From the law of excluded middle, formula ✸ 2. 1 in Principia Mathematica, Whitehead and Russell derive some of the most powerful tools in the logician's argumentation toolkit.

✸ 2. 1 ~ p ∨ p " This is the Law of excluded middle " ( PM, p. 101 ).

The proof of ✸ 2. 1 is roughly as follows: " primitive idea " 1. 08 defines p → q

✸ 2. 11 p ∨ ~ p ( Permutation of the assertions is allowed by axiom 1. 4 )

✸ 2. 13 p ∨ ~

✸ 54. 43: From this proposition it will follow, ... that 1 + 1 = 2

In 1927, it appeared in a second edition with an important Introduction To the Second Edition, an Appendix A that replaced ✸ 9 and an all-new Appendix C.

This is symbolized by the following equality ( similar to ✸ 13. 01 above:

* Proposition ✸ 54. 43 in a more modern notation ( Metamath )

Then, on July 2, there occurred another incident which set tongues to wagging at a furious clip.

On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.

It was to provide a safe and spacious crossing for these caravans, and also to make a pleasance for the city, that Shah Abbas 2, in about 1657 built, of sun-baked brick, tile, and stone, the present bridge.

In his Message of December 2, 1862, he put his purpose and his policy in these words -- which I would call the Lincoln Law of Liberty-and-Union: `` In giving freedom to the slave, we assure freedom to the free ''.

We assume for this illustration that the size of the land plots is so great that the distance between dwellings is greater than the voice can carry and that most of the communication is between nearest neighbors only, as shown in Figure 2.

In Figure 2, the points in the network are designated by a letter accompanied by a number.

In any social system in which communications have an importance comparable with that of production and other human factors, a point like f in Figure 2 would ( other things being equal ) be the dwelling place for the community leader, while e and h would house the next most important citizens.

This is important to understanding the position that doctrinaire liberals found themselves in after World War 2, and our great democratic victory that brought no peace.

Helen Deutsch informed us ( The Psychology Of Women, Vol. 2,, 434 ) that in all cultures `` the term ' stepmother ' automatically evokes deprecatory implications '', a conclusion accepted by many.

2.

While convalescing in his Virginia home he wrote a book recording his prison experiences and escape, entitled: They Shall Not Have Me Published originally in ( Helion's ) English by Dutton & Co. of New York, in 1943, the book was received by the press as a work of astonishing literary power and one of the most realistic accounts of World War 2, from the French side.

2.

On the morning of September 2 the Fourth Corps and the Armies of the Tennessee and the Ohio followed the line of Hardee's retreat.

In the midst of this gloom, at 10:05 P.M. on September 2, Slocum's telegram to Stanton, `` General Sherman has taken Atlanta '', shattered the talk of a negotiated peace and boosted Lincoln into the White House.

From the night of August 30 to the morning of September 2 there was no Union cavalry east of the Macon railway to disclose to Sherman that he was missing the greatest opportunity of his career.

The attack started on October 2, 1643, and the Gortonists held out for a day and a night.

2.

The wholesome activities were to be provided by many organizations including the YMCA, the Knights of Columbus, the Jewish Welfare Board, the American Library Association, and the Playground and Recreation Association -- private societies which voluntarily performed the job that was taken over almost entirely by the Special Services Division of the Army itself in World War 2.

The third Act of Faust 2, is a formal celebration of the union between the Germanic and the classic, between the spirit of Euripides and that of romantic drama.

Blackman was to be in New York by February 2, because they were sailing at 12:01 next morning.

The fourteenth name was ( Richard ) Buckenham, written Buckman, admitted to Christ's College under Scott 2 July 1625.

Citing the experience of the Combined Chiefs of Staff in World War 2,, Eden said that all would have been confusion and disarray without them.

At the end of World War 2,, free Europe was ready for a new beginning.

What is required is the full implementation of Article 2 of the Treaty, which provides: `` The Parties will contribute toward the further development of peaceful and friendly international relations by strengthening their free institutions, by bringing about a better understanding of the principles upon which these institutions are founded, and by promoting conditions of stability and well-being.

The editorial was based on a news association dispatch which said that the telegraphers had secured an agreement whereby they were guaranteed 40 hours' pay per week whether they worked or not and that a reduction in their number was limited to 2 per cent per year.

Inorganic structures are found in Chapters 2 - 12, organic structures in Chapters 13 - 15.

* 1, 524 to 2, 437 m: 12

Historically, the Western tradition identifies the general custom of praying for the dead dating as far back as 2 Maccabees 12: 42-46.

12 < sup > 2 </ sup >

The only engagement between the rival factions which is told at length is noteworthy, inasmuch as it was preceded by an encounter at Gibeon between twelve chosen men from each side, in which the whole twenty-four seem to have perished ( 2 Samuel 2: 12 ).

From the dry ground in late summer ( August in zone 7 ) each bulb produces one or two leafless stems 30 – 60 cm tall, each of which bears a cluster of 2 to 12 funnel-shaped flowers at their tops.

God will not hold back judgment because Israel refuses to listen to the prophets and even goes so far as to try to silence them ( 2: 12, 3: 8, 7: 10-17 ).

It lies on Abadan Island ( long, 3 – 19 km or 2 – 12 miles wide, the island is bounded in the west by the Arvand waterway and to the east by the Bahmanshir outlet of the Karun River ), from the Persian Gulf, near the Iraqi-Iran border.

* Stronger beer ( 6 %- 12 %) may contain as much as 2 units per half pint.

Launched from the Kennedy Space Center in Florida at 12: 54 PM EST on 16 April 1972, the mission lasted eleven days, one hour, and fifty-one minutes, and concluded at 2: 45 PM EST on 27 April.

The campaign by the name ' Tree Day-Plant Your Future ' was first organized on 12 March 2008, when an official non-working day was declared and more than 150, 000 Macedonians planted 2 million trees in one day ( symbolically, one for each citizen ).

Here Acts 12: 21-23 is largely parallel to Antiquities 19. 8. 2 ; ( 2 ) the cause of the Egyptian pseudo-prophet in Acts 21: 37f and in Josephus ( War 2. 13. 5 ; Antiquities 20. 8. 6 ); ( 3 ) the curious resemblance as to the order in which Theudas and Judas of Galilee are referred to in both ( Acts 5: 36f ; Antiquities 20. 5. 1 ).

* Saint James the Great executed ( 12: 1 – 2 )

( Ezra 2: 36-39 ; Nehemiah 7: 39-42 ; 12: 1 )

2: 13, 7: 6, 13-14, 12: 18 ; and Acts 19. 22 — all refer to the same journey of a single individual, Titus-Timothy.

The New Testament verses typically referenced are Matthew 26: 30 ; Acts 16: 25 ; Romans 15: 9 ; 1 Corinthians 14: 15 ; Ephesians 5: 19 ; Colossians 3: 16 ; Hebrews 2: 12, 13: 15 ; James 5: 13, which reveal a command for all Christians to sing.

2, 518 people or 15. 8 % are between 30 and 39, 2, 320 people or 14. 6 % are between 40 and 49, and 1, 987 people or 12. 5 % are between 50 and 59.

: HC ≡ CC < sub > 6 </ sub > H < sub > 12 </ sub > C ≡ CH + 2H < sub > 2 </ sub > O → CH < sub > 3 </ sub > COC < sub > 6 </ sub > H < sub > 12 </ sub > COCH < sub > 3 </ sub >

The legend is linked to an idea in the Book of Revelation ( 3: 12 and 21: 2 ) describing a Second Coming, wherein Jesus establishes a new Jerusalem.

There were 2, 481 households out of which 33. 9 % had children under the age of 18 living with them, 49. 0 % were married couples living together, 12. 7 % had a female householder with no husband present, and 33. 3 % were non-families.