A Tea Time Quiz - Ten Logical 'T's

Answer: Turing

First of all, an explanation of the solution:

The key is to work out the positions of the four longest words, 'Transistor', 'Therefore', 'Temporal' and 'Thought'. Logic 7 and Logic 10 share the same final letter, so have to both end in 'L'. Since Logic 5 has fewer letters than Logic 7, the latter must be 'Temporal' and Logic 10 must be 'T'Pol'. Logic 1 has six letters, so cannot be any of the remaining three longest words. Logic 5 and Logic 9 can be ruled out as they have the same number of letters as each other (either five or six). Logic 8, with fewer letters than Logic 5 and Logic 9, can also be eliminated. This leaves Logic 2, Logic 3, Logic 4 and Logic 6 as possible options for 'Transistor', 'Therefore' and 'Thought'.

Logic 4 must have a single vowel, as it has one fewer than Logic 9 - which we know has to have two vowels as that is the highest number of vowels included in any of the words with five or six letters. As a result it can also be added to the list of ruled out options. Logic 6 must therefore be 'Therefore' as it has to end in a vowel. This just leaves Logic 2 and Logic 3 available as the positions of 'Transistor' and 'Thought' and since Logic 3 has one more letter than Logic 6, it has to be 'Transistor' and Logic 2 must be 'Thought'.

Logic 9 has to have six letters precisely as all the five-letter words only have one vowel; so Logic 9, Logic 5 and Logic 1 are the three six-letter words and Logic 4 and Logic 8 must be the two five-letter words, 'Terms' and 'Truth'. The final letter of Logic 8 has to come before that of Logic 7 ('Temporal') alphabetically so we can safely allocate 'Truth' to Logic 8 and 'Terms' to Logic 4. Similarly, the final letter of Logic 1 has to come before that of Logic 8 alphabetically, so that has to be 'Turing'. Finally, 'Logic 9' cannot be 'Tarski' as that doesn't end in a consonant, so it has to be 'Theory' and Logic 5 has to be 'Tarski'.

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Alan Turing is a famous name in the field of mathematics, logic and cryptanalysis - or code breaking. Turing worked at Bletchley Park during the Second World War and was instrumental in the British success in cracking the code used by the Enigma machine, which allowed secret German messages to be deciphered and many British and Allied lives to be saved. Turing was awarded an OBE for his wartime work, but was convicted of "gross indecency" in 1952 as a result of his homosexual relationship with another man and he committed suicide in 1954. Queen Elizabeth II issued a posthumous royal pardon to Turing in 2013.

Answer: Thought

Philosophy and logic tend to go hand in hand with each other and academic study on the subject goes back to at least the 4th century BC and the work of the Greek philosophers Plato and Aristotle. These two famous names are traditionally credited with being instrumental in the development of the "three laws of thought", which are often described as the fundamental principles that underpin the idea of logic.

The three laws in question are: the law of identity, that everything has a distinct set of characteristics that can be used to differentiate it from something else; the law of non-contradiction, the idea that something cannot be both true and false simultaneously; and the law of excluded middle, that if you have two contradictory statements then one must be true and the other must be false.

Answer: Transistor

Logic gates are a key component of electronic circuits; they are digital switches that provide a means of selecting different outcomes based on the status of one or more inputs. For example, a simple lighting circuit has one lightbulb and two switches, A and B.

A logic gate is required to control the circumstances in which the lightbulb will be illuminated, such as if both A and B are on, A is on and B is off, or A is off and B is on. They work by measuring the voltage present in the different inputs and are built from electronic devices such as transistors, relays and valves. Transistors are a type of semi-conductor device and were invented in the mid-20th century.

Answer: Terms

In logical terms, one place where you will come across the term 'terms' is the concept of first-order logic, which is used in a wide range of subject areas, including mathematics, computer science and philosophy. First-order logic is a method for representing common reasoning in a formal sentence structure based on variables (or objects), predicates (statements that give information about the variable in question) and a variety of symbols or operators. The variables and predicates are sometimes collectively referred to as 'terms', while the symbols or operators can be known as 'formulae'.

A simple example of the idea - if you have a variable 'x' and two predicates "is a bird" and "is an animal" called 'B' and 'A' respectively, then a way of representing a potential logical connection between these terms would be the first-order logic sentence: "Bx --> Ax". This would translate as "if x is a bird then x is an animal".

Answer: Tarski

Alfred Tarski was an American-Polish mathematician and logician who taught at the University of California, Berkeley from 1942 until his death in 1983. His key areas of research included algebraic logic and model theory as well as the (slightly philosophical) idea of metamathematics - using mathematics to study the wider topic of mathematics itself.

His name has been given to a variety of theorems and problems such as 'Tarski's undefinability theorem', 'Tarski's circle-squaring problem' and 'the Banach-Tarski paradox'. Tarski's original surname was Teitelbaum; he adopted Tarski instead and converted from Judaism to Roman Catholicism in the early 1920s.

Answer: Therefore

'Therefore' is an adverb and a synonym for phrases such as 'for that reason' or 'as a result'. It is usually used to describe a logical inference between a cause and an effect, such as "the bird had a broken wing, therefore it could no longer fly". Unsurprisingly the etymology of the word 'therefore' suggests that it comes from the separate English words 'there' and 'fore'.

In this case 'fore' is the Old English form of 'for' meaning 'because of' rather than the front of something or a desperate warning shout in the game of golf.

Answer: Temporal

Temporal logic is a particular system of logic based on statements and reasoning that can change over time, for example "the bird can't fly until its broken wing has healed". The basic statement "the bird can't fly" may be true at the moment, but it can become false at a future point in time after another condition has been satisfied. Temporal logic uses similar symbols and operators to first-order logic, with the addition of extra ones to designate the passage of time and the state of the variable at different points.

The word 'temporal' derives originally from 'tempus', the Latin for time, and the Old French term 'temporel'.

Answer: Truth

Truth is a fundamental concept in the study of logic, which is underpinned by the idea of assessing whether a statement is true or false. There is also the specific idea of a 'logical truth', one which must always be true regardless of any situation or event surrounding it. Alternatively it could be also be a statement that is always true irrespective of how it is interpreted or a statement that would be true in all potential worlds that could have been created if any situation had turned out differently from history as we know it.

Therefore logical truths tend to be discussed by philosophers rather than mathematicians and, depending on the definition used, it is enormously difficult - if not impossible - to prove that they exist.

Answer: Theory

Simplistically, in mathematical logic a logical theory is a collection of sentences or statements that together provide all of the required context to allow the truth of an argument to be determined. A statement can be true under the terms of one logical theory, but not true under a second due to the different associated requirements. If that idea proves a bit hard to get your head around (and reading too much about mathematical logical theories certainly gives me a headache) then you can always stick to thinking about another type of theory - one which simply means an idea that is put forward to explain something. Logic is a key tool required for the process of proving or disproving a theory.

Answer: T'Pol

T'Pol was the name of a Vulcan character in the American TV sci-fi show 'Star Trek: Enterprise'. Commander T'Pol (to give her full title) was the Science Officer of the USS Enterprise, which was under the command of Captain Jonathan Archer. In the 'Star Trek' universe, Vulcans were particularly noted for their logical attitude to life and adherence to the idea of controlling their emotions.

However, several 'Star Trek: Enterprise' storylines revolved around T'Pol's experience of, and subsequent addiction to, emotional experiences. T'Pol was portrayed by the actress Jolene Blalock with the help of a pair of prosthetic pointy ears.