Logic and Mathematics

Natural Numbers- words used to count things.

Three basic approaches to number:

1)       Natural and can be empirically observed. -  Mill.

2)      They are institutions of a harmonic, perfect, platonic world. – Descartes.

3)      They are abstract logical objects constructed purely from syntax – Frege.

Syntax= logical system using rules of inference to alter the meaning of symbols.

Numerical Naturalism
Apes and stone age tribes appear to be able to judge empirical plurality, typically;
0 = Absence of a thing
1 = One banana/enough bananas
2 = A lot of bananas/unlimited bananas

“one thing” “more than one thing” and “lots of things” are the only number system they need.

Small number words are functionally different to large number words. If you come into a room and there is one person, you don’t consciously count that person, but people struggle once they get past 6/7 and have to physically count. So the number 7434 is a predicate symbol of more basic symbols organised according to known syntax, and as a predicate it can be analysed.

Pythagoreanism/Platonism
Prime numbers are pre-existing, eternal, supernatural forms. Necessary pre-conditions for consciousness. All other numbers are just rational combinations of prime numbers. Prime numbers exist in a non human dimesion and they are eternally true and ultimately mysterious. E.g. the religious significance of the number 3.

Pythagoras and (and all the Greeks) regarded only plurals as natural numbers so they begin counting with “two”.

Problem of nothing and zero
The concept of zero came from India, much later via Sufi Islam. The entire Arabic numerical system was introduced in the middle ages after the fall of Rome.
Zero =Nothing
Nothing = Something
Problem of the law of contradiction was solved by Leibniz’s monads that an object can contain its own negation. Modern philosophers have thus asserted that zero is a natural number. Logically derived as 1-1=0 “nothing” is a philosophical absurdity. The qualitative differential gap between 0=nothing and 1=something is as big as the universe.

The problem of nothing/zero remained unsolved until Frege.

Numbers as logical objects
Links logic and arithmetic in an overall system of philosophy of language, with arithmetic as a special case of language.

Axiom- all things which are identical are equal to themselves.
It follows – all things which are pairs are identical to all other pairs, regardless what they are pairs of.
The class of all pairs contains all pairs and this can be given a purely nominal symbol e.g. “two” a word or a numeral it doesn’t matter.

Epistemology
Mill went beyond his predecessors claiming that not only all science, but also all mathematics is derived from experience. The definition of each number contains the assertion of a physical fact. Every number (2, 3, 4 etc.) denotes physical phenomena and connotes a physical property of that phenomena. E.g. “two” denotes a pair of things, and connotes what makes them pairs. Two apples are physically distinguishable from three apples. They are a different visible and tangible phenomenon.

Mill doesn’t make it clear exactly what the property is that is connoted by the name of a number, and Mill also admits that the mind has some difficulty distinguished between 103 apples and 104 apples.

He also claims that “the sum of equals are equals” is an inductive truth, or a law of nature I the highest order. Inductive truths = generalisations based on individual experiences.

Newman belonged to the same empiricist tradition as Mill. Newman believed that the only direct acquaintance we have with things outside ourselves comes through our senses, to think we have faculties for direct knowledge of immaterial things is merely superstition. Our senses don’t let u go very far out of ourselves, we have to be near things to touch them and we can neither hear nor touch things from the past or future. Reason is our way of proceeding from things which are perceived to things that are not. The exercise of reason is to assert one thing on the grounds of another.

Newman identified two different aspects that are exercised when we reason; inference (form premises) and assent (to a conclusion). These two things are very different and assent may be given without grounds, or based upon a poorly constructed argument.  Arguments may be better or worse, but assent either exists or it doesn’t. Locke argued that there is there cant be a concrete assent, as the assent must be conditional. Newman didn’t agree with this stance, there is no such thing as degrees of assent. However he still argued that assent based on evidence that is merely intuition may still be valid, e.g. all of us are certain that we will one day die but we cannot give exact evidence to support this.

There is a difference between knowledge and certainty. If I know “p” then “p” is true, but I may be certain of “p” but “p” can still be false. 

WINOL - Week 5 - Botley Housing Development

Written Story:

Eastleigh borough Council have given a large scale housing development the green light. The development will see one thousand four hundred new homes being built on farm land and a golf course near Botley. The green belt development will also include a primary school and significant road changes.

Hundreds of people turned up on Monday to hear the verdict on the proposed Boorley Green housing plans. The meeting continued until 12:45pm and many residents were very disappointed when the council announced that the plans had been approved.

The controversial decision has become a key issue in the Eastleigh by-election. The Tory candidate, Maria Hutchings, says that she is disappointed and the council has made the wrong decision.

However the Liberal Democrats, who back the plans, think they will gain the respect of the voters as they make the hard decisions and criticised Maria Hutchings for not speaking up during the meeting. 

Video Report:

Extended Maria Hutchings - Conservative - Interview:

WINOL - Week 4 - Nick Clegg and Nigel Farage

As political reporter for WINOL I will be following the Eastleigh by-election over the next couple of weeks. This week was a highlight for me on WINOL as I was fortunate enough to be able to film Nick Clegg. Lou and I went to film with the vague hope of our own interview but unfortunately our dreams were too big! However I managed to get some fantastic footage.

On the saturday i got up early so I could film the first stage of the UKIP campaign and go an interview with Nigel Farage. Monday I filmed Nick Clegg and on Tuesday I went back to the UKIP campaign as they officially announced their candidate. I managed to get an interview with their candidate Diane James which I use in  my package and I also turned into an extended feature interview for WINOL.

Video Report:

Extended Interview with Diane James:

WINOL - Week 3 - Chris Huhne

WINOL week three I covered the Chris Huhne scandal. The footage for this piece was made up of archive footage, newspaper headline shots, interview, vox pops and my piece to camera. My main issue with this story was finding enough images to hold it all together, as it is a national story and I was unable to get any footage of Chris Huhnes resignation statement.

On the Tuesday I went to Eastleigh to interview Keith House (Lib-Dem) and Ray Finch (UKIP) and to also gather vox pops from residents. Unfortunately, due to technical problems with the camera and sound I was unable to use any of the vox pops I had gathered, or my piece to camera, or my interview with Ray Finch. I then went back to Eastleigh on Wednesday morning to re-do my piece to camera and the vox pops from the public.

After a very stressful morning of filming and editing, I managed to turn it around in time for the bulletin.

Written Story:

Chris Huhne has resigned as the MP for Eastleigh after pleading guilty to perverting the course of justice.

Allegations first surfaced in 2010 that Huhne had got his then wife, Vicky Pryce, to take speeding points for him. The Eastleigh MP and his family consistently denied the allegations.

Huhne’s marriage later ended after he had an affair with his PR adviser, Carina Trimingham. The turbulent relationships within his family were highlighted by texts from his son, which were revealed in court.

His constituents showed very little sympathy for Huhne, one resident said: “I think he owes everyone in Eastleigh an apology”.

A by-election will now take place and with Huhne having won his seat with a near four thousand majority, the Lib Dems are confident they can maintain it. Councillor Keith House said: “it’s a great shame that the events that happened, happened, but we move on, go into the by-election confident that we can hold the seat and elect a new MP for our community”.

The date of the by-election is yet to be announced but there is speculation that it will take place in early May so it coincides with the local elections.

Video Report:

Phenomenology and Existentialism - Seminar Paper

Kant first marks the departure from Descartes’ metaphysical philosophy by stating that “existence is not a predicate of consciousness”, it is a pre-condition of consciousness. Consciousness is not a proof of existence, consciousness just “is”, it doesn’t cause anything and isn’t caused by anything. To ask “how does consciousness arise?” is a stupid question, how could there not be consciousness? You cannot stand outside of consciousness. Consciousness is not individual, there is no “I” as in “I think therefore I am”, Descartes’ transcendent ego no longer works as a theory.

Like Freud, Husserl was Jewish, and he also attended lectures in Vienna. He too fell subject to Nazi anti-Semitism having his books burnt by German troops in 1939.
Husserl was greatly influenced by Franz Brentano who tried to relate Aristotelian philosophy of mind to modern experiment. Brentano’s publication: “psychology from an empirical standpoint” stated that the data of consciousness comes in two kinds: physical (colours and smells) and mental phenomena (thoughts which have content or are about an imminent object).

Husserl focused his philosophical approach on mathematics and his first publication was the “philosophy of arithmetic”. Here he tried to explain that our numerical concepts were originated in mental acts. However, because of his desire to connect mathematics and psychology, he ended up drawing some undesirable conclusions, such as denying that one and zero were numbers. Frege criticised this publication stating that the mental events that are private to the individual could not be the foundation of mathematics as that is public and is the same for everyone. After much criticism, Husserl abandoned this idea.

The beginning of the twentieth century marked the start of continental traditions and saw many philosophers making the distinction between logic and psychology. Husserl was no different. In his publication “logical investigations” he argued that logic cannot be derived from psychology, and that psychology is philosophy’s rightful home. Sciences and logic require factual enquiry. However Husserl took his theories further by stating that what is characteristic of mental phenomena is that they are directed to objects. “I think OF you” “I worry ABOUT my degree” the words “of” and “about” indicate intentionality. There are two things that are essential for thought: that it has content and a possessor. For example “I think of a cat”. The cat is the content and I am the possessor. So when talking about mental phenomena the three big things are the content, the possessor, and its intentionality. Many other people may also think of a cat which Husserl explained by saying that these other mental acts belong to the same species. The concept (a cat) is just the species to which all of these acts belong.

After drawing a distinction between psychology and logic, Husserl proceeded to go further and draw a distinction between psychology and epistemology, doing so through the new discipline of “phenomenology”. Phenomenology was developed in the beginning of the twentieth century by Husserl and a group of philosophers at Munich, who coined the phrase “phenomenological movement”. The aim of phenomenology is the study of immediate items of consciousness, without referring to what that consciousness might tell us about the extra-mental world. So basically its aim is to study consciousness as a thing in itself, in a purely logical way, and to avoid any metaphysical ideas. For Husserl it makes no difference whether the concept you have is of a real thing or a hallucination because the intentionality of you thought (e.g. the OF or the ABOUT) is exactly the same regardless of whether it’s about a cat or a unicorn. Husserl gave the example that “I think of Jupiter as I think of Bismarck”, Husserl may never have seen Jupiter but that doesn’t mean he can’t have the concept of it, as his intentionality is the same.

 In his publication Husserl left open the possibility that there may be realities of non-phenomenal objects, but such objects are to be no concern of the philosopher.  He states that this is because we can only speculate about the external world. Husserl makes the distinction between imminent perception and transcendent perception. Imminent perception is my immediate acquaintance with my own mental thoughts and is the basis of phenomenology. Transcendent perception is my perception of my own past actions and mental states, and of the contents of other people’s minds. Imminent perception is self-evident whereas transcendent perception is fallible as it leaves room for interpretation and error. Husserl stated that only consciousness has “absolute being”, all other forms of being depend on consciousness for their existence. He uses the same concept to describe phenomenology in that phenomenology is the most basic of all disciplines because its subject matter provides the basis for all other philosophy and science.

Heidegger was one of Husserl’s pupils and he claimed that up to this point phenomenology had been too half hearted. Phenomenology was supposed to examine the data of consciousness, but the terms used to describe it, such as “act” and “content”, had not been discovered in consciousness, but instead were just taken from earlier philosophy.

Heidegger maintained that the concept of “being” was the first task of phenomenology. We must understand “being” before we can consider the relationship between consciousness and reality. Heidegger argued that we must go back to the theories of the pre-Socratic philosophers to talk about “being” as they pre-date the formal philosophical vocabulary and all of the presuppositions which they carry with them. Heidegger set himself the task to re-invent the philosophical vocabulary, so we could discuss “being” without the complications of what the words used mean in other philosophical examples.

The main term in Heidegger’s vocabulary that you need to remember is “Dasein” which is essentially “being in the world”. Thinking is only one way of engaging with the world, acting upon it is just as important. For example a carpenter relates to the world through the use of his hammer and this is his true engagement with reality.  The concept of Dasein goes against the work of other philosophers, such as Descartes, who try to prove the existence of an external world. For Heidegger we are not separate beings detached from the world, trying to understand it through experiences, we are ourselves elements of the world. We are beings amongst other beings.

Dasein is not about thinking, it is about caring and it is purely instinctive. Only if you care about the world will you then be able to ask questions and give knowledgeable answers. Dasein is relative to the person and can be entirely ungrounded, or can even be affected by things such as mood or emotion. Dasein is the unfolding of a life, you are not stuck to one thing, you can be something you have never been before, and your potential is just as important as your achievements. What you are aiming for in life has the ability to determine the significance of where you are now. Reflection on the past can produce guilt and reflection on the future can produce dread, it is only when you are caring about the task in hand that you have Dasein. Freedom and authenticity lies in the complete absorption within a task. To live the “authentic life” would be somewhere along the lines of living a self-sustained, simple life in the woods. Whatever your achievements or potentialities were they all terminate in death, death does not complete them.

Through his interpretation of Dasein, Heidegger became the father of “existentialism”. This is the philosophy that we are not just members of a species bound by universal laws, we are what we take ourselves to be. The idea of such freedom can be alarming and result in unthinking conformity, but to do so is a betrayal of your Dasein. To make your own life you must acknowledge that there is no greater meaning for the choices you make and that no choice you make will bring a transcendent meaning to your life.

Sartre was a pupil of Heidegger for a brief period of time and he too developed a form of existentialism. Like Heidegger, Sartre also argued that Husserl had not taken phenomenology far enough. Husserl had accepted the Cartesian ego of the thinking subject, but in fact there is no such thing. When I am absorbed in what I am thinking or doing I have not thought of myself, it’s only upon reflection that we make ourselves the object. So to be thorough phenomenologists we must say that the “self” belongs to the transcendent world.
Sartre attacked the theories of Hume that the only difference between perception and imagination are that in perception the images are more vivid than they are in imagination. Sartre maintained that imagination relates us to extra mental objects not to internal images. For example when we imagine a real person who is not actually there we are creating an object in the world. For Sartre our emotions are not passive, they are not an impartial awareness of our environment. For example when we are depressed we change our perception of the world to make all interactions with it appear pointless.

After the war Sartre moved onto more existentialist philosophy in his publication “Being and Nothingness”. For Sartre, being underlies all the different things we encounter in consciousness. We sort things in accordance with what interests us and what will be of use to us. Sartre argues that we are the only beings for whom our existence comes before our essence. For example an oak tree has to follow a particular life pattern, it has no choice, however man does not belong to a structure in the same kind of way. It is up to you to decide what kind of thing you want to be. The life of a human individual is not determined in advance by a creator or moral laws. Human freedom is absolute but it is also alarming having the responsibility of ultimate choice. We try to hide this freedom from ourselves by trying to adopt some predetermined role given to us by society or religion, but we ultimately fail at doing so and are left in a condition that Sartre calls “bad faith”. The alternative is to embrace and accept our freedom and all of the responsibilities which come with it. Other than the obvious physical constraints to what you can achieve, it is you that must make your decisions entirely on your own.