CHAPTER 2 Are Women Better than Men, or Vice Versa?

CHAPTER 2 Are Women Better than Men, or Vice Versa?
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women are better than men.
Note:LA RETORICA COMUNE

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story about men being found to be superior to women in anything,
Note:MOLTO DIFFICILE

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Men Are Not Cost Effective
Note:TITOLI IN LIBRERIA

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Are Men Necessary?

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CcccccMAUREEN DOWD

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“Future generations might ask why a man can’t be more like a woman….
Note:TITOLO DELL ECONOMIST

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women are now the most powerful engine of global growth.”
Note:ANCORA

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women make better investors
Note:ANCORA...MA XCHÈ GLI INVESTITORI NN SONO ANCORA TUTTI DONNE?

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men had done a few good things in the past,
Note:FLEBILE CONCESSIONE...MA...LA DONNA AVREBBE FATTO CMQ MEGLIO

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On television, when commercials pit men against women, the women always win.
Note:TELEVISIONE...PEGGIO CHE ANDARE DI NOTTE

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My Three Sons and Father Knows Best depicted fathers as intelligent, competent, caring human beings,
Note:VECCHI TELEFILM

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Most Hollywood fathers are simply buffoons and caricatures.
Note:OGGI

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find a show that makes the woman look stupid while the man looks wise or kind.
Note:UN IMPRESA

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Sometimes, to be sure, both parents are depicted as stupid, but if only one parent is depicted as wise and kind, it is almost always the mother.
Note:NEI LIBRI X BAMBINI

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“masculinist” was bad and “feminist” was good,
Note:NELLE DISCUSIONI COMUNI E ACCADEMICHE

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this can all be dismissed as propaganda, as political correctness, as fear of boycotts, as mere fiction and poetic license.
Note:MA PROBABILMENTE

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Alice Eagly
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people do indeed think men and women are different.
Note:INNANZITUTTO

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“the WAW effect.”
Note:WOMAN ARE WONDERFULL...COME VIENE XCEPITA LA DONNA OGGI

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this is not the biased view of a small coterie of man-haters,
Note:QUALCOSA CHE RIGUARDA TUTTI

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women are better people than men.
Note:RIPETIAMO IL SENTIMANTO GENERALE

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men still outnumber women as top achievers in some domains.
Note:IRRILEVANTE...E PROVVISORIO...

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When men do worse than women, people say it’s because women are better at this or that. When men do better than women, people say it’s because women are oppressed,
Note:IL PROBLEMA DEI NS GIOVANI

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It Wasn’t Always Thus
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multitasking.
Note:UN TEMPO ANDAVA DI MODA ENFATIZZARE LA SUPERIORITÀ FEMMINILE

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if you search for actual scientific evidence the conclusion is dubious.
Note:MA...

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no difference.
Note:PIÙ PROBABILE

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recent evidence suggests that multitasking—doing several things at once—mainly leads to doing a worse job at all of them.)
Note:INOLTRE

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If someone had asserted that men were better at it, immediately there would have been skepticism
Note:A PARTI INVERTITE IL MITO NN SI SAREBBE MAI DIFFUSO

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the “man bites dog” principle.

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COSA STA SOTTO QS DINAMICHE

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They think people are still surprised to hear about women being superior to men.
Note:I GIORNALISTI

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people do like to hear news that confirms their stereotypes,
Note:DOPO LA NOVITÀ CI SONO ALTRI MOTIVI X INSISTDRE

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in the past, most people thought men were better than women
Note:L ASSUNTO DI PARTENZA

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In essence, we have been rebelling against the assumption of male superiority
Note:RIBELLIONE NN INFORMAZIONE

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Prevailing Views About Men and Women
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Up till the 1960s, psychology focused on men and used men as the model
Note:PRIMA FASE

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Periodically psychologists would suggest that one or another general principle might be slightly different for women. These differences sometimes took the form of implying that women lacked a bit of something,
Note:IMPLICAZIONE

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in the 1970s there was a brief period of denying that there were any real differences between the sexes.
Note:SECONDA FASE...LA CULTURA SPIEGA TUTTO

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If we could eliminate prejudices and discrimination
Note:LA SPERANZA...

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gender inequalities and even gender differences were all due to socialization
Note:L IDEA DEL MOMENTO

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enlightened parents
Note:FIGURE DI MODA

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Since the late 1970s, the field has largely taken the view that women are superior, and men are an inferior copy. In essence, it is the same approach that was used before 1960, but with the genders switched. Now women are the model
Note:TERZA FASE

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men better than women, no difference, and women better than men.
Note:RIASSUNTO DELLE TRE FASI

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These shifts in theory came about more from political than scientific factors.
Note:TESI

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scientists climbed on the feminist bandwagon.
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The early feminists wanted equality, and it served their goal to deny that there were any real gender differences. But female chauvinists were among them, those who resented and disliked men,
Note:LE DUE ONDATE

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Gradually the feminists in gender studies abandoned the idea of equality.
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The Puzzling Thing
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How could such a dramatic switch occur in such a short time?
Note:IL MISTERO DELLA TEMPISTICA

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an aspiring science such as psychology loses credibility when it just shifts from one theory to the opposite
Note:LA SCIENZA PSICOLOGICA

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psychology’s switch mirrored what was happening in the society at large,
Note:PARTE DELLA RISPOSTA....CI CONCENTREREMO SUL RESTO

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Women and Science
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In January 2005, Lawrence Summers,
Note:RIEPILOGO DELLA VICENDA SUMMERS

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he didn’t actually say anything that constituted oppression
Note:ALL APPARENZA

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His crimes were crimes of thought.

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TABÙ

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He wondered whether there were more men than women at the highest levels of intellectual
Note:LA SOLA DOMANDA...

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The only debate was as to how severely he should be punished
Note:IL DIBATTITO

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there might be more men than women with the high level of innate ability required
Note:L IPOTESI TABÙ

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Before he resigned, he had to go beyond apology
Note:FINALE

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Louann Brizendine, in her book The Female Brain, says Summers was “dead wrong”
Note:REAZIONI....TERMINI FUORI DAL LINGUAGGIO SCIENTIFICO

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there is a small difference between average male and female scores
Note:I DATI....IN PARTE POSSONO ANCHE ESSERE PORTATI DAGLI ACCUSATORDI

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hardly enough to explain the severe gender imbalance
Note:Ccccccc

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Average IQ scores are about the same in men as in women.
Note:ANCORA

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(Throughout childhood, girls score higher than boys, and then the boys catch up and move very slightly ahead in adulthood.)
Note:DINAMICA

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Patriarchy—the idea that culture is a conspiracy by men to oppress women
Note:COSA SPIEGA LA COMPOSIZIONE TOP SCIENTIST? L UNICA SPIEGA AMMESSA

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Strictly Speaking
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What Dr. Summers said was that at the high end—where the math and science genius-level intellects are found—there are more men than women.
Note:MA COSA DISSE SUMMERS ESATTAMENTE?

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a surplus of men at the high end could also mean that there are more men at both extremes.
Note:ALTERNATIVA ALL IPOTESI DELL INTELLIGENZA MEDIA

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The crucial test case, therefore, is to look at the extreme low end.
Note:IL TEST CRUCIALE

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researchers study mental retardation far more than they study giftedness.
Note:SIAMO FORTUNATI

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There are more mentally retarded boys than girls.
Note:DATO

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as you move from the mildly retarded levels to the most severely retarded, the gender difference gets bigger
Note:NN SOLO

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the same pattern found with genius: as you go from mild to moderate to extreme, there are fewer and fewer girls relative to the number of boys.
Note:GENIO

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All those retarded boys are not the handiwork of patriarchy!
Note:E LA PATRIARCHIA?

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Nor is it some unlucky stereotype or the product of biased socialization.
Note:ALTRE IPOTESI DA ESCLUDERE

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If the oversupply of retarded boys is not the result of men defending patriarchy, then quite likely the oversupply of genius boys isn’t either.
Note:INDIZIO

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influence of Mother Nature produces both extremes.
Note:PROBABILE

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There are plenty of female geniuses, just like there are plenty of mentally retarded females.
Note:RESTA VERO CHE...

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Dr. Summers was quite right,
Note:IN QS SENSO

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Men at the Extremes

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Ttttttttt

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Just as more men than women are self-made millionaires, more men than women end up in prison.
Note:PATTERN VISIBILE IN SOCIETÀ

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height also show the male extremity pattern.
Note:MA ANCHE IN NATURA...

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What about personality?
Note:MATERIA BOLLENTE

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the Positive Psychology Center at the University of Pennsylvania,
Note:STUDI CRUCIALI

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Men outnumber women at both extremes on these measures. Whether we are talking about kindness versus cruelty, curiosity versus closed-mindedness, wisdom versus immature pigheadedness, self-control versus self-indulgence, or humility versus narcissism,
Note:ESITO

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“Big Five” dimensions. On these, the experts do not find greater variation among men than women.
Note:ECCEZIONI

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Damn Lies and Statistics
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Even if men and women are exactly equal on average, almost paradoxically, you can get statistical data showing a difference between the male and female averages. All it takes is to use some kind of measure that is restricted at one end.
Note:INGANNO DELLA STATISTICA

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Let’s start with grades in college.
Note:UN CASO DI BALLA DELLA MEDIA

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The highest possible grade in most colleges, or what statisticians call the ceiling, is an A.
Note:C È UN TETTO X QS I RAGAZZI SONO MEDIAMENTE PIÙ SCARSI....CAUSA INFLAZIONE NEI VOTI

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the low-achieving males will pull the male average down.
Note:MENTRE I MIGLIORI INCIDONO POCO SULLA MEDIA

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The result? Women will get better grades than men, on average.
Note:ESITO INGANNEVOLE

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The average performance quality was exactly the same
Note:INVECE

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salary.
Note:ALTRO ESEMPIO

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With salary, the problem is the floor.
Note:COME PRIMA MA ROVESCIATO

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the average inputs are exactly the same for men and women:
Note:PROB

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There may be a minimum salary, but there is no maximum.
Note:FLOOR

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These differences are not temporary conditions that will go away. Nor are they problems needing to be solved. These differences will be permanent.
Note:TUTTO FISSO

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women score higher grades than men in college and earn lower salaries.
Note:LA CONSEGUENZA....CORRETTA MA INGANNEVOLE

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the higher earning power of men is not taken to mean that men are better workers than women. It is usually ascribed to some kind of evil conspiracy by men (patriarchy), and many people quickly think the gender gap in salary is proof of male wickedness and the oppression of women.
Note:ESEMPIO DI EQUIVOCO

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in principle, one could just as well draw the opposite conclusions.
Note:VALIDA ANCHE LA CONCLUSIONE CONTRARIA: UOMINI DISCRIMINATI A SCUOLA

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My point is that neither conclusion is really justified.
Note:TESI

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Revisiting the Contradictory Stereotypes
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how psychology in particular and Western society more generally could have switched from one prejudice to its opposite in a little more than a decade.
Note:TORNIAMO ALLA NS DOMANDA

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Most of them have some fairly sizeable amounts of truth. Research by Lee Jussim

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PRIMA UNA COSA SUGLI STEREOTIPI

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most people aren’t bigots and are even somewhat careful
Note:Cccccccc

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they try to establish whether their stereotypes are true but not whether they are false.
Note:COME SI CEMENTANO GLI STEREOTIPI

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confirmation bias.
Note:Ccccccc

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That’s where male extremity comes in. It is ready-made for producing opposite stereotypes, by working with the confirmation bias.
Note:E QUI IL PATTERN ENTRA IN CAUSA...CONFERMA E SMENTISCE MA ALLE SMENTITE NOI NN DIAMO PESO

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you will be easily able to find plenty of real and valid examples to support your belief.
Note:Cccccccc

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Want to believe men are superior to women? Easy.
Note:CONFERME

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Want to believe men are inferior to women? Easy.
Note:E CONFERME

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men really are better AND worse than women.
Note:CONCLUSIONE SYEREOTIPATA

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The Theory We’ve Never Tried
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Different but equal
Note:LA NUOVA TEORIA DEGLI ESTREMI

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Cultures exploit men and women differently. And they do this for a practical reason. Men and women are different and hence are useful to culture in different ways.
Note:TESI

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if the genders are different, then successful cultures will figure out which gender is better suited to which of its tasks, and assign them thus.
Note:CULTURE EFFICIENTI

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equality not by sameness but by tradeoffs.
Note:TRADEOFF

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Gender and Tradeoffs
Note:Tttttttttt

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taking care of babies and fighting in battles are not fully compatible.
Note:SPECIALIZZAZIONE

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cultures need both of those jobs to be done.
Note:ESIGENZA

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Babies need to be watched constantly and fed every day,
Note:ROUTINES

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Battles may require moving around frequently and unpredictably, taking chances, getting hurt, doing without regular meals and/or sleep,
Note:Ccccccc

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A gentle, loving nature may be best suited for taking care of babies, but it may be counterproductive on the battlefield.
Note:INCOMPATIBILITÀ

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an important point: tradeoffs.
Note:QUESTO ERA SOLO UN ESEMPIO

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fixing one problem often creates another.
Note:OGGI VOGLIAMO UNA LEGGE X TUTTO A TUTELA DELL EGUAGLIANZA TRA I GENERI

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there are real differences
Note:NELL EGUAGLIANZA COMPENSATIVA

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Every time you hear of one gender being better at something, stop to think what is on the other side of that coin. What inferiority is tied to that superiority?
Note:CONCLUSIONE SAPIENZIALE

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One Size Doesn’t Fit All?
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Culture can reduce the effects of nature,

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QS VALE SEMPRE

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Small natural differences in inclination may become giant differences in society,
Note:EFFETTO VALANGA

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women are all kept at home
Note:ESEMPIO

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Biologically based differences are put there by evolution.
Note:LA COLPEVOLE DELLE DIFFERENZE

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This is why it is implausible that one gender is innately better than the other across the board.
Note:PENA ESTINZIONE

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Every time you hear that one gender is better than the other, ask yourself: Why would nature make one gender better than the other? Why would it preserve that difference,
CONCLUSIONE SAPIENZALE @

Emisferi

There seems to be a lot of disagreement on how best to summarize how the hemispheres differ. Here are two summaries:

The left hemisphere deals with hard facts: abstractions, structure, discipline and rules, time sequences, mathematics, categorizing, logic and rationality and deductive reasoning, knowledge, details, definitions, planning and goals, words (written and spoken and heard), productivity and efficiency, science and technology, stability, extraversion, physical activity, and the right side of the body. … The right hemisphere specializes in … intuition, feelings and sensitivity, emotions, daydreaming and visualizing, creativity (including art and music), color, spatial awareness, first impressions, rhythm, spontaneity and impulsiveness, the physical senses, risk-taking, flexibility and variety, learning by experience, relationships, mysticism, play and sports, introversion, humor, motor skills, the left side of the body, and a holistic way of perception that recognizes patterns and similarities and then synthesizes those elements into new forms. (more)

The [left] is centered around action and is often the driving force behind risky behaviors. This hemisphere heavily relies upon emotional input leading it to make brash and uncalculated decisions. … The [right] … relies primarily on critical thinking and calculations to reach its decisions.[11] As such the conclusions reached by the [right] often result in avoidance of risk taking behaviors and overall inaction. … . In environments of scarcity, … taking risks is the foundational approach to survival. … However, in environments of abundance, as humans have observed, it is far more likely to die to damaging stimuli. … In areas of prosperity, … [right] domination is prevalent. … In areas of scarcity where cold and limited food are concerns [left] domination is prevalent. (more)

After reading a bit, I tentatively summarize the difference as: the right hemisphere tends to work bottom-up, while the left tends to work top-down.

Separate Top-Down, Bottom-Up http://www.overcomingbias.com/2018/08/separate-top-down-bottom-up.html

L'AMBIGUO DESTINO DELLA COMPETENZA

Riccardo Mariani

12 agosto alle ore 09:52 · 

L'AMBIGUO DESTINO DELLA COMPETENZA

La distinzione competenti/incompetenti ha il solito difetto: la prima fazione è zeppa di incompetenti che vogliono farsi notare in compagnia dei competenti, la seconda di competenti un po’ narcisi che vogliono sentirsi “originali”.

ILFOGLIO.IT

Ribellarsi contro gli incompetenti

Burioni, Boeri, Bentivogli, Cottarelli. Un partito dei competenti per passare come una ruspa sulla truffa populista

9 Numbers

9 Numbers
Note:9@@@@@@@@

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9.1   Cardinal numbers as properties
Note:Ttttttt

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what is a number?
Note:IN CERCA DI TEORIE ALTERNATIVE

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A cardinal number is a kind of property.1 These properties are best ‘defined ostensively’, that is, by giving examples.
Note:DEF...SI PARTE DA ESEMPI

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I would show them something like Figure 9.1. In that picture, there are two stars, two hexagons, and two lightning bolts.
Note:COME INSEGNARE IL NUMERO 2

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It is no coincidence that this is how children are actually taught
Note:BAMBINI

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The ontological status of the number two is thus the same as that of other universals,
Note:ONTOLOGIA

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9.2   Frege’s objection
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the same concrete thing can be said to instantiate different numbers. Suppose you have a deck of cards. What is the number that it instantiates? Well, it is one deck, but it is fifty-two cards.
Note:OBIEZIONE DEL MAZZO DI CARTE

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Therefore, number is not a property of a concrete object, such as the deck of cards. Instead, Frege proposes, numbers must be properties of ‘concepts’

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SOLUZIONE FREGE...OB IDWALISTA...ACCETFABILW IMO

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we resolve the puzzle of the deck of cards by saying that there are two distinct concepts: the concept ‘deck’ (or maybe, ‘deck that is on this table now’) and the concept ‘card’ (or, ‘card that is on this table now’),
Note:SOLUZIONE

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Cantor and Russell, on the other hand, would ditch the talk of concepts and say that there are two distinct sets:
Note:SOLUZIONE RUSSELL

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Each number is a property of a concrete particular
Note:L ASSUNTO CONSIDERATO DA FREGE

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there is only one number that is capable of being a property of a concrete particular, and that is the number 1. It is logically impossible, for example, for the number 2 to be a property of a concrete object; the number 2 can only be a property of two concrete objects.
Note:L ASSUNTO CORRETTO E IMPERMEABILE ALLA CRITICA DI FREGE

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it is not that twoness applies to the set {a,b};
Note:CccccccccFACCIAMO A MENO DEGLI INSIEMI

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If we’re talking about the aggregate of the cards, that instantiates the number 1.
Note:QUINDI

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9.3   Arithmetical operations
Note:Tttttttttttt

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‘Two apples plus three apples make five apples’ means something like this: if you have two apples, and you also have three more apples (that is, three that are each different from either of the original two), then you have five apples.
Note:ADDIZIONE....E COSÌ LE ALTRE

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It is not, for example, a matter of bringing the apples into spatial proximity.
Note:L OPERAZIONE NN È FISICA

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Adding two apples to three apples is solely a matter of considering two apples and, without making any changes to any of the apples, considering an additional three apples,
Note:OPERAZIONE MENTALE

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There is not even any passage of time assumed:
Note:TEMPO

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This is why arithmetical statements are necessary and knowable a priori.
Note:A PRIORI

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9.4   The laws of arithmetic
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a+b = b+a    (Commutative Law of Addition)
Note:LA PIÙ FAMOSA DELLA LEGGI

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Why do these hold, and how do we know them? In essence, the reason why (a + b) is equal to (b + a) is that the expressions ‘(a + b)’ and ‘(b + a)’ are synonymous:
Note:SINONIMIA

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9.5   Zero
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If the number n is instantiated by n things, then the number zero must be instantiated by zero things. But there cannot be a property that,
Note:OBIEZIONE

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Reply: zero is not the same kind of thing as one, two, three, and so on.
Note:RISPOSTA

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zero is not a number.
Note:INFATTI

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if I have zero cookies, I should not say, ‘I have a number of cookies’;
Note:SENSO COMUNE

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It is no coincidence that the concept of zero has a quite different history
Note:INFATTI

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Objection: ‘But we can do arithmetical operations using zero. How could that be, if zero is not a true number,
Note:OBIEZIONE

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When we decide to extend the number system by including zero, we define arithmetical operations for zero in such a way as to keep the whole system coherent.
Note:RISPOSTA...SEMPLIFICAZIONE

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Famously, there is one case in which we do not define the arithmetical operations for zero, namely, the case of division.
Note:E LE ECCEZIONI NN MANCANO...A RIBADIRE CHE...

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what is the referent of ‘0’ in its noun usage?

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LA DOMANDA CHE RESTA

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The answer is that the symbol does not require a referent to be meaningful. In the same way that the noun ‘nothing’ lacks a referent,
Note:RISPISTA

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The point is simply that ‘zero’ functions differently in some important ways from ‘one’, ‘two’,
Note:NN SI TRATTA DI VOLER ESPELLERE LO ZERI DAI NUMER

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9.6   A digression on large numbers
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there are about 1080 atoms in the observable universe;
Note:STENOGRAFIA

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Now we can define another operation known as ‘tetration’, symbolized by ‘↑↑’, to represent repeated exponentiation.
Note:X È UN RIPETUTO + E ESP È UN RIPETUTO X

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After that, there is the operation of pentation (symbolized by ‘↑↑↑’), which is repeated tetration.
Note:OLTRE

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9.7   Magnitudes and real numbers
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9.7.1   Magnitudes vs. numbers
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The concept of magnitude is probably undefinable,
Note:OCCORRONO ESEMPI

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the height of the Eiffel Tower, the temperature of a cup of coffee, the mass of the Milky Way Galaxy.
Note:ESEMPI

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properties of concrete objects.
Note:MAGNITUDO

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refers to a dimension
Note:Ccccc

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refers to a particular value
Note:Ccccccc

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Magnitude values are represented using real numbers. The magnitudes, however, are not themselves numbers.
Note:M E N

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The Eiffel Tower is approximately 324 meters tall, which is to say about 1063 feet tall. If the height of the Tower is a number, which one is it? Is it around 324, or around 1063?
Note:QUI FREGE HA RAGIONE

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the number that we use to represent the height of the Tower is not a property of the tower. But the height is a property of the tower. So the height is not a number.
Note:ALTEZZA E NUMERO

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9.7.2   Real numbers as relationships
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What, then, is a real number?
Note:PRIMA AVEVAMO DEFINITO I N NATURALI COME UNA PROP DEGLI OGGETTO...ORA DEFINIREMO I REALI COME UNA RELAZIONE...I NUMERI QUANDO ESPRIMONO UN UNITÀ DI MISURA

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start with how we use real numbers to describe the world.
Note:PROCEDIMENTO

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Eiffel Tower is 324 meters tall.
Note:2

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‘324’ records a relationship between the height of the Tower and a unit,
Note:ALTEZZA E METRI

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The metaphysical background is that magnitude values come in classes that are comparable to each other.
Note:CONFRONTABILITÀ XFETTA

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When a magnitude is greater than another magnitude, this greaterness comes in degrees.
Note:NUMERI E MAGNITUDO

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9.7.3   In defense of the bifurcated account of number
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‘324 is a real number, since an object could be exactly 324 times as long as the standard meter. 324 is also a natural number. But on your account, a natural number is a property, whereas a real number is a relationship.
Note:OBIEZIONE DELLA BIFORCAZIONE

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It turns out that there are two numbers 324: the cardinal number and the real number.
Note:RISPOSTA

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Now you might wonder: why not take a uniform view of cardinal numbers and real numbers?
Note:DUBBIO

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Frege’s deck-of-cards problem by saying that the same physical aggregate is differently related to two different units: it bears the ‘52-fold’ relationship to the unit ‘card’, while bearing the ‘one-fold’ relationship to the unit ‘deck’.
Note:SOLUZIONE SEMPLICE

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The relationship theory requires that there be an object to be the first relatum, that is, the thing that is supposed to stand in a relationship to a unit.
Note:INCONVENIENTE

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suppose there are seven reasons for being suspicious of set theory.
Note:DOV È QUI L OGGETTO?

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an object that has each of the seven reasons as parts?
Note:L OGGETTO MISTERIOSO....SETTE RAGIONI SETTE METRI

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9.7.4   Measures and magnitudes
Note:Tttttttttttttrr

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measure theory,
Note:BRANCA DELLA MATEMATICA

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9.7.5   Intensive vs. extensive magnitudes
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Extensive magnitudes are those that are additive across the parts of an object.
Note:ESTENSIVE

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the magnitude values of all of these parts will contribute additively to the magnitude value of the whole.
Note:Ccccccccccc

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length is an extensive magnitude.
Note:ESEMPIO

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Similarly for volume:
Note:ALTRO ESEMPIO

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Intensive magnitudes, by contrast, are magnitudes that do not arise from adding together the magnitudes of the parts of an object,
Note:INTENSIVE

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For example, the temperature
Note:ESEMPIO

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There may be ambiguous cases. Consider the property of mass.
Note:A METÀ

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9.7.6   Natural vs. artificial magnitudes
Note:Ttttttttt

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schmass of an object is defined to be the reciprocal of 3 minus the object’s mass in kilograms:
Note:MAGNITUDO INVENTATA...SI PUÒ

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I will soften that a bit and simply call schmass an ‘artificial’ magnitude,
Note:ARTIFICIALE

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As a first approximation, I will take causal efficacy as the test of naturalness.
Note:SEMPLICITÀ

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9.8   Indexing uses of numbers
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suppose you are in a hotel, in room 210.
Note:NUMERO INDICE

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indicating that there are 210 of something;
Note:NUMERO NATURALE?

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indicating that something is 210 times greater than
Note:NUMERO REALE?

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‘210’ is simply being used as a name for that room.
Note:USO IN QS CASO

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a number term being used in a way that does not really refer to a number.
Note:CONCLUSIONE

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This is what I refer to as an indexing use of numbers. In an indexing use, some number is used as a name for a more or less arbitrary item or value,
Note:INDEXING

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9.9.1   Rational vs. irrational numbers
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9.9.2   Negative numbers
Note:Ttttttt

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9.9.3   Imaginary numbers
Note:Ttttttttt

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x2 = −1’.
Note:NUMERI IMMAGINARI

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One cannot conjure such a number into existence just by fiat, as the standard approach seems to suppose. Trying to solve the equation ‘x2 = −1’ by inventing a new number is like trying to solve the equation ‘x + 1 = x’ by inventing a new number,
Note:DIFFICILI DA CONCEPIRE

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9.9.4   Infinitesimal numbers
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An infinitesimal number is a number that is smaller than any positive real number but yet greater than zero.
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