In some circles, "masters" means only one thing, and it certainly is not higher education, especially at this time of year. For early April is when the year's first major golf competition, the Masters Tournament, gets under way in Georgia.
The Masters, its rich history and traditions and the majestic setting of Augusta National Golf Club would make for an excellent tale. It is, however, a story better suited for a journalist hoping for a magical storyline that enters Masters folklore, or perhaps to see Tiger Woods "take it to the limit" one more time (a story best left out of bounds here).
My story here is about another tradition, the master's degree. Today, there is growing interest, debate, reflection and concern about what constitutes a sound, high-quality master's degree. But there seems to be little movement. Universities seldom go out of their way to call a penalty on themselves, unlike genuine golfers who embrace the rules that govern their sport as sacred literature. Whether it is admissions debacles, suspect practices on athletics programmes or diploma-mill marketing, it is often left to those outside the academy to add up the penalty strokes on the ethical scorecard.
In discussing the master's, academics argue over quality parameters, content, research requirements and other intricacies of the degree, but perhaps the issue that causes most argument is that of course length. Here again is an analogy to the golfer, for whom the ability to get length or distance on a drive is a tactical and strategic advantage. In the university, however, the issue is simply what is the optimal length of time in which to complete a 21st-century master's degree.
The range of viewpoints on this question is diverse. Across the globe, master's degrees range from nine months to more than two years in length. Many academics do not see a problem with this variety: it's our degree and it's accredited, they argue, so we decide, period (mix academic freedom with a dose of parochialism and the similarities between a graduate degree and a 300-yard drive begin to diverge).
Golfers who desire greater length on the course must make physical changes to their swing, work on their timing and put in hours of practice to improve. As rules governing the design of golf clubs and balls are regularly revised to ensure that equipment does not provide an unfair competitive advantage, this facet of the game is the same for all players. The individual decides to make changes and choices with the goal of hitting the ball farther.
It's a different story for the graduate student. The length of time required to complete a master's is never a student's decision. The student's only control is selecting a course. Of course, given a choice between a one-year master's and a two-year master's, the student will always take the longer degree to perfect their expertise and skills, right? Wrong - two-stroke penalty and no frequent-flyer miles.
It's time to hit into the rough and look at the real behind-the-tree issues.
The central issue in this debate about the optimal length is competition, not quality, as many academics would argue.
A programme that allows students the choice of a shorter degree timeframe gains a competitive advantage over those of rival institutions. Of course, students assess a programme on more factors than length alone: reputation, quality, cost, available graduate assistantships, financial assistance, compatibility with work and family obligations and a host of other considerations all come into play.
And for institutions, longer master's degrees must mean more revenue for the programme. If so, why move towards shorter master's degrees? The answer is competitive advantage - or, more precisely, perceptions of competitive advantage.
Today's global higher education landscape is one in which providers are competing for students amid unprecedented financial challenges. This terrain is further complicated by the fact that higher education systems across the world have different traditions, funding patterns and philosophical tenets.
In Europe, there is a long history of free university education at the undergraduate and postgraduate levels for the masses, although most graduate programmes charge minimal tuition fees. Why would degree length be an issue? The funding comes in and the students don't pay exponential increases from their personal income regardless of course length.
In other nations, most notably the US, the money issue is paramount. Tuition fees are already high at all levels of higher education, and they continue to rise. The length of a degree is a crucial consideration for students and for institutions running graduate programmes. Students love shorter courses because they are cheaper, although the issues for students are not exclusively about cost. Institutions, on the other hand, see that the longer they can keep students in their clutches, the more money there is for the programme and the university.
In America, the key factor making degrees longer is a "more is better" strategy that has resulted from the push for assessment and student learning outcomes over the past decade - rather an ironic strategy for enhancing academic quality and student performance considering that it is not uncommon for a US undergraduate to take five to six years to finish a first degree. Don't expect to see three-year bachelor's or one-year master's from US universities any time soon. A few institutions may experiment with these, but mass adoption is not on the cards given the amount of money generated from tuition and fees and also some very powerful philosophical tenets about graduate education.
Variations in traditions and history among global higher education systems create myriad perceptions of the experience and the ideal. Many Europeans are astounded by the amount of money that US students pay for higher education. They find it inconceivable that the richest country on the planet does not provide its citizens with free higher education. But the point is that different systems have evolved in different countries and that making direct comparisons is often complex, enigmatic and foreign to many outside a particular system.
Clearly the length of a master's degree is determined by several factors - national and cultural variations, competition and the search for market advantage, financial concerns and quality considerations. Some would argue that the differences between institutions are primarily self-serving rather than motivated by desire to provide a qualitatively superior graduate experience for the student. So, what club do we hit on this academic course?
Having pondered the conditions, I offer the following premise to consider: the length of a master's degree is inextricably tied to course quality, and shorter master's degrees detract disproportionately from the quality of the programme, the academic experience and skills mastered by students, and the long-term sustainability and reputation of the programme.
Do I have your attention? Good. Now, you may ask, how am I going to defend this premise?
Let's start with the basic philosophical tenets of graduate education. Again, there is considerable variation across higher education systems, and I plead guilty to having received my graduate degrees in America. As such, I'll use this as the baseline for my arguments to engage those outside the US in constructive dialogue, not as a strategy to win the match. Moreover, my obligation as an educator is to provide an objective, fair assessment of this issue devoid of an Anglo-American justification for my points. I will make every effort to articulate my commentary in simple language that is clear and comprehensible to even the novice golfer and academic.
At its core, a master's degree is an empirical and scholarly degree. This means that despite a student's participation and engagement in graduate seminars, internships, special projects, collaborative learning and small-group analysis, the purpose is to teach the fundamental aspects of scholarly and empirical research, critical analysis and synthesis, and objective interpretation of the research process, methodology, results and conclusions.
Moreover, these essential skills are prerequisites for analysing and interpreting other scholarly research as a member of one's profession. Without the fundamentals, one cannot objectively assess, comment on and learn from other research. As such, this sounds like golf, in which poor fundamentals equal poor results (don't just take my word, greats such as Jack Nicklaus, Annika Sorenstam, Nancy Lopez, Phil Mickelson, Sir Nick Faldo and Tony Jacklin all say the same).
Most graduates do not follow research careers. Recognising this fact, US universities during the past 15 years have increasingly added a "research project" option as an alternative to the traditional master's thesis (research). (In the US, the term "dissertation" is reserved solely for the doctoral research component.) The research project at the master's level, although grounded in basic research methodology, tends to be more focused on practical applications and looks more like applied research than a typical master's thesis model.
It is important to recognise that the focus on research is designed to enhance rather than minimise the other components of a master's degree. The rationale is that participation in seminars, collaborative presentations, constructive dialogue with faculty and student peers, internship experiences and so on are more meaningful when coupled with and informed by the acquisition of research skills, knowledge and expertise.
Another essential component of the master's degree is "enlightenment". Golfers may be acquainted with this from the axiom that most amateurs hit the ball farther when they swing easier. Unfortunately, they usually have to hit their first ball out of bounds to discover this eternal truth when hitting their second ball (third stroke) off the tee. Why? It is not because velocity is not related to distance, of course it is. It is because most amateurs can maintain a more consistent and effective motion by swinging the golf club slower.
The enlightenment aspect of the master's degree is helping students to see the interconnected and multidisciplinary nature of knowledge. When I was an undergraduate, my European history mentor would seldom discuss the more intricate political aspects of historical events and trends. When I asked him if he could do this, he suggested that I enrol with another professor for her European political systems course.
I offer this anecdote not as a criticism of undergraduate education, but rather to show that the organisational principle of pre-21st-century universities was to segregate knowledge in academic departments and disciplines. I call this the "everyone's an expert complex".
We are starting to see more interdisciplinary approaches at the undergraduate and graduate levels, which are benefiting staff as well as students in their research and teaching.
This philosophical basis of graduate education plays out in a number of important ways that bring us back to the "length" controversy. I would like to explore them in the context of comparing a one-year versus a two-year master's degree.
In considering what we want graduate students to gain, we cannot ignore academic preparation. Many graduate disciplines admit students who were not required to major in that discipline as an undergraduate. Because such students enter a graduate programme with minimal knowledge and content expertise, they must simultaneously learn the discipline and the research process. Once again, this is not a criticism but is framed within the context of awarding a one-year master's degree. If the aim is student mastery at the graduate level of research knowledge and skills to a specific discipline, this goal will be difficult for even the most talented students to meet in one year.
On a master's programme, students are learning their scholarly craft, and as we all know practice makes perfect (actually if it were possible, perfect practice makes perfect, but these notable quotes make good folklore). However, if we subscribe to the premise that mastery of the fundamentals is essential to high-quality performance over the long term, then the research and golf analogy returns. The best golfers all have sound fundamentals, spend endless time and effort returning to these first principles when their game is in trouble, and will tell you that when they first learned the game (the right way), they spent years honing these basic skills.
We want graduate students to reach the top level, but can this happen when we expect them to master the fundamentals of the research process in the briefest time possible while they are also learning about their discipline and the interdisciplinary connectedness of knowledge?
Those seeking mastery of a skill or craft will know that practice improves quality, which in turn means improved performance. If we provide the graduate student with the time to master research skills, integrate discipline and interdisciplinary knowledge, reflect on practice and research within and outside the discipline, collaborate with peers and faculty, we will produce a graduate with a sound set of skills and knowledge that will enhance long-term performance in their profession.
At this point, the reader may be tempted to conclude that I must believe that the only reasonable thing to do is to banish one-year master's degrees from the face of higher education for eternity. This, however, is not my aim. Why? Because good graduate education also provides students with one more important life-essential lesson - there are few either/or answers to important questions. As H.L. Mencken stated: "There is always an easy solution to every human problem - neat, plausible, and wrong."
What I argue is that the most appropriate length for modern master's degrees is inextricably tied to the philosophical basis of graduate education and the primacy of the empirical and scholarly research process. If for any unknown reason I missed the memo announcing that we have dispensed with the essential components of graduate education, I apologise and will calmly take a two-stroke penalty and become an advocate for six-month master's degrees. Moreover, if we can cut the undergraduate degree to two years and doctoral study to one year, then we could begin producing PhDs in three-and-a-half years. Indeed, this would certainly serve the higher education sector and planet more effectively for the duration ... or would it? Illusions of progress are often our greatest barrier to true advancement.
In the final analysis, I have great confidence that the global higher education community understands the complexity of these issues and will respond with prudence, humility, insight, innovation and with a greater awareness of the competitive advantage argument in concert with the tenets that contribute to high-quality graduate education.
Given the absence of either/or answers at our local clubhouse, I suspect that the optimum length of the master's degree probably falls somewhere between 15 and 24 months. That's a rather short period of time considering that the world's best golfers spend years simply learning the fundamentals of their profession. There will, of course, be extreme pressures for universities to offer accelerated programmes at all levels in response to financial necessity and to the competitive forces impinging on higher education. For now, I'm going to presume that the aforementioned memo dispensing with the historical tenets that underpin high-quality graduate education, while perhaps written, has not been sent.
What is certain is that the next player to top the leader board after navigating the course at Augusta National Golf Club and emerge as the Masters champion will undoubtedly be one with sound fundamentals that hold up under the most extreme pressures of his sport. Indeed, successful golfers are inherently better researchers than researchers are golfers. Perhaps this will not go unnoticed by graduate educators across the globe next April - even though they won't get to slip on a green jacket at the end of the day.
Mention a "master's degree" in the UK and you could be talking about a nine- or 12-month postgraduate degree, a taught or research postgraduate degree, an undergraduate degree in a science or mathematical subject, or an honorary title bought by Oxbridge graduates.
The picture is a little clearer in the rest of Europe, after the drive to harmonise education systems through the Bologna Process and create a common bachelor's, master's, doctorate cycle of uniform length.
Overall, the UK is different from continental Europe in terms of master's provision. While a master's has generally become a two-year postgraduate course in the rest of Europe under the Bologna Process and the undergraduate master's phased out, the UK has been able to persist with its one-year postgraduate master's, arguing that the greater intensity of such courses gives them equivalent value to longer ones.
So what does a UK master's degree mean to students, universities and employers?
In September 2009, the Quality Assurance Agency (QAA) launched a consultation on a draft document called Master's Degree Characteristics, which is intended to offer "a framework that higher education providers can use in describing the nature of the master's degrees they offer".
On the purpose of master's programmes, the document says universities may offer the courses to allow students to focus on a particular area of study they have previously encountered, to learn how to conduct research, to undertake a particular research project, or to become specialised in a field of knowledge related to a profession.
The document goes on to say that master's degrees may be one year or two years in length; they may be modular; they may be delivered partly through an employment setting; they may be delivered as part of a four-year course that includes a bachelor's degree; they may even be delivered through a four-year integrated programme that includes a doctorate.
If that leaves you confused, the UK Council for Graduate Education (UKCGE) sympathises.
In a submission to the Department for Business, Innovation and Skills' review of postgraduate provision, the UKCGE says: "The use of the title 'master's' across the sector is currently in a confused and confusing state."
It outlines three broad uses of the term: postgraduate (taught and research), undergraduate and honorary (at the universities of Oxford and Cambridge, graduates can convert their bachelor's degrees into master's for a small fee).
Malcolm McCrae, chair of the UKCGE, says: "It is confusing for employers. It is confusing for students coming from outside the UK. What is it they are buying into?"
The UKCGE suggests adding prefixes to denote whether a master's is undergraduate, postgraduate or honorary.
But does the UK's system of one-year courses mean lower-quality qualifications?
McCrae says there is a strong argument that "the intensity is at a higher level for a shorter period of time, and that the overall amount of time of learning is roughly equal (to that of longer courses). You have to be careful about equating length with quality if you don't take any account of intensity."
Comparing the UK with the US, he says longer master's may be the norm across the Atlantic because students "come off the back of undergraduate degrees that are less specialised than is the case in the UK".
When the Bologna Process began, some feared that the UK would be forced to adopt the two-year postgraduate master's courses common in the rest of Europe. But the UK HE Europe Unit, funded by Universities UK, the QAA and the funding councils, was among those to argue successfully that one-year courses could be accommodated.
Paul Dowling, policy officer at the unit, says: "It is probably true that the two-year master's degree is more popular and widespread across European institutions. There would have been some nervousness in the UK, asking whether we are more lightweight. But that debate has eased with the recognition that master's can be designed for different things."
A master's degree must have between 90 and 120 credits under the European Credit Transfer System, with the UK's one-year courses valued at 90 credits.
Dowling adds that the emphasis is on learning outcomes under this system. "It is not about the time studied; it is about what a student can do at the end of it."
Howard Davies, HE consultant, and former UK Bologna Expert, wrote Survey of Master Degrees in Europe for the European University Association in 2009.
In it, he argues that the master's is still not "readable" across all 47 countries involved in the Bologna Process. To make it easier for students and others to see what a master's offers, he believes that at-a-glance markers should be developed to identify factors such as duration, credit value, any professional accreditation and whether work placements are included.
He also notes "the problem of nomenclature", which means there is "only limited pan-European understanding of how different master's stand in relation to each other". And distinctions made to clarify matters at national level could further hinder transparency at European level, he warns.
Davies identifies three types of master's provision: taught courses with professional development application; research-intensive courses often functioning as pre-doctoral courses; and courses delivered mainly to returning learners.
He says in the report that master's courses have "a crucial role to play in the knowledge society", offering a foundation for doctoral research and the development of "human capital in many fields". All of which means the courses should be accessible "by as many persons as possible".
But Davies adds that of the three Bologna cycles, the master's is the most "marketised", with fees for the courses often very high.
To assume that master's courses "will thrive on competition alone is incautious", he says, urging that it is "time to consider issues of student finance and equal opportunity of access".


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text:
A Frege-kalkulus egy matematikai logikai kalkulus (levezetőrendszer), azaz egy alapjelekből, axiómákból, levezetési szabályokból álló formális nyelv vagy elmélet, melyet Gottlob Frege jénai matematikus alkotott meg 1879-ben megjelent, Fogalomírás (Begriffsschrift) c. könyvében.

A levezetési szabályok

Két levezetési szabályt használ: a modus ponenst és a generalizációs törvényt. Ezen kívül említ még egy konvenciót, amit, lévén máshová még kevésbé sorolható, itt  említünk.

 A modus ponens a következő: amennyiben érvényes  és  is, akkor  is (tehát "ha A igaz és a-ból következik, hogy B, akkor B is igaz").
 A behelyettesítési szabály: ha X összetett ítélet, melyben Y egy függvény argumentumának, függvénynek vagy határozatlan ítéletnek a jele (változója), akkor az Y betű minden X-beli előfordulása helyébe egy megfelelő típusú másik betűt vagy összetett kifejezést –  függvény argumentumát, függvényjelet vagy ítéletjelet – helyettesítve az így kapott Z ítélet érvényes, ha X is az volt.
 A generalizációs szabály konvenciója: egy  alakú kifejezésen a következőt kell érteni:  . Tehát megengedhető ítéletben betű szabad előfordulása, de ez mindig univerzális kvantorral kötött előfordulást jelent (ez a konvenció egyszerűsíti az ítéletek formáját, könnyebb kiolvasást téve lehetővé).

Az axiómák

A kilenc axióma

Frege kilenc axiómára alapozza a Fogalomírás rendszerét (axiómák azok az ítéletek, melyeket szemantikailag és nem szintaktikailag igazol).

Ezek a Fogalomírás számozása szerinti (1), (2), (8), (28), (31), (41), (52), (54), (58) tételek (a változókon és egyéb betűkön kívül az első háromban csak a feltételesség, a második háromban a tagadás jele is szerepel, az utánuk következő kettőben az egyenlőségjel is, végül az utolsó, kilencedik axiómában pedig az univerzális kvantifikáció). Az axiómák modern logikai átiratban:

Az axiómák értelmezése régen és ma

Ezeken az axiómákon Frege a generalizációs konvenció alapján másodrendű ítéleteket ért. Például

 ⊢ A→(B→A)
azt jelenti, úgy kell érteni,
 ⊢ ∀A∀B: [A→(B→A)].
A modern logikatankönyvek általában nem követik ezt a felfogásmódot (tekintve, hogy a másodrendű logika még csak nem is egyetemi tananyag, ez nem is igen lenne lehetséges). A legelterjedtebb modern felfogás szerint az axiómák sémák, azaz maguk nem ítéletek, csak ítéletváltozókból és logikai operátorokból álló jelsorok; melyekben a betűk helyébe megfelelő módon ítélet(nev)eket helyettesítve, igaz ítéletet kell kapnunk bármely helyettesítéssel (azaz tautologikus sémák).

A nulladrendű logika vagy ítéletkalkulus szintaktikus (más néven axiomatikus) felépítésének legismertebb módszere, a Hilbert-kalkulus, gyakorlatilag ma is a Frege által használt axiómarendszerre  lentebb  épül, noha hangsúlyozzuk, Frege axiómái nem nulladrendű, hanem (legalább) másodrendű logikai axiómák.

Az axiómarendszer bizonyításelméleti értékelése

Ha Frege logikai rendszerét elsőrendűnek tekintjük (ez megfelelő szintaktikai korlátozásokkal elérhető), akkor eme korlátozott rendszert komplettnek, teljesnek nevezhetjük. Az erre vonatkozó tételt Kurt Gödel bizonyította 1930-ban  (ld. az irodalomjegyzéket) ) . Eszerint ha az  jól képzett (értelmes) ítéletséma nem vezethető le az elsőrendű logikában, akkor szerkeszthető hozzá "cáfoló interpretáció" (azaz olyan matematikai struktúra, melyben nem érvényes).

A Frege-axiómarendszer viszont nem független. A nulladrendű logika felépítéséhez három axióma is elegendő (az első, második és negyedik), de már Frege is javasol egyszerűsítéseket és összevonásokat műve Előszavában a formálisan elsőrendű (egyenlőségjelet vagy kvantort tartalmazó) axiómákra is.

Sorozatelmélet

A Fogalomírás III. fejezetében Frege felépít egy nagyon alapszintű sorozatelméletet (definiálja a "megelőzés", "rákövetkezés", "egyértelmű reláció") fogalmakat. Frege elmélete erősen másodrendű, rengeteg, függvényekre vonatkozó kvantifikációt foglal magában (a lentebbiekben Ruzsa Imre szóhasználatát és jelöléseit alkalmazzuk, melyek eltérnek Fregéétől).

A legalapvetőbb Frege definiált reláció (a 69-es számú tétel) az öröklődés. Egy predikátumot (egyargumentumú függvényt) öröklődőnek vagy hereditáriusnak nevezünk egy relációra (kétargumentumú függvényre) nézve, ha abból a két tényből, hogy (i) előbbi egy individuumra fennáll, és (ii) utóbbi fennáll az előbbi individuum és egy másik individuum közt, következik, hogy a predikátum fennáll ama másik individuumra is. Jelekben:

   .

Frege ezután definiálja a megelőzés relációját (76) egy r relációra nézve; ezzel pedig lehetőség nyílik, hogy ha adott egy r reláció, akkor annak segítségével különfle "sorozatokat" képezzünk (pontosabban, egy r meghatároz egy "sorozatot").

Tehát a és b egymás rákövetkezői az r relációra nézve, ha minden e relációra nézve öröklődő predikátum igaz b-re, mely igaz az a-val r relációban lévő dolgokra is.

Ezután rengeteg tételt bizonyít, melyek főképp <r tranzitivitásának (98) belátásához kellenek:
   .

Végül definiálja az egyértelmű (univalens) reláció fogalmát (115), és bizonyít még 11 ezzel kapcsolatos tételt:

   .

A Fogalomírásban rendszerének műveleti szintaktikája és szemantikája

Frege az 1. f. 7. §.-ban kimutatja, hogy a tradicionális logikában használt logikai műveletek (melyeket az "és", "vagy", "sem-sem" .. stb. ) kötőszavak reprezentálnak a köznyelvben, kifejezhetőek fogalomírása segítségével. Ez pusztán a tagadás és a feltételesség jelének kombinációit felírva megtehető.

Az áttekinthetőség kedvéért foglaljuk össze, hogy az 1. f. 7. §.-ban Frege mely példákat veszi sorra (nyomdatechnikai okok miatt modern jelölésben közöljük):
 , ma  exklúzió, Sheffer-művelet;
 , ma  alternáció (diszjunkció); emellett beszél a "vagy" kötőszó kizáró (diszjunktív) használatáról, de csak az 5.-6. példa alatt formalizálja;
  , ma  (háromváltozós) alternáció;
  , ma  konjunkció;
  , ma  (háromváltozós) konjunkció.
  , ma  antivalencia (kontravalencia);
  , ami szintén az antivalencia egy lehetséges formalizálása a fogalomírásban;
  , az  művelet;
  , ugyanaz mint az előbbi;
  , ma a Webb-féle  "sem-sem" (konnegáció) művelet.

Logikai műveletek formalizálása a fogalomírásban

Sorra véve, hogy két A,B ítélet, a tagadás és a feltételesség jeléből összekombinálva milyen logikai függvények kaphatóak, azt tapasztaljuk, hogy az összes fontos (a modern logika által számontartott) kétváltozós logikai művelet előáll Frege rendszerében.

Az alternáció előállítása
Például egyszerűen látható, hogy a "megengedő vagy", azaz alternáció (vagy diszjunkció) művelete hogyan fejezhető ki. Mivel

"tagadja azt az esetet, amikor B-t állítjuk és A-t tagadjuk", ezért ennek állítása azt jelenti, hogy B-t nem állítjuk, vagy pedig A-t nem tagadjuk. Azaz hogy B-t tagadjuk és A-t állítjuk. Ezért

tagadja, hogy B tagadását állítjuk és A-t tagadjuk, azaz azt, hogy B-t és A-t is tagadjuk, tehát B-t nem tagadjuk vagy A-t nem tagadjuk. Ez tehát azt jelenti, hogy A-t állítjuk, vagy B-t. Ez tehát a "vagy" kötőszóval leírt diszjunkció. Mai jelölésekkel elmondva,  .

Implikáció

 "ha … akkor …" művelet, kondicionális (vagy implikáció):

( alapján)

Exklúzió

 "A kizárja B-t" művelet, Sheffer-művelet (exklúzió, 7. §. 1. példa):

(  alapján)

Alternáció

 "vagy" művelet, alternáció (7. §. 2. példa):

( alapján)

Szubtrakció

 " … és nem … " művelet (kivonás, szubtrakció; mely kétféleképp is kifejezhető: a 7. §. 7. példa illetve a 7. §. 8. példa szerint):

(  , illetve     alapján, láthatóan tagadása az implikációnak)

Konjunkció

 "és" művelet, konjunkció (7. §. 4. példa):

( alapján, láthatóan tagadása a Sheffer-műveletnek)

Webb-művelet

 "sem-sem" ("Nor" vagy Webb-féle) művelet, konnegáció (7. §. 9. példa):

(    alapján, láthatóan tagadása a diszjunkciónak)

"Retrokondicionális"

Végül nézzük meg az utolsó kombinációt, amelyben két tagadás szerepel (és ezzel az összes lehetséges kombinációt megnéztük két argumentum esetében); mármost az  ítélet fog adódni  (frege nem tárgyalja):

( itt        és     alapján.

Ekvivalencia művelete

Frege néhány "nem-kétargumentumú" feltételességet is megvizsgál.

 "pontosan akkor … ha …" művelet, ekvivalencia (ezt Frege nem tárgyalja):

( alapján).

Háromargumentumú alternáció

Ezen kívül szerepel még a háromváltozós  alternáció is, tehát háromváltozós műveletek is formalizálhatóak a fogalomírásban (7. §. 3. példa):

( alapján)

Antivalencia

Szerepel még a manapság -tel vagy  -val jelölt "(kizáró) diszjunkció" avagy antivalencia  művelete is, melynek a köznyelvben leginkább a "vagy … vagy …" kettős kötőszó használata feleltethető meg. Frege kétféleképp is formalizálja (7. §. 5-6. példa):

(mindkét példa az    azonosságon alapul (ez az  felhasználásával látható be), mivel  és  is ezzel ekvivalens.)

Ma már tudjuk (ahogy azt fentebb említettük), hogy a fregei fogalomírás funkcionálisan teljes, azaz minden n-változós logikai művelet formalizálható benne, nem csak az itt említettek. Ez következik például abból, hogy a konjunkció és a negáció, azaz a  műveletpár funkcionálisan teljes rendszert alkot, és a fogalomírásban mindkettő formalizálható. De már a puszta Sheffer-művelet  is bázisa az összes n-változós logikai műveletnek (mivel  alakban a negáció is kifejezhető vele), és ez is formalizálható a fogalomírásban.

A "láncformula"

A feltételesség jeléből és hasonló építőelemekből (a fogalomírás mint nyelv betűiből/szavaiból) már sok mindent lehet építeni.
Például
                     ├────┬────── A
                          │
                          └──┬─── B
                             │
                             └─── C
azt az esetet tagadja, amikor
                     ├──────┬──── B
                            │
                            └──── C
-t állítják és A-t tagadják, azaz amikor tagadják azt, hogy egy időben tagadják hogy C-t állítják és B-t tagadják, valamint állítják A-t. Mai jelöléssel ezt  vagy  formában írnánk. Megjegyezzük, hogy a Fogalomírás eredeti szövegében, amint erre Ernst Schröder egy, a könyvről írott recenziójában (1880) felhívja a figyelmet, tévedés található ezzel kapcsolatban: "… azt az esetet tagadja, amikor C-t állítják, és B-t és A-t pedig tagadják … " szerepel. Ez és általában ezek a fajta, "balrekurzív" formulák, melyek előtagja is implikációs formula,  csekély fontosságúak, például az axiómák alakjából is látható, hogy Frege előnyben részesíti a jobbrekurziót.

Fontosabbak tehát azok a "jobbrekurzív" implikációs formulák, melyek utótagja is implikáció. A legfontosabb és legegyszerűbb ilyen a következő formula, nevezzük láncformulának (Frege nem ad neki külön nevet), melyet modern jelöléssel egyébként  alakba írhatnánk:
                       ├──┬───┬─── A
                          │   │
                          │   └─── B
                          │
                          └─────── C
Ennek állításával tagadjuk, hogy C állítandó s egyszersmind
                      ├──────┬──── A
                             │
                             └──── B
tagadandó. Mármost ha egy állítás tagad valamit, akkor pontosan abban az esetben hamis, ha igaz, amit tagad. Tehát azt a nehézkes fregei beszédmódot, hogy "az F ítélet tagadja, hogy G" úgy is kifejezhetjük: "az F ítélet pontosan akkor hamis, ha igaz G". Tehát a láncformula pontosan akkor hamis, ha C igaz, és
                     ├──────┬──── A
                            │
                            └──── B
mégis hamis, utóbbi pedig " … tagadja, hogy …", azaz " … pontosan akkor hamis, ha …" B igaz és A hamis. Összegezve: a láncformula pontosan akkor hamis, ha C és B igaz és A hamis.

Mellesleg ez Frege implikációra adott definíciója értelmében megfelel az  formulának (a fogalomírásban nem tudjuk a láncformulánál egyszerűbben felírni, mivel nincs egyszerű, elemi jel a "C és B" formulára, de mai jelölésekkel azt mondanánk, ). Erre Frege axiómáinak szemantikai levezetésekor is hivatkozik, de a modern levezetéselméletben (Hilbert-kalkulus) még fontosabb, és szintaktikai jelentősége is van. Azt hozzá kell tennünk, Frege szerint az itt leírt ekvicalenciát az implikáció definíciója alapján "könnyű felismerni", de bizonyítást nemigen ad rá (csak nagyon elnagyoltan, pár szóban). Megjegyezzük még, hogy a láncformula  alakban is felírható.

A Fogalomírás levezetőrendszere értő használatának egyik kulcsa, hogy tudatában legyünk a formulák jobbrekurzív jellegének. Frege levezetési szabálya, a modus ponens is ilyen alakba formalizálható a modern ítéletkalkulusban: , vagyis itt is egy A→(X→B) alakú vázról van szó. Mindez azzal van kapcsolatban, hogy Frege – tudatosan vagy intuitíven – a logika formalizálásakor erősen épít a manapság Az eldöntésprobléma alaptételének nevezett tétel szintaktikus változatára.

Logika

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The case pitting some Roman Catholic Bishops, Principals and Principals against 'Consortium of Parents' initially programmed at the Bamenda Court of First Instance on April 21, 2017 has been postponed to an unknown date.
A release from the Mezam High Court Wednesday afternoon said due to the fact that they are bereaved and will be accompanying one of their colleagues to the 'Journey of no return', there shall be no court case as a result. The release further states that those who had cases should consult the board to have updates when they will finally be heard.
Wednesday's release means the case between Catholic Bishops will no more hold this Friday as planned.
The announcement to postpone the unprecedented case which had caught national attraction with wagging tongues swearing that the Catholic Church cannot be dragged in the mud by anybody.
Archbishop Samuel KLEDA, President of National Episcopal Conference had maintained that the Catholic Church was not responsible for the stalemate in the Anglophone crisis.
The 'Consortium of Parents' through their legal representative is demanding the sum of 150.000.000 FCFA as special and general damages.
In a release through his legal Counsel,retired Colonel Tamabang says he is not part of the said Consortium of Parents which dragged some Catholic Bishops to court.The communique says, "Our Client retired Colonel Tamabang Simon NCHE wishes to state publicly and categorically that he is not connected in any way to the so called CONSORTIUM OF PARENTS.He has never contacted any lawyer or bailiff to initiate court acion against the above mentioned servants of Gods."


text:
Key West hurricane evacuation | Part 2 | What to do if you leave the island
(Editor's note: Second in a three-part series on Key West hurricane prep. Part One covers hurricane prep basics. Part Two helps decide when to evacuate and what to do. Part Three covers the how-to of sheltering in place.)
Next time you're in need of a rousing, potentially chair-tossing, foot-stomping discussion that does not involve post-2016 politics or Covid, toss this one out: Are you going to leave? Little is so fraught as asking folks if they're going to heed the mandatory hurricane evacuation orders and get the heck out of the Keys.
Ranger Ed and I used to be part of the heck-no-we-won't-go crowd. We're seasoned campers (tents, no toilets, pack in, pack out). We are "second responders" with the Monroe County Emergency Reserve Corps. And, it's a major headache to wrangle five cats into five carriers and pray that someone will take us in.
We reconsidered after Hurricane Irma in September 2017. Irma wasn't, as my dad used to say, "much punkin" when she crossed Key West, but her Cat 4 damage in the Lower Keys made for serious adjustment in that we-won't-go strategy.
It was clear — at least to us — that our house and much of Key West would not fare well, to put it mildly, were we to be hit like Cudjoe and Big Pine in 2017. For all our unseemly island swagger about "surviving" Irma, Key West's Irma experience was barely a tropical storm.
That's when we bench marked "probably get the heck out" to a Cat 3. If a Cat 3 is forecast for Key West, we will be packed — with the Cat 5s, too — and ready to join the trek to safer locales. Anything higher? We're gone. Lower than a Cat 3? We'll decide at the last minute.
Most folks need to get gone.
Though damage in Key West from Hurricane Irma (September 2017) was minimal, winds still created major headaches.
Hurricane evacuation | How to know IF you should leave
When an evacuation order is in effect, you should leave the island if:
You do not have the skills and resources to take care of yourself for at least three weeks. Assume no electricity, no water, no cell service, no replacements for food, water and other life-sustaining supplies. Assume no access to medical care. If you cannot 100 percent take care of yourself, go.
You do not have a chain saw on your back porch. Seems silly, right? Except people with chain saws on their back porches are pretty handy in physically-demanding situations. They can probably build things, fix things and generally lift-and-tote things. Manual labor isn't limited to opening the wine bottle cork.
You have ANY medical or physical condition that would make you dependent on someone else if anything went wrong.
Your residence is flood prone, not up to code or can't be buttoned up tightly. If your roof is sketchy, get out.
You are a swaggering ijit who thinks roughing it is warm bar beer.
Hurricane Evacuation | How to know wHEN you should leave
Timing your evacuation can be challenging, especially if, as with Hurricane Irma, the hurricane path is unpredictable. Visitors are generally required to leave three-five days before the storm is expected to make landfall. I'd say most folks ought to be headed up the Keys and toward safety no less than a day or so after the visitors are kicked out.
If you're planning on flying out, you're going to need at least that much time to book a rare available seat.
A "last minute" departure ought be considered two-three days before landfall. Why? Because the Keys have to get some 75,000 residents and perhaps another hundred thousand visitors off the island chain in less than 48 hours. You know what traffic is like on a holiday weekend. Oh, and there's the whole nastiness of the Seven Mile Bridge in hurricane-a-coming winds.
Gasoline will be scarce to non-existent the more you procrastinate. Ditto the closed restaurants, bathroom stops, official shelters or hotels willing to stay open for those coming off the Keys. You best have a family or friend way up the mainland, preferably inland, north and west.
If you're going, go early. I know our Cat 5s will not be particularly welcome anywhere, but forcing our contingent on the kids in Atlanta beats, well, dead.
Hurricane evacuation | Prepping the house before you go
Whether you go or stay, house prep is the same drill. And unless you want to live buttoned up for five months, you're going to do most of this in the week before landfall. This is our preferred order:
Cut off the coconuts. You should have done this weeks before, but you cannot use a hurricane as an excuse to cut down trees.
Get most everything inside up off the floor by four feet. Seal it in waterproof bags. Chairs, pillows, things in closets, cardboard boxes, electronic devices. Anything that would stay damp and mold. Put it on table and counter tops or the top shelves of a closet. Not the attic! You could lose your roof. It's an awful job, but if there's flooding, you'll be the one person on your block whose "stuff" stayed dry.
Empty the refrigerator and freezer. You will not get back in time and you likely won't get electric back before everything spoils. Do you really want to deal with rotting stuff?
Bring everything outside inside. Yes. Everything. If you can move it, I guarantee hurricane winds will. Don't throw it in the pool. It will rust.
Put up the shutters. On every opening. Even if you so-called have impact windows.
Turn off — at the main — the propane tanks, electricity and water.
And, you're done. Hunker down or hit the road.
The best links for hurricane Evacuation and prep information
Hands down, the best overall link comes from FEMA: How to prepare for a hurricane. Before, during and after. Everything you could want to know — plus a wonderful, interactive checklist. Get busy with this one.
Monroe County Emergency Management is the best resource for Key West and the Keys' hurricane season. From how to prepare and how to download alerts to where to find emergency shelters, bookmark this link. Contains the best local information available for the Keys and Key West.
The best apps and websites to stay informed, get alerts and avoid the "media hype": Download or sign up for Monroe County and Key West alert apps. You can get them on the county and city's website. Bookmark the websites and bookmark the Facebook Pages for Key West, Monroe County Emergency Management, the Sheriff's Department and both the National Hurricane Center and the Key West National Weather Service. You might also like Mike's Weather Page if you are a weather junkie.
As we did during Hurricane Irma in September 2017, Key West Island News will provide news and information before, during and after a major hurricane. We will aggregate the best information from other, trusted sources, post updates on our Facebook Page and include more detailed information on our website.

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San Diego Comic-Con gave us a glimpse of what's to come for a lot of DC's franchises. When it comes to BLACK LIGHTNING, we got a panel as well as a season 2 trailer. The trailer is, by and large, a recap of the first season, but when paired with information from the panel, it still gives us a good idea of what's the come. It highlights what we should hone in on from season one and what storylines — and characters — are going to take the forefront.
The trailer focuses on a question at the beginning: "Do you remember why you became Black Lightning?" The trailer answers this for us, in a way — giving us glimpses back to the 100 kidnapping Anissa and Jennifer, the initial reason Jefferson decided to use his powers again. Nonetheless, it's deeper than that.
BLACK LIGHTNING is a story about a hero who's decided to take up the mantle again. When someone asks Jefferson why he became Black Lightning, there has to be more than one answer. Sure, he became Black Lightning again to save his daughters. There's still the matter of why he originally took up the mantle.
The trailer has an answer for this too: for Freeland. At the core of everything, Jefferson's family, school, and community all tie together to make Freeland as a whole. In the panel at SDCC, there was a lot of talk about community and what Black Lightning means for Freeland as well as the real-life black community.
The trailer also gives us the idea that there are more family team-ups to look forward to. There's going to be more action with Black Lightning and Thunder, of course, but it seems like Jennifer hasn't fallen entirely to the wayside. Jennifer represents the voice of someone who doesn't want their powers — someone who wants to live a normal life. It doesn't seem like this has been brushed entirely to the side either.
There is a surprising amount of focus on Jennifer's scenes in the trailer — hopefully, this means we'll be able to expect more training and more chances for Jennifer to own her powers. Jennifer's powers are special. She produces her own energy and she's able to save her father in more ways than one. Even if she doesn't become a superhero, I'd love to see her come into her own with her powers, and it'd be great to watch Jefferson, Lynn, and Anissa help her there in their own ways.
There are three reasons why the family dynamic in BLACK LIGHTNING works: the drama, the heartwarming moments, and the cool superhero team-ups. It's likely we can expect all of that from season two, with the action cranked up to 11.
We know for sure from the trailer that the 100 and the ASA are still big threats in BLACK LIGHTNING. Even though our heroes exposed the ASA, there's still a mess left to clean up because of them. The 100 provides street-level drama to balance out the government conspiracy plot, although both intertwine because of things like Greenlight.
It's been confirmed in the panel that Khalil, stepping forward as Painkiller, will be a regular. We'll be seeing more of him, likely with a focus on the drama between him and Jennifer. The trailer specifically honed in on the tension between them when Khalil first attacked in season one.
Then, of course, there's Tobias. Season one closed out with the implication that Tobias can take down Black Lightning permanently. We can expect Tobias's plan to play out in this season, giving us some answers, but possibly give us more questions as well. The clash is sure to be high-energy no matter what.
BLACK LIGHTNING: Trailer or Recap?
Some people have already come out of the woodworks (mostly on YouTube, shocker) to complain that the trailer is truly a recap. However, the idea of using footage from season one seems pretty smart to me. It helps hype up fans, and, honestly, it's been a while since season one. Not everyone has time for a full rewatch before new seasons drop, so I'm all for recaps.
This Week On The Arrowverse Week 23: BLACK LIGHTNING Season 1 Finale Shocks!
On top of that, supercuts are made purposefully. What scenes they decided to hone in on from season one tells us a lot about what we should be looking forward to. The trailer we were given wasn't slapped together at random. This is a video specifically crafted for SDCC — it has to serve a specific purpose, and it did.
Paired with the panel and some of the things confirmed in it, the recap gives us a pretty solid idea of what season two holds. The panel lets us know about show regulars, giving us a confirmation that Painkiller is now going to be a regular villain. The panel also discussed deeper matters when it comes to BLACK LIGHTNING… the ideas of community and family that carry through and give us the heart of the show.
It's a great first taste of what's to come. Keeping us on our toes, looking forward to the stories we've already become invested in, and not revealing too much. I can say that it definitely has me hyped up for season two.


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Vol. 20 - Num. 79
Experiences relating to motherhood: aspects to consider for the promotion of child health
Elena López de Arana Pradoa, Alexander Barandiaran Arteagab
aFacultad de Educación y Deporte. Universidad del País Vasco. Vitoria-Gasteiz. España.
bFacultad de Humanidades y Ciencias de la Educación. Universidad de Mondragon. Escoriaza. San Sebastián.
Correspondence: E López de Arana. E-mail: elena.lopezdearana@ehu.eus
Reference of this article: López de Arana Prado E, Barandiaran Arteaga A. Experiences relating to motherhood: aspects to consider for the promotion of child health. Rev Pediatr Aten Primaria. 2018;20:237-43.
Published in Internet: 25-07-2018 - Visits: 9959
Introduction: one of the main demands of mothers in paediatric primary care is to feel understood as they take on this new role. Objective: the study aims at exploring the experiences of motherhood described by a group of women to identify the aspects that need considering for the purpose of child health promotion.
Materials and methods: we conducted a qualitative study with a phenomenological approach. The sample consisted of seven mothers. The discussion groups were recorded and their contents transcribed for subsequent analysis. The latter was performed collaboratively following the methodology of open coding until theoretical saturation was achieved.
Results: the most relevant experiences could be fitted into three categories. When it came to their relationship with their children, mothers highlighted that it gave them "happiness," although they pointed out "work" as a significant barrier to it. When it came to themselves, they reported feeling "constant alarm," "worried" and "fearful" in regard to childrearing and needing "time for themselves". As for social support, they stated that while their partners were "involved," they tended to "feel bad" in response to comments made by their own mothers and also "pressured" by paediatricians.
Conclusions: emphasising communication skills during training could aid the development of doctor-patient rapport in paediatric primary care so that mothers can reflect on childrearing and not feel blamed, thus promoting adherence to paediatric recommendations and consequently child health.
● Child health ● parental responsibility ● Primary Health Care
Paediatric primary care (PPC) has traditionally been mainly associated with responding to the health-related needs that emerge in children. However, this purpose has been evolving and becoming more complex1. On one hand, the residency training of physicians (MIR programme) has expanded the skills of professionals in this field, preparing them to manage at the primary care level health problems that used to be treated exclusively at the hospital level. On the other hand, as a consequence of public health interventions implemented over the years, such as vaccination, some of the diseases that used to be among the main reasons for using these services have been eradicated. Also, maternal education and school-based health programmes have led to a significant decline in child mortality due to accidental injury.
Under the present circumstances, we need to recognise that there has been a qualitative shift in child health priorities1,and therefore in the perception of paediatricians of their own role, which is now within the framework of health promotion2,3. Thus, paediatricians are currently considered the main professional source of support for families on the development and upbringing of their children.4,5
To support families in childrearing, paediatricians need to try to understand the feelings that arise in mothers in response to the new challenges posed by maternity6. Yet one of the main demands expressed by women in relation to PPC is the need to feel understood or supported as they assume their new role7,9.
In facing this challenge, it is important to be aware of what motherhood involves, the vital transformation it entails, as it produces significant biopsychosocial transformations in women10,11. The mother is born psychologically as the baby is born physically, giving rise to a new identity that will be continuously evolving12. This is reflected in the changes that women report experiencing in their priorities, values and attitudes in relation to motherhood12,14.
Furthermore, there is evidence suggesting that the doctor-patient relationship can be perceived as a source of support in the transition to motherhood15as long as it is based on communication that encourages the expression of questions and concerns16. The development of this new interactive framework can promote the attachment between mother and child17,18and facilitate the understanding of and adherence to professional advice16.
In recognition of the challenges posed by women who use paediatric primary care services, our study aimed at exploring the experiences described by a group of women in regard to motherhood with the purpose of identifying the factors that need to be considered in child health promotion. Although there are other studies focused on how motherhood is experienced13,15,these were based on group interventions that addressed women in at-risk groups, as opposed to discussion groups of women not at risk. Thus, it was necessary to explore the experiences of mothers outside risk groups13, which can help define potential strategic plans in PPC.
The phenomenological design of the study allowed us to delve into the individual subjective experiences of the participants19, that is, into the perceptions of motherhood and the meaning these experiences have20 for the women that attended the discussion group.
Sample and participants
In collaboration with the Department of Youth and Education of the Town Council of Escoriaza (Guipuzcoa), the School of Humanities and Education Science of the Universidad de Mondragón invited families with children aged 0 to 3 years residing in this town to meet and share their experiences in motherhood.
We included all the individuals that agreed to participate, a total of 7 mothers whose characteristics are presented in Table 1, as they all met the necessary characteristics to carry out the study. Thus, it could be said that we selected participants by purposive sampling21, as the selection was based mainly on the topic under study and the availability of the individuals we had approached.
Table 1. Sociodemographic characteristics of the mothers that participated in the discussion group
Age Number of children Had a partner Currently employed
M1 30-40 2 Yes Yes
M2 30-40 1 Yes No
M3 30-40 1 No Yes
We fitted a space in the Museum of Escoriaza where we held five monthly meetings in the format of a discussion group22,23. Each of the meetings lasted two hours.
The discussions were facilitated by the authors of the present article using a "funnel" approach24. This technique is based on the establishment of a positive atmosphere–as Morgan described25, reciprocal and interactive–and keeping the discussion focused on the subject at hand, in this case motherhood, facilitating the progression from general aspects to more specific aspects.
After obtaining the necessary authorizations and the informed consent of the mothers, we recorded the meetings on tape and transcribed their contents for subsequent data analysis26. The unit of analysis was the sentence. After reading and analysing the individual transcripts, we developed a system of categories and codes collaboratively following the open coding approach, which dispenses with the use of a theory from which to apply definitions, laws or dimensions to the discourse under study27, allowing the emergence of the categories and codes by induction until theoretical saturation is achieved28.
Three categories emerged in relation to how participants described their experiences in motherhood. These categories are detailed in Table 2, along with some of the most relevant verbatim quotes.
Table 2. Categories based on which participating women described their experiences of motherhood
Categories Codes Most relevant quotes from participating mothers
Experiences of mothers in regard to their relationship with their children Enjoyment of relationship "I am very happy when I spend time with my son" (M3), "I am very happy when I am with my son" (M2), "Giving my child a sense of security feels great to me" (M7), "I sleep with my child and this is a beautiful experience for me" (M3)
Factors influencing the relationship "I am doing very well with the leave, enjoying my child" (M7), "If the mother does not have to go to work, the mother feels at ease, and so does the child" (M1), "When I don't have any chores to do, I have a good time with my son" (M7, M4), "Not having time has an impact on our children" (M1)
Experiences of mothers in regard to themselves Stress associated with motherhood "Constant alarm" (M2 and M6), "I am worried about making a mistake or not noticing something" (M1), "I worry when my child seems unwell" (M3), "It worries me that I cannot tell who caused this dependency, he or I" (M3), "The world has changed a lot… I am afraid of the Internet, for example, there's too much information and bullying in it" (M1)", "I need time for myself" (M2, M3, M4, M5, M6), "The most important thing is the child, then the chores, then our partners, then the child again, and last of all us mothers" (M1)
Experiences of mothers in regard to their social network Perceived support "I am thankful because so far we get along well" (M2), "I have no complaints about my partner, he is very involved" (M7), "My husband is really involved" (M1)
Perceived absence of support "When the grandparents tell me that my child does not misbehave with them, they make me feel as if I were doing something wrong" (M6), "My mother is always telling me that we do very stupid things nowadays …" (M1), "Paediatricians put pressure on us, as do grandmothers" (M3))
Maternal experiences regarding the relationship with their children
As described in previous studies13,29, mothers in our sample experienced their relationship with their children from a place of "happiness", "joy" and "enjoyment". Despite this very positive perception of motherhood, mothers that participated in our study highlighted that for this to be the case, they need to be released from various duties, either related to work outside the home or with "house chores", as these tasks take "time" away from enjoying the relationship.
The identification of "work" outside the home as a barrier to the relationship is not new13. It is believed that employed mothers, that is, those employed outside the home, attempt to compensate for their absence by striving to ensure that the time they do spend with their children is quality time30.
When it comes to housework, some researchers assert that the joys of parenting are often compromised by the increase in housework associated with having children31, with additional tasks generally falling to mothers.
Maternal experiences regarding themselves
Participants reported living in a state of "constant alarm" in relation to childrearing. In this regard, they assert that motherhood involves, on one hand, "worry" in perceiving at times that their babies are not doing well, or not knowing whether they are doing the right thing—statements that were consistent with the study by Wilkins14– and on the other "fear" caused by uncertainty, or not knowing the challenges or dangers that their children may face in the future.
In addition, mothers in our study declared that they "need time for themselves". This statement is consistent with previous studies where mothers have reported feeling stressed, tired and overwhelmed13,29, signs that they perceive that they have lost control of their own lives to some extent32. If they had the choice, mothers in our study would spend the "time" that they demand being by themselves to try to reconnect with who they used to be by doing things as simple as reclaiming some of the hobbies they had before having children.
The feeling of losing control over their lives was intimately linked to the hierarchy of priorities that they reported, in which "the child is first, then house chores, then the partner, then the child again and last of all themselves". In the words of Gilligan33, it could be said that women develop an "ethic of care" that revolves around their responsibility toward others.
Maternal experiences regarding perceived social support
Most mothers reported feeling fortunate that they "got along" with their partners and that their partners were "involved" in parenting. When it came to their extended families, on one hand they acknowledged the help they receive, especially from their own mothers, but on the other they generally agreed that this help is often accompanied by some criticism of their parenting style, which often makes them "feel bad".
This "pressure" is compounded by the pressure that comes from paediatricians. It appears that when mothers are informed that their children are developing well, they tend to interpret this as an indirect statement that they are doing a good job, so these interactions are experienced in a positive light34. On the other hand, when the opposite occurs, that is, when mothers learn that their children are not growing as expected or desired, the interaction may become a negative experience resulting from the perception that their performance as mothers is being evaluated.
The accounts we obtained were consistent with those reported in previous studies34,35, where mothers expressed the social pressure that they felt subjected to.
As was the case in previous studies13,14,32, the women who participated acknowledged the joy they derive from motherhood, and identified the difficulty in achieving an adequate work-family balance as a barrier to it. Thus, many women, especially those who are actively employed, seem constantly torn between how they would like to approach motherhood and the reality of what they can actually do. Therefore, it would be beneficial to share with them the conclusions of the available literature36,37, which suggest that in this day and age maternal employment does not have a negative impact on the developmental outcomes of children, as fathers are more involved in parenting than they were before and the quality of child care services has increased substantially.
As others did in the past14, our study revealed that women experience motherhood from a state of constant alarm, worry, doubt, uncertainty and fear due to the considerable demands and responsibility associated with it. Alleviating this anguish could be one of the tasks of PPC professionals. Establishing the doctor-patient dynamic from the awareness of the ethic of care developed by women may be key in achieving this goal33. Furthermore, paediatricians can try to help mothers identify the individual needs of their children, freeing them from the yoke of rigid beliefs that do not acknowledge the existence of this diversity6.
The narratives of the mothers were homogeneous when it came to the role of fathers in parenting and the social pressure they were subjected to. This complaint has also been reported in other studies34,35, where, as occurred in ours, paediatricians were identified as agents that compounded the perceived external demands. To discourage this perception, it would be useful to consider the demands made by mothers, who express the need to feel understood, receive emotional support and think about childrearing without feeling judged15,38.
However, this type of doctor-patient relationship is not the most prevalent, as different studies show that doctors frequently give recommendations and directives, whether they are requested or not16,39. Therefore, the identification of practices that push the boundaries of the traditional technical and evaluative model of care could be a way to develop new approaches fitting the needs expressed by mothers. Education seems to be the key to facilitate this change. If greater emphasis is placed on the influence of the personal background of each paediatrician40 and on interpersonal communication16, it is possible to make paediatricians competent in addressing developmental difficulties while avoiding blaming mothers and helping them deconstruct the fantasy of the perfect mother41 to ensure greater and better adherence to paediatric recommendations8,42, thus promoting child health.
Lastly, while it may be considered sufficient on account of the homogeneity of participants43, the small size of the sample limits the generalizability of the results of this study. This suggests that future studies should have samples that are not only larger but also more heterogeneous in order to explore the diversity that exists in the experience of motherhood. This would allow us to better fit our approach to the needs of the diverse mothers that seek PPC services.
The authors have no conflicts of interest to declare in relation to the preparation and publication of this article.
MIR: medical resident • PCP: primary care paediatrics.
We want to thank the Department of Youth and Education of the City Council of Escoriaza (Guipuzcoa), which collaborated in the study by helping us recruit the sample and providing a space to hold the discussion groups.
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An adult hedgehog is between 24-34cm in length and excluding their face are covered all over in sharp, brown spines, used to deter predators. Their faces and undersides are covered in brown fur. As with any insectivores (species that eat insects) they have relatively pointy noses. Occasionally, albino (all white) hedgehogs are found in the wild. If alarmed, hedgehogs will roll into a ball to defend themselves from predators.
Hedgehogs have poor eyesight and rely heavily on hearing and smell for navigation. In search if prey or a mate, they are known to snuffle very noisily like pigs, which is thought to have earned them their 'hog' name.
No other animals in Britain can be confused with the European hedgehog – if it's prickly – it's a hedgehog!


Dr. John D. Wildgen received his DDS degree from the University of Missouri Kansas City Dental School in 1982. After graduation he served in the army for 6 years. He continued his dental career serving Lake of the Ozarks since 1991. Dr Wildgen has had additional extensive training in cosmetic dentistry, implant surgery, periolase (laser surgery) for gum disease, and NTI appliances for TMJ Disorder. Dr Wildgen enjoys lake activities with his children and granddaughter. He also enjoys scuba diving with his wife and friends in exotic places.


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Show transcribed image text Kim, a U.S. citizen and resident, owns and operates a novelty goods business. During 2016, Kim reports taxable income of $100,000: $50,000 from foreign sources and $50,000 from U.S. sources. In calculating taxable income, the standard deduction is used. The income from foreign sources is subject to foreign income taxes of $26,000. For 2016, Kim files a joint return claiming his three children as dependents. a. Assuming that Kim chooses to claim the foreign taxes as an income tax credit, what is his income tax liability for 2016?
Kim, a U.S. citizen and resident, owns and operates a novelty goods business. During 2016, Kim reports taxable income of $100,000: $50,000 from foreign sources and $50,000 from U.S. sources. In calculating taxable income, the standard deduction is used. The income from foreign sources is subject to foreign income taxes of $26,000. For 2016, Kim files a joint return claiming his three children as dependents. a. Assuming that Kim chooses to claim the foreign taxes as an income tax credit, what is his income tax liability for 2016?
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About 300 former national security officials and ex-White House staff sign open letter accusing Trump of possible 'unconscionable abuse of power' over Ukraine call
Sinéad Baker
President Donald Trump at the CIA headquarters in Langley, Virginia, on January 21, 2017.
Olivier Doulier/Getty Images
About 300 former national security officials, White House staffers, and other ex-officials signed a letter describing President Donald Trump's actions in a call with Ukraine as possibly constituting "an unconscionable abuse of power."
They said Trump, in a call with Ukrainian President Volodymyr Zelensky, "appears to have leveraged the authority and resources of the highest office in the land to invite foreign interference into our democratic processes."
A White House memo summarizing the call shows that Trump asked Zelensky to investigate former Vice President Joe Biden and his son Hunter Biden.
The letter was coordinated by National Security Action, a pressure group that has long criticized Trump. Its signatories include many officials who served under Democratic presidents but also former Republican-era officials.
About 300 former national security officials, diplomats, and ex-White House staff have signed a letter saying President Donald Trump appears to have committed "an unconscionable abuse of power" in a call with the leader of Ukraine and applauding the launch of impeachment proceedings against him.
The statement is signed by former intelligence officers, ambassadors, secretaries of state, major generals, chiefs of staff, and advisers from the US's leading defense and security bodies including the CIA, the Department of Defense, and the State Department.
It was organized by National Security Action, an activist group that opposes what it calls Trump's "reckless leadership."
The statement said the many signatories had "long been concerned with President Trump's actions and their implications for our safety and security."
It noted that some had spoken out against Trump before while others were publicly doing so for the first time in the letter.
Read more: The US's top intelligence watchdog found Trump's conduct so alarming it could expose him to blackmail
The document said new revelations that Trump asked Ukrainian President Volodymyr Zelensky to investigate former Vice President Joe Biden — a 2020 election rival — meant Trump "appears to have leveraged the authority and resources of the highest office in the land to invite foreign interference into our democratic processes."
It added: "That would constitute an unconscionable abuse of power."
The CIA logo.
Saul Loeb/AFP
The roughly 300 signatures, which take up 13 pages of the document, include those of former officials from:
Office of the Director of National Intelligence
House Armed Services Committee
Department of the Air Force
National Counterterrorism Center
Many signatories are people who served under Democratic presidents, especially Barack Obama.
But the statement says it includes people who "worked across administrations of both parties to uphold and advance those national interests."
Among those who signed are Nancy McEldowney, the ambassador to Bulgaria under President George W. Bush, and Matthew Olsen, who led the Justice Department's national security division under Bush and the National Counterterrorism Center under Obama.
Ukrainian President Volodymyr Zelensky met with US President Donald Trump at the United Nations General Assembly in New York City on Wednesday.
REUTERS/Jonathan Ernst
"Having worked across administrations of both parties to uphold and advance those national interests, we consider the President's actions to be a profound national security concern," the statement said.
Some of its members have previously spoken out, the statement said, but "many of us have eschewed politics throughout our careers and, as a result, have not weighed in publicly."
The statement was released in response to an explosive whistleblower complaint that forced the White House to publicly release a memo summarizing a phone call in which Trump asked Ukraine's president to investigate Biden as well as aspects involving the 2016 US election.
Read more: A timeline of Trump's campaign to pressure Ukraine's president into investigating Joe Biden
The complaint, from an anonymous intelligence officer, also alleged that White House officials were alarmed by Trump's comments in the call, prompting them to try to "lock down" the statement and store it in a secure system typically used only for issues concerning national security.
Democrats launched a formal impeachment inquiry into Trump in response.
House Speaker Nancy Pelosi addressing reporters at the Capitol on Thursday.
The National Security Action statement said that its signatories did not want to "prejudge the totality of the facts of Congress' deliberative process" but that "there is no escaping that what we already know is serious enough to merit impeachment proceedings."
Read more: Trump is facing the biggest firestorm of his presidency because his own White House staffers blew the whistle on him
It said "all of us recognize the imperative of formal impeachment proceedings to ascertain additional facts and weigh the consequences of what we have learned and what may yet still emerge."
"We applaud those Members of Congress, including Speaker Pelosi, who have now started us down that necessary path," it said.
It said using the office of the president to encourage foreign election interference "would represent an effort to subordinate America's national interests—and those of our closest allies and partners—to the President's personal political interest."
Read more: Trump officials were reportedly so alarmed by his Ukraine call that the transcript had to be printed out and passed around by hand
"The introduction of any other considerations of the President debases our democracy, has the potential to make us more vulnerable to threats, and sends a message to leaders around the world that America's foreign policy can be dangerously corrupted by catering to a single individual," the statement said.
"If we fail to speak up—and act—now our foreign policy and national security will officially be on offer to those who can most effectively fulfill the President's personal prerogatives."
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