Thursday, February 23, 2017
Gender and other categories: The 'No True Scotsman' logical fallacy
The 'No True Scotsman' logical fallacy is one that shows up quite often in discussions/ arguments about gender, ethnicity, religion, culture and many other discussions that involve categorizations of people or things.
‘No True Scotsman’ Fallacy
The no true scotsman fallacy is a way of reinterpreting evidence in order to prevent the refutation of one’s position. Proposed counter-examples to a theory are dismissed as irrelevant solely because they are counter-examples, but purportedly because they are not what the theory is about.
Example
The No True Scotsman fallacy involves discounting evidence that would refute a proposition, concluding that it hasn’t been falsified when in fact it has.
If Angus, a Glaswegian, who puts sugar on his porridge, is proposed as a counter-example to the claim “No Scotsman puts sugar on his porridge”, the ‘No true Scotsman’ fallacy would run as follows:
(1) Angus puts sugar on his porridge.
(2) No (true) Scotsman puts sugar on his porridge.
Therefore:
(3) Angus is not a (true) Scotsman.
Therefore:
(4) Angus is not a counter-example to the claim that no Scotsman puts sugar on his porridge.
This fallacy is a form of circular argument, with an existing belief being assumed to be true in order to dismiss any apparent counter-examples to it. The existing belief thus becomes unfalsifiable.
Real-World Examples
An argument similar to this is often arises when people attempt to define religious groups. In some Christian groups, for example, there is an idea that faith is permanent, that once one becomes a Christian one cannot fall away. Apparent counter-examples to this idea, people who appear to have faith but subsequently lose it, are written off using the ‘No True Scotsman’ fallacy: they didn’t really have faith, they weren’t true Christians. The claim that faith cannot be lost is thus preserved from refutation. Given such an approach, this claim is unfalsifiable, there is no possible refutation of it.
Another example, this one about things:
One could make a statement like, 'All teacups can hold hot tea' -- and that is generally so, as holding hot tea is generally the function of a teacup.
However, there are counterexamples, like Oppenheim's fur teacup, or a broken teacup.
The 'No True Scotsman' fallacy would claim that such counterexamples were not true teacups. An alternative approach would be to open up the question, asking what these and other counterexamples offer us as new spaces for thinking about what a 'teacup' might be.
These questions also lead to ideas from Eleanor Rosch's Category Theory (1978), where some things or qualities seem very central to a particular human-made category, and others lead to questions of whether our definitions work at all.
Here is an explanation of this logical fallacy from <http://www.logicalfallacies.info/presumption/no-true-scotsman/>:
‘No True Scotsman’ Fallacy
The no true scotsman fallacy is a way of reinterpreting evidence in order to prevent the refutation of one’s position. Proposed counter-examples to a theory are dismissed as irrelevant solely because they are counter-examples, but purportedly because they are not what the theory is about.
Example
The No True Scotsman fallacy involves discounting evidence that would refute a proposition, concluding that it hasn’t been falsified when in fact it has.
If Angus, a Glaswegian, who puts sugar on his porridge, is proposed as a counter-example to the claim “No Scotsman puts sugar on his porridge”, the ‘No true Scotsman’ fallacy would run as follows:
(1) Angus puts sugar on his porridge.
(2) No (true) Scotsman puts sugar on his porridge.
Therefore:
(3) Angus is not a (true) Scotsman.
Therefore:
(4) Angus is not a counter-example to the claim that no Scotsman puts sugar on his porridge.
This fallacy is a form of circular argument, with an existing belief being assumed to be true in order to dismiss any apparent counter-examples to it. The existing belief thus becomes unfalsifiable.
Real-World Examples
An argument similar to this is often arises when people attempt to define religious groups. In some Christian groups, for example, there is an idea that faith is permanent, that once one becomes a Christian one cannot fall away. Apparent counter-examples to this idea, people who appear to have faith but subsequently lose it, are written off using the ‘No True Scotsman’ fallacy: they didn’t really have faith, they weren’t true Christians. The claim that faith cannot be lost is thus preserved from refutation. Given such an approach, this claim is unfalsifiable, there is no possible refutation of it.
*******************
Another example, this one about things:
One could make a statement like, 'All teacups can hold hot tea' -- and that is generally so, as holding hot tea is generally the function of a teacup.
However, there are counterexamples, like Oppenheim's fur teacup, or a broken teacup.
The 'No True Scotsman' fallacy would claim that such counterexamples were not true teacups. An alternative approach would be to open up the question, asking what these and other counterexamples offer us as new spaces for thinking about what a 'teacup' might be.
These questions also lead to ideas from Eleanor Rosch's Category Theory (1978), where some things or qualities seem very central to a particular human-made category, and others lead to questions of whether our definitions work at all.
Readings for our March 2 class: Sociomathematical classroom norms
Here are our three readings for next week's class!
1) Yackel & Cobb's foundational article from 1996 (note that Tsubasa should pick a different reading as this was part of his paper!)
2) Yackel & Rasmussen: Beliefs and norms in an undergraduate mathematics class 2002
3) Levenson, Tirosh & Tsamir: Students' perceived mathematical norms 2009
1) Yackel & Cobb's foundational article from 1996 (note that Tsubasa should pick a different reading as this was part of his paper!)
2) Yackel & Rasmussen: Beliefs and norms in an undergraduate mathematics class 20023) Levenson, Tirosh & Tsamir: Students' perceived mathematical norms 2009
Thursday, February 16, 2017
Our readings in gender and mathematics learning for our off-campus class next Thursday Feb. 23
Next Thursday, we will meet at 4:30 at the Allegro Coffee Bar at the Whole Foods store at Cambie 510 W 8th Avenue. You can buy coffee, tea and snacks at the café, and/or buy food in the grocery or other food spots downstairs and bring food up to the café.just north of Broadway. <http://www.vancitybuzz.com/2015/01/whole-foods-market-cambie-new-allegro-cafe/> The café is upstairs from the main store, and the main store is at
Here are our three readings for next week:
1) Valerie Walkerdine 1990 article on gender, cognition and math
2) Indigo Esmonde: Snips, snails and puppydog tails -- Genderism and math ed
3) Leder et al: Gender and math from a Swedish perspective
Thursday, February 9, 2017
Thursday, February 2, 2017
Five Grade 6 & Grade 9 word problems...but a little unfamiliar
(1) ஜென்னி $ 9.95 ஒவ்வொரு,
7 டி-ஷர்ட்டுகள், தன் ஏழு சகோதரர்கள் ஒவ்வொரு ஒரு வாங்கினார். காசாளர் தனது விற்பனை வரி கூடுதலாக $13.07 விதிக்கப்படும். அவர் ஒரு measely $ 7.28 கொண்டு கடையில் விட்டு. ஜென்னி எவ்வளவு பணம் ஆரம்பித்தீர்கள்?
(Tamil)
(2) Есть 22 золотых
монет и 9 серебряных монет в коллекции монет Чарли. Каково отношение количества
золотых монет на количество серебряных монет? (Russian)
(3) አንድ applesauce ኩባንያ ፖም
7 ላኩ አዘዘ. በእያንዳንዱ የጭነቱ
ውስጥ 9.851 ሮማኖች ነበሩ. ምን
ያህል ፖም ሁሉ ውስጥ ኩባንያ
ትእዛዝ ነበር? (Amharic)
(4) Bíll fer frá A til B á hraða 40 mph þá skilar, með því
að nota sömu leið, frá B til A á hraða 60 mph. Hvað er meðalhraðinn fyrir
hringferð? (Icelandic)
(5) А прямоугольник далалық 300 шаршы метр аумақты және 80
метр периметрі бар. кен ұзындығы мен ені қандай? (KazakH)
(And the original word problems:)
(And the original word problems:)
(1) Jenny bought 7 t-shirts, one for each of her seven
brothers, for $9.95 each. The cashier charged her an additional $13.07 in sales
tax. She left the store with a measely $7.28. How much money did Jenny start
with?
(2) There are 22 gold coins and 9 silver coins in Charlie's
coin collection. What is the ratio of the number of gold coins to the number of
silver coins?
(3) An applesauce company ordered 7 shipments of apples.
There were 9,851 apples in each shipment. How many apples did the company order
in all?
(4) A car travels from
A to B at a speed of 40 mph then returns, using the same road, from B to A at a
speed of 60 mph. What is the average speed for the round trip?
(5) A rectangle field has an area of 300 square meters and a
perimeter of 80 meters. What are the length and width of the field?
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