History and context of journalism - lecture/seminar two;

Natural numbers are words used to count things. To count is to create an abstract category or group. Words/abstract symbols for plural categories requires a system of words and logical syntax to combine those number words to imply further or predicate number words.

Syntax – logical system using rule.

There are three attitudes to numbers;

-          They are natural and can be empirically observed.

-          They are intuitions of harmonic, perfect platonic world. (Pythagoras)

-          They are abstract, logical objects constructed of syntax (Frege/ early Russell)

Numerical naturalism/ Evolutionary psychology;

We are only able to judge simple plurality;

0 – the absence of a thing

1 – one thing

2 – more than one thing/ many things

Simple numbers are seen as a plurality with no need to count them. Theres no need to count the number of people in a room. 

Pythagoreanism/ Platonism;

Prime numbers are pre-existing, eternal super natural forms. All other numbers are rational combinations of prime numbers.

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Frege on Logic, Psychology and Epistemology; 

Frege was interested in epistemology for its on sake, butwas concerned to set out the relationship between it and other relativedisciples.

In the tradition of Descartes, Frege believed epistemologyhad been given a fundamental role in philosophy and should be assigned tologic. It was though empiricists had confused logic with psychology.

Making him anxious to show the differences in the nature androle between logic, psychology and epistemology.

Frege adopted and took over Kants distinction between apriori and a posteriori knowledge.To ensure there is no confusion between a priori knowledge and psychology and logic Frege reminds us that it’s possible to discover the content of a proposition before we have hit on proof of it. We the must distinguish between how me first come to believe a proposition and how we justify it. There must be justification – it is absurd to find mistakes in a priori propositions because we only know what is true.

If the proposition is a mathematical one, its justification must be mathematical. It cannot be a psychological matter of processes in the mathematical mind. Sensations and mental images mathematicians have are nothing to do with what arithmetic is about. Different mathematicians have different images with the same number.

Arithmetic is concerned with the truth of propositions. Psychology with the occurrence in thought – a proposition may be thought of without being true and true without being thought of.

Psychology is uninterested in the cause of our thinking. Maths is proof of our thoughts. Cause and proof are completely different.

Thoughts deal with the laws of thought. Logical laws are laws of thought only in the same sense as moral laws are laws of behaviour. Actual thinking doesn’t always obey the laws of logic any more than actual behaviour obeys moral law.