Lecture: Numbers and Logic

This blog is on the lecture concerning numbers and their relationship with logic.

The use of numbers originated from a very simple tribal system. Instead of numbers apes or stone-age tribesman would refer to objects as ‘one thing’ or ‘more than one thing’ as well as ‘many things’. Small numbers could be considered to be completely different from large numbers. Small numbers are generally considered countable up to the number 7. Large numbers can be considered to be any number above 7. The difference lies in the size of the number, for example, if you went to a friends house and 3 of your friends were there, you would instantly be able to count how many people were there. However if you went to a football match, it would be near impossible to be able to count how many people would be at the game.

Ancient civilisations had hieroglyphs for numbers and the number 0 did not exist, even the number 1 wasn’t regarded as a number, therefore to begin counting you would have to start with the number 2. It was the concept of zero which meant it didn’t exist as it refers to the paradox that nothing can exist as something, and 0 equals nothing. This contradicted with Aristotle’s law of Contradiction which was the foundation of all logic.

Leibnitz solved this problem by saying that an object can contain its own negation and the number zero can mean that there are no numbers (of whatever it is being counted) in the room opposed to literally nothing.

Numbers were seen as magic, floating, prefect platonic forms, this was especially considered with the numbers 3, 7, 12 and 13.

Bertrand Russell believed that numbers were synthetic a priori propositions and can in principle be defined logically from a limited set of axioms.

Peano’s Axioms;

1)     

      constant zero is a natural number and you can count using zero. It doesn’t mean nothing in the metaphysical sense. 

For Russell this fact about zero was assumed and not proven which he believed was a significant weakness.

2)      X=X, every number is its own equivalent

3)      Every natural number has a successor number, this was known as the infinity paradox

4)      No Natural number exists who’s successor is zero (negative numbers)

5)      If the successor of N is equal to the successor of M, then N is equal to M

Zero, Number and Successor were never explained by Peano and Bertrand Russell wanted to complete this theory further.

Tabloid nation: In the Land of the Legless

Section 3 in Chris Horrie's Tabloid Nation is an informative and hilarious piece of writing which aimed to explain the motions by which the Daily Mirror erupted with success and then proceeded to crumble due to the rise of The Sun newspaper as well as the fall of the Daily Express. 

The daily Mirror, under Hugh Cudlipp in 1950 went international and became increasingly successful. The newspaper upped its number of employees even bringing in university graduates to work for the newspaper. The Mirror strictly supported labour as far as politics were concerned. Nener was introduced to the paper and made sure the mirror had its daily injection of sexual interest and he took charge of the front page and eventually became editor.

Shock issues were introduced and Cudlipp made the claim that this was his own invention. This saw stories aimed to give ‘an exercise in brutal mass education’. These issues ranged from poverty, child abuse, to suicide cults and motorcycle gangs. This helped increase the sales of ‘The Mirror’ and actually gave it a sharp increase in sales than that of their competing paper, ‘The Daily Express’, despite the express having higher 

sales figures overall this was still quite an achievement.

Expense fiddles started to emerge in ‘The Daily Mirror’ as a result of the papers success. Writers used the mirrors bank account like that of a high street cash machine to pay for alcohol and even call girls. This was seen as a way of paying people ‘cash in hand’ and keeping the official salary figures down.

‘The Daily Mirror’ proceeded to raid The Daily Express for their writers and ended up with more staff than the express, this was seen not as an overly expensive workforce but as a display of the journalistic strength of the newspaper.

The introduction of television however meant that the number of pages in newspapers throughout England had to be reduced. This inevitably led to a decrease in ‘the mirrors’ revenue as television was now the primary source in which younger people fled to.

Cudlipp decided to re-launch The Mirror and aim it towards a young market, this ended up with a series of cringe-worthy articles with the ancient heads of the Daily Mirror making poor attempts at being cool and hip.

The incredibly old style of The Express however meant that there was a gap in the newspaper market, which the mirror managed to grab due to its efforts to be young and cool (even though still having all the old editors and story writers in charge during the war period). Therefore the mirror continued to grow and prosper, founding a new office near Fleet Street nick-named the ‘Taj-Mahal of journalism’.

By 1964 The Daily Mirror was regularly selling more than five million copies a day which meant that it had become the largest selling newspaper in the world. During this period of boom for the newspaper, the Mirrorscope was created as a pull out paper which had the intention of becoming its own separate paper further down the line.

Cudlipp continued to enjoy the luxuries of his success by undertaking in the purchase of a ‘Mirror Dinghy’; however he was caught up in a series of affairs which led him to instate Cecil King as one of the most important figures in the paper in Cudlipp’s absence. After seizing control, King used the wealth and power provided by the mirror to create a huge private office which took up a majority of the ninth floor of the new ‘Taj-Mahal’ office.

King aimed to make the mirror a powerful organization and started buying out other papers and companies. The mirror and Sunday mirror became only small parts of a new IPC conglomerate or in other- wise known as the ‘Odhams international publishing corporation’. King ended up in control of over 200 consumer magazines, nineteen different printing plants and a large stake in ITV commercial television, a record company, and several paper mills.

King aimed to scale down the Herald newspaper and turn the market over to the sun however wasn’t able to achieve this due to the labour parties threats to push for a referral to the competition authorities. This meant that king was forced however to maintain the Herald and attempt to push it into some form of success. The herald eventually flopped and wreaked havoc with Kings Finances, it became known as ‘kings cross’ due to bringing King’s spending to a standstill.

The herald was re-launched as the sun in order to combat its massive losses. The paper Targeted a very young new audience and maintained key focus on things such as the modernisation of Britain with automation, computers, electronics etc… it ultimately failed and Cudlipp sought to be rid of the paper as soon as he met the agreement of labour to keep it running in one way or another for an extended period of time.

During a period in which economic instability was looming in Britain, King published a front page article with the headline ‘enough is enough’ calling for Harold Wilson to leave his office as prime minister. King wrote in an article that Wilson had ‘lost all credibility, all authority’.

King looked for an alternative leader to take charge which would inevitably oust Wilson from his leadership role and the conservatives would take power with this alternative leader. King looked to King-Mosley to be that man.

After disregarding King-Mosley due to his age, King attended a meeting between Mountbatten and Zuckerman to discuss the mirrors role in helping to elect a new form of government. King during the meeting insisted on Mountbatten to form a new government as soon as possible. This form of government would see military dictatorship take over democratic procedure in preparation of the looming recession.

Two men, Penrose and Courtiour opened the case and examined this meeting as it was allegedly a ‘coup’ which was formed in order to oust Wilson with the collaboration of the MI5. After this, apparently 30 intelligence officers had come to the conclusion that Wilson was in fact a threat to national security. They were secretly plotting with the IRA to create a united Ireland, this was known as ‘operation clockwork orange’, this was designed to undermine and remove the labour government. It was reported that following this king had actually worked for the British intelligence in Ireland.

Following this discovery Cecil King was sacked by Hugh Cudlipp. This was due to his association with national affairs and he had been accused of creating a situation between him and his colleagues at IPC. His article ‘enough is enough’ was considered as the piece of work which ended his career. His room was efficiently removed of any trace of King almost immediately.

Rupert Murdoch bought the news of the world in 1968 and instantly made a few simple changes to restore the newspapers profitability. After effectively managing to gain a foothold in the industry, Murdoch looked to buy another newspaper to expand his potential profitable empire within the media.

Murdoch flew over to Rome to speak with the print union leader Richard Briginshaw, he promised that if he bought the sun newspaper off of IPC (or Cudlipp) there would be no redundancies which is exactly what the unions wanted to hear which obviously got the unions on his side. Murdoch managed to buy the paper for an ‘astonishingly low’ amount of money following this meeting, and held off Maxwell (another potential buyer) from purchasing the paper off of Cudlipp.

This was a somewhat fatal error on Cudlipp’s part as he severely underestimated Murdoch as any kind of serious threat despite being aware that the paper would be in direct competition with The Mirror.  However at this point in time Cudlipp wanted rid of the paper after keeping it going for far longer than he had ever intended it to be in production for and suffering heavy losses because of it.

Murdoch invited Larry Lamb (former employee of IPC) for a ‘quiet dinner’ to talk things through with the basic aim of gaining a chief editor. They discussed how to go about making the sun newspaper similar to that of the glory days of which the mirror experienced by making the paper anti-establishment, campaigning, radical and sexy.

Feeling potentially threatened Cudlipp introduced the mirror magazine which was aimed to see off Murdoch’s newly founded newspaper. Cudlipp filled the magazine with a new and up-and-coming team of journalists fresh from graduation. However, Cudlipp’s magazine failed miserably, it was criticised to not fit with the agenda and type of stories and photography which ran throughout their main newspaper, The Mirror. This failure unfortunately occurred just before the sun was released.

Murdoch’s paper was released, and it was rife with sex, scandal and shocking stories such as filled the mirror in the 1930s. Murdoch’s plan to present the paper just like that of its previous successor had worked and the sun overtook The Mirror in sales to become the world’s best-selling newspaper. The Daily Mirror now had the dilemma of how to turn around their paper to either compete with the sun or enter a slightly or entirely different market to keep it afloat.

Hugh Cudlipp left the daily mirror in 1974 and threw a party of astronomical proportions to be sent on his way. The Mirror went downhill from here. Cudlipp handed the role of editor over to Tony miles, who then died, which resulted in Mike Molloy taking over. Following this Clive Thornton took over as chief executive at the mirror who ruthlessly cut staff expenses and attempted to reorganize the company in an effort to maintain profitability. After Thornton had failed, Maxwell who had been circling the office for weeks was given the job. He immediately dipped into the company’s finances and made un-kept promises about how he intended to return the newspaper to its former glory of the 1960s.

The New Journalism

American journalism began with the penny papers. These papers were deeply partisan and were filled with merchants and politicians. However by the mid 19^th century objectivity was required in order to be profitable.

The first new journalism appeared as the yellow press late in the 19^th century. The two major players in this new form of journalism were that of William Randolph Hearst of the New York Journal and Joseph Pulitzer of the New York World.

This new age of the yellow press implemented something known as sensationalism. This saw huge emotive headlines and big striking pictures appearing on the front page of newspapers in order to attract customers into buying the newspaper. All newspapers before this had been mainly focused on political and economic issues. This new type of news had exclusives, dramatic stories, romantic stories shocking stories, crime stories etc. Many called this yellow journalism the new journalism without a soul as all the stories were about sex, sin and violence.

By the 1960’s and 1970’s the yellow press started to write about foreign wars, political or social upheaval or military threats. Journalists ended up recording the events of the day in a very formulaic way. However there was a lot to write about in this decade. Firstly the JFK assassination, then the refusal by Muhammed Ali to be conscripted for the Vietnam war, the Vietnam war itself, the sexual revolution, the pill, the student movement, the protests in 1968. There was a very anti0-establishment movement spreading across England and America.

Following this there was a shift from the act of ‘seeing’ to the act of ‘telling’ readers or in other words objectivity is disregarded in favour of subjective experience and storytelling.

One of the most recent forms of journalism is known as Gonzo Journalism. This involved the idea that a journalist would participate in a form of performance journalism, for example the journalist presented in Fear and loathing in las vegas or supersize me fit this category. Journalists were effectively seen as adventurers who risked their jobs, their health and maybe even their lives in pursuit of a hot story.

Logic and Language

The Hobbesian account presents the idea of the Two-name theory of the proposition, this is evident also in Nominalism. This theory states that a proposition is only true if both predicate and subject are names of the same thing.

John Stuart Mills however believed this theory to be wrong and that it only makes sense when both predicate 

and subject are proper names. He presented this idea with his book ‘System of logic’ which included his theory on language with his theory of naming.

Mills considers a name to be either a description, for example, ‘that book is red’…  an actual name, for example, ‘Helen’…  as well as general terms such as ‘man’ or ‘wise’. All names he considers to denote things. Proper names denote the things they name and general terms denote the things they are true of. General terms also have a connotation, they connote the attributes they signify. Every proposition is therefore a conjunction of a name.

Mills believed that there are two types of inference in any proposition, both verbal inference and real inference. Verbal inference implies that the knowledge of language alone is enough to understand the premiss. In other words that language has the ability to ascertain validity and truthfulness, for example, the two statements ‘no great general is a rash man’ and ‘no rash man is a great general’ maintain the same conclusion and are therefore verifiable.

The other type of inference Mills refers to is that of a ‘real inference’. A real inference therefore infers to a truth in the conclusion which is not contained in the premiss.

Outside of his book, Mills explained that new truths could be discovered by general reasoning by accepting that all reasoning was syllogistic. This meant that any conclusion from an inference is actually implied or contained in the premiss.

Frege believed however that there was an evident fallacy in the use of subject and predicate in order to explain language. He presented this idea in his ‘refoundation of logic’. He believed that logic was a priori and analytic and can be considered to be the second founder of logic.

Frege argued that in order to resolve the problem surrounding the two terms subject and predicate it was necessary to replace them with the two terms argument and function. This, he suggested provided more flexibility when analysing the logic behind language.

He proposed that the argument is the constant or ‘fixed’ element in a sentence or proposition, for example, the first part of the sentence; ‘wellington defeated Napolean’, can be changed to ‘Wellington defeated Nelson’. Napolean can be changed whether it makes the statement verifiable or not but the first part of the sentence is the argument and therefore the changeable word or (name) can be considered in this case to be the function, e.g. ‘William defeated…’ is the argument and ‘Nelson’ is the function. This method provides flexibility because you can name or choose different parts of the sentence according to the circumstance. The word ‘defeated’ could also be considered the argument with the functions both ‘Wellington’ and ‘Nopolean’ (or Nelson) as the elements of the propositions which can be changed.

Frege wrote more specifically on theories in language with his work ‘sense and reference’ in 1892

He addressed the topic of meaning and aimed to uncover some of the fundamental flaws within meaning in language. Some of the questions which he aimed to explore where; what do words and sentences signify? How do they signify and do they all signify in the same way? What is the relationship between meaning and truth?

He aimed to achieve this by attempting an explanation of what identity could be considered as. He went about this by using the two terms sense and reference.

What he meant by a reference can be explained as relational to that of an object to which a name, sentence or word refers to. An example of this is that the planet Venus can be the reference of ‘the morning star’.

The sense of an expression however is the particular mode in which a sign presents what it designates, for example ‘The evening star’ differs in sense from ‘the morning star’ even though it has been discovered that both expressions refer to venus.

Therefore, an identity statement will be true if the sign of the identity is flanked by two names with the same reference but different senses… generally.

He explains that there are items at 3 levels… signs, sense and reference. ‘By using signs we express a sense and denote a reference.’