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In [[formal logic]], '''nonfirstorderizability''' is the inability of an expression to be adequately captured in particular theories in [[first-order logic]].  Nonfirstorderizable sentences are sometimes presented as evidence that first-order logic is not adequate to capture the nuances of meaning in natural language.
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The term was coined by [[George Boolos]] in his well-known paper "To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)."  Boolos argued that such sentences call for [[second-order logic|second-order]] symbolization, which can be interpreted as plural quantification over the same domain as first-order quantifiers use, without postulation of distinct "second-order objects" ([[properties]], sets, etc.).
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A standard example, known as the ''[[Peter Geach|Geach]]–[[David Kaplan (philosopher)|Kaplan]] sentence'', is:
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: Some critics admire only one another.
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If ''Axy'' is understood to mean "''x'' admires ''y''," and the [[universe of discourse]] is the set of all critics, then a reasonable translation of the sentence into second order logic is:
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: <math>\exists X ( \exists x,y (Xx \land Xy \land Axy) \land \exists x \neg Xx \land \forall x\, \forall y (Xx \land Axy \rightarrow Xy))</math>
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That this formula has no first-order equivalent can be seen as follows. Substitute the formula (''y'' = ''x'' + 1 v ''x'' = ''y'' + 1) for ''Axy''. The result,
<ul>
 
 
: <math>\exists X ( \exists x,y (Xx \land Xy \land (y = x + 1 \lor x = y + 1)) \land \exists x \neg Xx \land \forall x\, \forall y (Xx \land (y = x + 1 \lor x = y + 1) \rightarrow Xy))</math>
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states that there is a nonempty set which is closed under the predecessor and successor operations and yet does not contain all numbers. Thus, it is true in all [[Non-standard model of arithmetic|nonstandard models of arithmetic]] but false in the standard model. Since no first-order sentence has this property, the result follows.
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== See also ==
  <li>[http://www.kamijo-sh.com/cgi-bin/bbs.cgi http://www.kamijo-sh.com/cgi-bin/bbs.cgi]</li>
* [[Plural quantification]]
 
* [[Reification (linguistics)]]
</ul>
* [[Branching quantifier]]
* [[Generalized quantifier]]
 
== References ==
* {{cite journal | author=George Boolos | authorlink=George Boolos | title=To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables) | journal=[[Journal of Philosophy]] | year=1984 | volume=81 | pages=430–49| doi=10.2307/2026308 | issue=8 | publisher=The Journal of Philosophy, Vol. 81, No. 8 | jstor= 2026308 }}  Reprinted in {{cite book | first=George | last=Boolos | authorlink=George Boolos | coauthors= | year=1998 | title=Logic, Logic, and Logic | edition= | publisher=[[Harvard University Press]] | location=[[Cambridge, MA]] | isbn=0-674-53767-X }}
 
[[Category:Logic]]
{{logic-stub}}

Latest revision as of 00:02, 23 November 2014

gX5C82 Brazil 6s 99uazpDc

The grand opening of the Mall at Bay Plaza brings nearly 780,000 square feet of retail space and more than 100 stores. It is the first fully enclosed fashion shopping mall in the borough in four decades.Holder called on to investigate Eric Garner's deathHolder called jordan 6 sport blue on to investigate Eric Garner's deathUpdated: Thursday, August 14 2014 6:01 PM EDT2014 08 14 22:01:08 GMTMembers of jordan 6 sport blue New York's congressional delegation are asking the Justice Department to formally investigate the police custody death of Eric Garner and the law enforcement strategy known as broken windows.

Patterson Cos.: James Wiltz, chief executive officer, sold 50,000 shares Feb. 1 at $28.58 per share, 10(b) 5 1 Plan; and 50,000 shares March 1 at $29.97 per share, 10(b) 5 1 Plan; holds 742,567 shares. 3 years, 1 month agoWCNC StaffUnion County deputies have caught an armed suspect who was hiding out in a campsite near .3 years, 1 month agoWCNC Staff police search for vandals police search for vandals police are looking for vandals that broke several windows out of a building in the. Police are looking for vandals that broke several windows out of a building in the historic district of .

August 11, 2014: Robin Williams was found dead in his California home Monday, a possible suicide, according to investigators. He was 63. B) Look up/get recommendations to an auto body/repair shop near your home or work. That's where it should be towed to.

Bill Watterson, the cartoonist and creator of the beloved "Calvin and Hobbes," has lived a reclusive lifestyle after ending his popular comic strip back in 1995. Since sending his popular cartoon duo down a snowy hill to explore the world over 18 years ago, Watterson has shied away from interviews and sport blue 6s hasn't picked up a pen or drawn another published comic strip.. 相关的主题文章:

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Royle St. The shelter is providing food, water and lodging.No significant damage has been reported in Marshall. They attending an alternative school inside the local justice centre. Their attorneys say the case should be moved out of Steubenville because of the publicity and closed to the public to protect witnesses..

Researchers in Boston and Japan exposed cells from spleens of newborn mice to a more acidic environment that they're used to. In lab tests, that turned them into stem cells, showing enough versatility to produce the tissues of a mouse embryo, for example.

The report did not identify the witness but added it was the same person who pulled Woods from the vehicle after the accident outside his home. Woods' wife, Elin, has told police that she used jordan 6 sport blue a golf club to smash the back windows of the Cadillac Escalade to help her husband out..

It's kind of a juggling act. I think a lot of business owners have to deal with that.". This brings me to one of the main reasons that jordan 6 sport blue I have kept my disease secret: the stigma of 'mental illness'. Because most people do not understand Parkinson's, it may be confused with cognitive disorders such as schizophrenia and Alzheimer's disease.

They say one of.Eyes in the Skies, Drones in MississippiFriday, August 15, 2014 12:41 AM EDTRAYMOND, Miss. Flying up and out of sight, you can barely even hear it once it's up in the air. Cependant, la diffrence de cette dernire, ces plantes n pas jordan 6 sport blue refroidi et seraient donc demeures plus volumineuses. Valuer le rle de l dans ce type de stimulation. 相关的主题文章:

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Two years ago at this podium, I urged spending restraint. I asked that billions of surplus funds be deposited in state savings. In this video sport blue 6s tutorial, viewers learn how to fix the Wi Fi problem on an iPod Touch or iPhone. Begin by clicking on Settings and select General.

By day 25, all three conditions yielded TUJ1+ neurons (Fig. 2a) and cells expressing TH, the rate limiting enzyme in the synthesis of DA. Physicians have noted a correlation between stomach ulcers and Parkinson's disease as far back as the 1960s, before it was even known sport blue 6s that H. Pylori was the cause of ulcers.

Electrodes were deep in her brain. A small box spitting electric impulses into her nervous system was implanted in her chest.The road she was on was much longer than the 5K she was running.NOT AT THIS AGEBailey, 37, jordan 6 sport blue was a registered nurse at Marshall Browning Hospital in Du Quoin, Ill., when the tremors began.She figured it was stress.

Bill Miller said at an evening news conference.The injured were taken to the University of Tennessee Medical Center in Knoxville. Late Wednesday, center spokesman Jim Ragonese said 14 people from the crash were being treated at the hospital. Acrophobia Known by a number of names Acrophobia, Altophobia, and Fear of Heights being the most common. Acrophobia can be dangerous, as sufferers can experience a panic attack in a high place and become too agitated to get themselves down safely.

The 2013 Alaska track field championships are wrapping up Saturday, May 18th in Fairbanks. A couple impressive winners were Wasilla's Peggy Mathis, the girl's 100 meter dash champion with a time of 13.06 seconds. With regard to Mr. Glover, she does not know why the report, written more than a decade ago, cites 'personal reasons' or what is meant by that.". 相关的主题文章: