Posts Tagged ‘Frege’
“One cannot conceive anything so strange and so implausible that it has not already been said by one philosopher or another”*…
Wisdom for the exquisite Existential Comics (“A philosophy comic about the inevitable anguish of living a brief life in an absurd world. Also jokes.”)…
Frege was an early philosopher of language, who formulated a theory of semantics that largely had to do with how we form truth propositions about the world. His theories were enormously influential for people like Russel, Carnap, and even Wittgenstein early in his career. They all recognized that the languages we use are ambiguous, so making exact determinations was always difficult. Most of them were logicians and mathematicians, and wanted to render ordinary language as exact and precise as mathematical language, so we could go about doing empirical science with perfect clarity. Russell, Carnap, and others even vowed to create an exact scientific language (narrator: “they didn’t create an exact scientific language”).
Later on, Wittgenstein and other philosophers such as J.L. Austin came to believe that a fundamental mistake was made about the nature of language itself. Language, they thought, doesn’t pick out truth propositions about the world at all. Speech acts were fundamentally no different than other actions, and were merely used in social situations to bring about certain effects. For example, in asking for a sandwich to be passed across the table, we do not pick out a certain set of facts about the world, we only utter the words with the expectations that it will cause certain behavior in others. Learning what is and isn’t a sandwich is more like learning the rules of a game than making declarations about what exists in the world, so for Wittgenstein, what is or isn’t a sandwich depends only on the success or failure of the word “sandwich” in a social context, regardless of what actual physical properties a sandwich has in common with, say, a hotdog.
“Is a Hotdog a Sandwich? A Definitive Study,” from @existentialcomics.com.
* René Descartes
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As we add mayonnaise, we might send thoughtful birthday greetings to Norbert Wiener; he was born on this date in 1894. A computer scientist, mathematician, and philosopher, Wiener is considered the originator of cybernetics, the science of communication as it relates to living things and machines– a field that has had implications for implications for a wide variety of fields, including engineering, systems control, computer science, biology, neuroscience, and philosophy. (Wiener credited Leibniz as the “patron saint of cybernetics.)
His work heavily influenced computer pioneer John von Neumann, information theorist Claude Shannon, anthropologists Margaret Mead and Gregory Bateson, and many others. Wiener was one of the first to theorize that all intelligent behavior was the result of feedback mechanisms and could possibly be simulated by machines– an important early step towards the development of modern artificial intelligence.
Infinitely infinite…
The folks at Plus polled their readers for the questions they’d most like answered. The winner: “Does Infinity Exist?,” which cosmologist John D. Barrow answers…
This is a surprisingly ancient question. It was Aristotle who first introduced a clear distinction to help make sense of it. He distinguished between two varieties of infinity. One of them he called a potential infinity: this is the type of infinity that characterises an unending Universe or an unending list, for example the natural numbers 1,2,3,4,5,…, which go on forever. These are lists or expanses that have no end or boundary: you can never reach the end of all numbers by listing them, or the end of an unending universe by travelling in a spaceship. Aristotle was quite happy about these potential infinities, he recognised that they existed and they didn’t create any great scandal in his way of thinking about the Universe.
Aristotle distinguished potential infinities from what he called actual infinities. These would be something you could measure, something local, for example the density of a solid, or the brightness of a light, or the temperature of an object, becoming infinite at a particular place or time. You would be able to encounter this infinity locally in the Universe. Aristotle banned actual infinities: he said they couldn’t exist. This was bound up with his other belief, that there couldn’t be a perfect vacuum in nature. If there could, he believed you would be able to push and accelerate an object to infinite speed because it would encounter no resistance.
For several thousands of years Aristotle’s philosophy underpinned Western and Christian dogma and belief about the nature of the Universe. People continued to believe that actual infinities could not exist, in fact the only actual infinity that was supposed to exist was the divine.
But in the world of mathematics things changed towards the end of the 19th century… In mathematics, if you say something “exists”, what you mean is that it doesn’t introduce a logical contradiction given a particular set of rules. But it doesn’t mean that you can have one sitting on your desk or that there’s one running around somewhere.
And that was only the beginning; then came advances in physics and cosmology… Find out what happened, and whether infinities do in fact exist (plus, discover– finally!– the attraction of string theory) in “Do Infinities Exist?”
[TotH to 3 Quarks Daily]
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As we remind ourselves that there’s always room in Hilbert’s Hotel, we might spare a well-ordered thought for German mathematician and logician (Friedrich Ludwig) Gottlob Frege; he died on this date in 1925. Frege extended Boole’s work by inventing logical symbols, effectively founding modern symbolic logic. He worked on general questions of philosophical logic and semantics (indeed, his theory of meaning, based on distinguishing between what a linguistic term refers to and what it expresses, remains influential). But relevantly here, Frege was the first to put forward the view that mathematics is reducible to logic– thus creating the context in which mathematical infinites can “exist” (in that they do not contradict that logic)…
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