 

Solution: The fallacy present here is that of affirming the consequent. Here, I essentially argue that if Vulcan users are noobs, then I'll 'cri' at Night-Sisters' ignorance - and because I cried and Night-Sisters is ignorant, Vulcan users are noob. This incorrectly makes use of the IF/THEN statement backwards - it's like arguing that if it rains, the grass gets wet - and because the grass is wet, it has rained. Whilst the IF/THEN statement is true in the forwards direction, it is not necessarily the case when taken 'backwards'; in this case, someone could have just watered the grass, making the conclusion drawn incorrect.

 

Also, this argument does not actually suffer from any appeal to emotion as although emotions are included within the argument to some extent, there is no specific attempt to manipulate your emotions as the reader. Nor does the argument suggest that GoldRock would 'cri' on the grounds that Vulcan users are both not noobs and are noobs - because what Night-Sisters says is irrelevant to what Vulcan users actually are. The argument never says that Vulcan users are not noobs, only that Night-Sisters thinks so. Both of these potential points were intentionally thrown in to be misleading. Hehe. 

4. ...and how about the logical flaw in this deceptively simple one? (Note: there are two possible correct answers, both of which will earn the marks - one is easier to get, but discovering the other will help you with a later question. You can submit either.)

The Conclusive Argument as to Why Vulcan Users are not Better Players:

Better players necessarily have more skill than worse players,

Vulcan users don't necessarily have more skills than worse players,
∴ Vulcan users are not better players.

 

Two approaches were possible here:
Solution 1: The second premise is meaningless. Vulcan users not necessarily having more skills than worse players could still mean that some of them do, or some of them don't, or even that all of them do/don't. All the premise means is that it doesn't have to be the case that all Vulcan users have more skills than worse players, and so does not entail anything about the actual situation. Therefore, it is incorrect to draw the conclusion that Vulcan users are not better players, when some or even all of them may be as per the first two premises.

 

I deducted a mark if it was argued that the second premise means that some Vulcan users don't have more skills, because in theory, all Vulcan users could still have more skills than worse players by chance and without it necessarily having to be the case. This would still satisfy the premise. As before, the second premise does not actually mean anything in terms of whether Vulcan users do or don't have more skills than worse players - it only means that one scenario doesn't have to be the case, but equally, it still could be.

Solution 2: Nobody actually got this one, although it was originally intended to be the only flaw in this argument - so you guys are lucky there was another solution! Anyway, there was also a fallacy of equivocation here if you look carefully. Specifically, the words 'skill' and 'skills' had two different meanings. In the first premise, 'skill' must mean something similar to 'expertise' (considering the singular use of the word) - whereas in the second premise, 'skills' must mean something similar to 'abilities' (considering the plural use of the word). Both are valid definitions of the word, but it means that the two premises are technically arguing about different things, making the conclusion drawn invalid.

 

Very difficult questions (worth 3 points each):

 

5. How is this argument logically flawed (2 points), and how could it be fixed (1 point)?

Why, as Worse Players, Vulcan Users Lack Social Skills:

If Vulcan users don't necessarily have more skills than worse players, either all players have all skills possible or Vulcan users do not have all skills possible,
If all players have all skills possible, then Vulcan users have all skills possible,

All players do not have all skills possible,

∴ Vulcan users do not have all skills possible,

If Vulcan users do not have all skills possible, then Vulcan users lack skills,

Social skills are a type of skills,
If Vulcan users lack skills, then they lack skills in all types of skills,
∴ Vulcan users lack social skills. 

 

Solution: The fallacy here is denying the antecedent. In this specific scenario, I stated that if all players have all skills possible, then Vulcan users have all skills possible (a valid IF/THEN statement, P → Q). I then argue that as all players do not have all skills possible, one must conclude that Vulcan users do not have all skills possible (not-P → not-Q). This is invalid as my IF/THEN statement never asserted what would happen if all players do not have all skills possible, and so it is a fallacy to draw the given conclusion from it. To give an example, it is like arguing that: "If it is raining, the grass is wet. It is not raining, so the grass is not wet". This, obviously, can be false - the grass could be wet via other means e.g. someone watering it. It's the same 'grass and rain' scenario which I used above, only this time to demonstrate a different logical fallacy.

 

To fix this argument, one can simply insert the premise that Vulcan users don't necessarily have more skills than worse players*, to make the very first IF/THEN statement apply. Then, as it's already stated that all players do not have all skills possible, the last part of the IF/THEN statement ("...either all players have all skills possible or Vulcan users do not have all skills possible") must be true. This essentially proves the conclusion "∴ Vulcan users do not have all skills possible" via a different, valid logical method. 

The rest of the argument is logically correct. In this context, 'lack' means "not having all", a valid use of the term. As in the premise on the second-last line, it is thus reasonable to infer that if Vulcan users don't have all the skills there are, they lack skills in all areas (e.g. they don't have all the social skills that it is possible to have, or all the dancing skills etc.). In any case, the question did not enquire about the truth of premises, but only about how the argument was logically incorrect i.e. how it didn't link together in a valid way.

 

*[More advanced point of note - don't worry if you don't understand!] This premise can actually be logically derived from "all players do not have all skills possible" - validly deriving not-Q → not-P from P → Q (contained within the first IF/THEN statement). In other words, "If Vulcan users don't necessarily have more skills than worse players, either all players have all skills possible or ..." can be rewritten as "If either all players do not have all skills possible or ... , then Vulcan users do necessarily have more skills than worse players". So, "Vulcan users don't necessarily have more skills than worse players" can be logically derived from "all players do not have all skills possible". This is called transposition (in the field of logic), and I'm very impressed that firebolt55439 spotted that. Once again, I didn't even notice it myself!

 

6. Identify one logical fallacy in this argument and state where it is present (1 point); identify another potential logical fallacy in this argument and state where it is present (1 point); and without removing the final conclusion, which line(s) could be removed to make the argument both potentially logically valid and true (1 point)?

GoldRock's Master Argument - Why Vulcan Users Have No Friends:

If Vulcan users are noobs, then they are not perfect,
If Vulcan users are not perfect, then they lack bonds of mutual affection,
Either Vulcan users are noobs or Vulcan users are not noobs,
Vulcan users are not perfect,
∴ Vulcan users lack mutual bonds of affection,
A friend is defined as a person with whom one has a bond of mutual affection,

All Vulcan users who lack bonds of mutual affection have no friends,

∴ Vulcan users have no friends.

 

Both logical fallacies are contained within the line "All Vulcan users who lack bonds of mutual affection have no friends". The first logical fallacy is that two different definitions of the word 'lack' are used in the argument (a fallacy of equivocation, as above). Throughout the argument, 'lack' is used to mean "not having all", as used in the previous argument. However, within this premise, the term is clearly implied to mean "not having any" or "completely without", since it argues that 'lacking' bonds of mutual affection entails no friends. This means that the argument makes use of two definitions of the word 'lack', thus making the conclusion drawn from this line inconclusive since it makes use of a different definition of 'lack'.

 

The second, potential logical fallacy (which nobody managed to get, although one entrant touched upon it without quite managing to work it out) is also located within "All Vulcan users who lack bonds of mutual affection have no friends", as stated previously. Here, there is a potential vacuous truth fallacy. As per the meaning of 'lack' within this line (as having an implied meaning of "not having any"), this premise applies to all those Vulcan users who don't have any bonds of mutual affection and so who don't have any friends. However, there is a reasonable chance that no Vulcan users have no friends (considering that the first 5 lines of the argument failed to adequately prove that Vulcan users lack mutual bonds of affection in the sense of "not having any" which is required here), thus making this statement about Vulcan users who have no friends meaningless and empty. It's like saying "all players who were wearing a bowler hat whilst they entered this contest were also standing on one leg". This is probably true, but only because it's probable that it applies to nobody!

 

The way to make this argument potentially logically valid and true (in other words, the second fallacy above can be left in since it might not be the case!) would be to remove lines 2 and 5, which make use of the first meaning of the word 'lack' in proving the common-sense conclusion that "Vulcan users don't have all mutual bonds of affection possible". This is basically irrelevant to the final conclusion, which seeks to prove something else completely. Removing these two lines means that you're left with an argument only using one meaning of the word 'lack' (as in the second-last line), and so the fallacy of equivocation is fixed. One can't remove the second-last line to fix it, because this would completely invalidate the final conclusion, which is central to the overall argument. Alternatively, all of the first 5 lines could be removed - because the 1st, 2nd and 4th lines are essentially meaningless and so unnecessary once the 2nd and 5th lines are taken out. 

 

Note that "bonds of mutual affection" and "mutual bonds of affection" essentially have exactly the same meaning, regardless of the fact that the words are spun around. That was just a little red herring I through in to make this question really evil and to try and catch you guys out; and again, my evil trick worked on a few of you. Hehe.

 

 

To all other entrants - I will be PMing each one of you individually with some specific feedback on your entries. Hope you guys enjoyed the contest!

Edited November 18, 2017 by Flexoo

[beaku 2,656]

K... Cool. I got more than I was expecting. :p

[MegaPeg 3]

Lol 2nd place isn't too bad. Congrats to firebolt55439 for the win!

Edited March 6, 2016 by MegaPeg

[firebolt55439 1]

Thank you so much GoldRock for the consideration, and congratulations to the other winners! :)

That last question belongs in a logic textbook though - it's absolutely brilliant.

Edited March 6, 2016 by firebolt55439

[MOO_I_AM_A_COW 110]

I sucked so bad :-)

[Zenyth 6,494]

Well congrats to the winners

I was getting around 4 right but didn't submit.. :mellow:

[Spit_Fyre 334]

Kudos to the deserving winners!

 

And ah! the vacuous truth...

[Typo 1,299]

Cool I won a consolation. First win :D

[Amateur 829]

Congrats for the winners!

[sudeeprauta 150]

Congo people

[rippr 21]

Congrats to all the winners and participants! I'd like to express my great sorrow at not being able to participate in this contest... I'm made for things as such! Logic, reason, arguments, calling vulcan users noobs! Oh man... I'd love to see a round 2 of this in which I sure as hell will participate...

[BlueDragon_tamki 3,204]

Congrats to the winnera

[BLASTER872 1,892]

gg winners! too bad i couldn't participate...