LoF ( T14-15 ) proves the pa analog of the well-known Boolean algebra theorem that every formula has a normal form.

LoF emerged out of work in electronic engineering its author did around 1960, and from subsequent lectures on mathematical logic he gave under the auspices of the University of London's extension program.

( The Four Color Theorem and Fermat's Last Theorem were proved in 1976 and 1995, respectively, using methods owing nothing to LoF.

The semantics of the primary arithmetic are perhaps nothing more than the sole explicit definition in LoF: Distinction is perfect continence.

" Laws of Form " sometimes loosely refers to the pa as well as to LoF.

LoF argues that the pa ( primary algebra ) reveals striking connections among logic, Boolean algebra, and arithmetic, and the philosophy of language and mind.

pa demonstrations and calculations often require no more than J1a, J2, C2, and the consequences () A =() ( C3 in LoF ), (( A ))= A ( C1 ), and AA = A ( C5 ).

The consequence ((( A ) B ) C ) = ( AC )(( B ) C ), C7 in LoF, enables an algorithm, sketched in LoFs proof of T14, that transforms an arbitrary pa formula to an equivalent formula whose depth does not exceed two.

LoF shows how the pa can interpret the syllogism.

Appendix 2 of LoF shows how to translate traditional syllogisms and sorites into the pa. A valid syllogism is simply one whose pa translation simplifies to an empty Cross.

Laws of Form ( hereinafter LoF ) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy.

LoF has appeared in several editions, the most recent being a 1997 German translation, and has never gone out of print.

LoF also echoes a number of themes from the writings of Charles Sanders Peirce, Bertrand Russell, and Alfred North Whitehead.

Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic, praised in the Whole Earth Catalog.

Those who agree point to LoF as embodying an enigmatic " mathematics of consciousness ," its algebraic symbolism capturing an ( perhaps even the ) implicit root of cognition: the ability to distinguish.

LoF has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken.

A concept peculiar to LoF is that of canon.

While LoF does not define canon, the following two excerpts from the Notes to chpt.

T13 in LoF generalizes C2 as follows.

LoF asserts that concatenation can be read as commuting and associating by default and hence need not be explicitly assumed or demonstrated.

LoF ( excluding back matter ) closes with the words:

He claimed to have seen the fabulous Irem, or City of Pillars, and to have found beneath the ruins of a certain nameless desert town the shocking annals and secrets of a race older than mankind.

Another major criticism point has been that although the filter is claimed to stop certain materials, the underground rings dealing in such materials will not be affected.

During the 11th Party Congress Alexander Shliapnikov, the leader of the Workers ' Opposition, claimed that certain individuals from the Central Committee had threatened him.

* In many schools, though seats for students are not assigned they are still " claimed " by certain students, and sitting in someone else's seat is considered an insult

Political leaders are known to have claimed actual divinity in certain early societies — the ancient Egyptian Pharaohs being the premier case — taking a role as objects of worship and being credited with superhuman status and powers.

King Philip II of France claimed that certain properties in Normandy belonged to his half-sister, Margaret of France, widow of the young Henry, but Henry insisted that they had once belonged to Eleanor and would revert to her upon her son's death.

While Fascism claimed that corporatism gave workers power alongside employer in workplaces in reality the concept of " Fuhrerprinzip " gave employers and State-appointed workplace managers absolute control over the workplace as dictated by the State-owned German Labor Front ; based on the Social Darwinist ideology that certain individuals are " gifted " and " born to rule ", employers thought to be part of that group.

In Parzival, Wolfram von Eschenbach, citing the authority of a certain ( probably fictional ) Kyot the Provençal, claimed the Grail was a stone ( called lapis exillis ) that fell from Heaven, and had been the sanctuary of the neutral angels who took neither side during Lucifer's rebellion.

William Whiston, who created perhaps the most famous of the English translations of Josephus, claimed that certain works by Josephus had a similar style to the Epistles of St Paul ( Saul ).

Falwell repeatedly denounced certain teachings in public schools and secular education in general, calling them breeding grounds for atheism, secularism, and humanism, which he claimed to be in contradiction with Christian morality.

In 774, Duke Arechis II of Benevento, whose duchy had only nominally been under royal authority, though certain kings had been effective at making their power known in the south, claimed that Benevento was the successor state of the kingdom.

In addition, relying upon the definition of " sexual relations " as proposed by the prosecution and agreed by the defense and by Judge Susan Webber Wright, who was hearing the Paula Jones case, Clinton claimed that because certain acts were performed on him, not by him, he did not engage in sexual relations.

Murray's ideas nevertheless exerted great influence on certain pagan currents ; in the 1940s, Englishman Gerald Gardner claimed to have been initiated into a New Forest coven.

Donaghy claimed in 2008 that certain refs were friendly with players and " company men " for the NBA.

On alleged " star treatment " during Game 6 by the refs toward certain players, Beech claimed, " there does seem to be issues with different standards and allowances for different players.

* Organisationally, like many other procedures, once torture becomes established as part of internally acceptable norms under certain circumstances, its use often becomes institutionalised and self-perpetuating over time, as what was once used exceptionally for perceived necessity finds more reasons claimed to justify wider use.

K. Paul Johnson suggests in his book The Masters Revealed: Madam Blavatsky and Myth of the Great White Brotherhood that the Masters that Madam Blavatsky claimed she had personally met are idealizations of certain people she had met during her lifetime.

Herodotus claimed Nile crocodiles had a symbiotic relationship with certain birds, such as the Egyptian plover, which enter the crocodile's mouth and pick leeches feeding on the crocodile's blood ; with no evidence of this interaction actually occurring in any crocodile species, it is most likely mythical or allegorical fiction.

A German General Staff publication claimed " Germany had been brought near to certain destruction ( sicheren Untergang ) by the Flanders battle of 1917 ".

World peace is sometimes claimed to be the inevitable result of a certain political ideology.

The injury claimed by the plaintiffs was that damage would be caused to certain species of animals and that this in turn injures the plaintiffs by the reduced likelihood that the plaintiffs would see the species in the future.

The first German raiding party to enter the fort was led by Leutnant Eugen Radtke, Hauptmann Hans Joachim Haupt and Oberleutnant Cordt von Brandis ( after the war, a certain Feldwebel Kunze claimed to have been first to enter Fort Douaumont but this was never confirmed officially ).

Throughout history, there have been many who have claimed having secret knowledge was result of great often supernatural powers, insofar as certain platitudes alluding to an ability and knowledge of the occult ( literally, " hidden ") techniques oft felt could be of great import.

The state claimed certain proportions of all crops, stock, etc.

* The rapid spread of the Bacchanalia cult throughout the Roman Republic, which, it is claimed, indulges in all kinds of crimes and political conspiracies at its nocturnal meetings, leads to the Roman Senate issuing a decree, the Senatus consultum de Bacchanalibus, by which the Bacchanalia are prohibited throughout all Italy except in certain special cases which must be approved specifically by the Senate.