I'm reproducing a few paragraphs from chapter 7 of Peter Smith's Introduction to Formal Logic below. The thought is that if and when we teach a machine, it will at a minimum, expose the implicit assumptions in our metaphysics. There's more to think about than just the paragraphs below, but this much will do, I think.
7.1 Types vs tokens
We begin with two sections introducing relevant distinctions. Firstly, we want the distinction between types and tokens. This is best introduced via a simple example.
Suppose then that you and I take a piece of paper each, and boldly write ‘Logic is fun!’ a few times in the centre. So we produce a number of different physical inscriptions – perhaps yours are rather large and in blue ink, mine are smaller and in black pencil. Now we key the same encouraging motto into our laptops, and print out the results: we get more physical inscriptions, first some formed from pixels on our screens and then some formed from printer ink.
How many different sentences are there here? We can say: many, some in ink, some in pencil, some in pixels, etc. Equally, we can say: there is one sentence here, multiply instantiated. Evidently, we must distinguish the many different sentence-instances or sentence tokens – physically constituted in various ways, of different sizes, lasting for different lengths of time, etc. – from the one sentential form or sentence type which they are all instances of.
We can of course similarly distinguish word tokens from word types, and distinguish book tokens – e.g. printed copies – from book types (compare the questions ‘How many books has J. K. Rowling sold?’ and ‘How many books has J. K. Rowling written?’).
What makes a physical sentence a token of a particular type? And what exactly is the metaphysical status of types? Tough questions that we can’t answer here! But it is very widely agreed that we need some type/token distinction, however it is to be elaborated.
Types are very natural to us humans. We train deep neural networks to distinguish between types, like recognizing cats and dogs. But if you think about it, we've already "told" the neural network that types are important.
One can imagine that the ability to come up with types is very useful from the point of view of evolution, (e.g., identifying predator tokens as a type might be efficient), and that humans with faulty type mechanisms turn out to be evolutionary dead-ends. The thought experiment that might help to figure out where types come from is to figure out how to get a machine to come up with types from tokens without implicitly requiring that it must do so in the first place.
Edward Measure · 208 weeks ago
Edward Measure · 208 weeks ago
Arun · 208 weeks ago
-Arun
Arun · 208 weeks ago
Peter Smith provides a couple of pages outlining the philosophical difficulties, and then proceeds:
(b) We will have to leave that question hanging. Having flagged up two different ways of thinking about propositions – as sentences and as contents – we aren’t going to develop either approach any further, let alone decide between them.
Now, sitting on the fence about the nature of ordinary propositions, i.e. about the nature of premisses and conclusions in everyday arguments, may sound ir- responsible; how can we possibly leave unresolved such a very basic question as what are arguments made of? For our purposes in this book, however, it turns out that we happily won’t need to adjudicate this tricky issue in ‘philosophical logic’. Why so? Because – spoiler alert! – our key technique for assessing everyday arguments will involve (a) rendering them into artificial formalized languages, and then concentrating our logical efforts on (b) assessing arguments once tidily formalized. Stage (a) won’t require us to say that the formal versions are the very same arguments, just that they are close-enough translations. And crucially, the sentences of our artificial formalized languages explored at stage (b) will by de- sign be free of ambiguities and context dependence – they will come already fully interpreted, stipulated to have a determinate sense. This means that formalized sentence types and the messages they convey will be neatly aligned, and for our purposes we needn’t fuss too much about distinguishing them.
Z Shadow · 198 weeks ago
Z sHadow · 198 weeks ago
ccsu time table · 198 weeks ago
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