Semantics, "internalism" and visual thinking questions
I've been trying to look into why models / modelling / model theory let us down (I suspect it is because they are being misused) and I got hold of Burrow & Walsh, Philosophy and model theory, Oxford, 2018. Every here and there I find a "juicy" philosophical bit, which sets me off.
The authors won't admit to pushing "internalism", which seems to be about inference yet it is stated that it is free of "semantics".
My own instincts lie in semiotics, phenomenology, and the kind of reasoning (which I have been calling "inference") which I find in Jevons, Thouless, or books cowritten by Fosl.
To my mind "semantics" as a word means the exact opposite to its apparent specialised meaning in "formal logic".
Would I be right in thinking that cross checking "logic" by actual inference is likely to produce fairly reliable results because it is often not too vast in scale to fall greatly foul of Godel's incompleteness theorem?
Do professional "formal logic" practitioners think the general public wouldn't be interested and that a strange notation has to be denoted the sole entry point (and to what we might ask)? Do they think it wouldn't be good to simultaneously paraphrase as they go along, not only to inspire newcomers, but as a cross check for themselves?
I know abstracts are abstract, but they are still kinds of things. When I read string theory books or recursion books, there are lovely pictures of the topology I was always so fond of as an infant (with no-one to help me then), but not in "logic" books, where they would be equally appropriate.
Why do authorities underestimate the intelligence and flair of outsiders and then complain there aren't enough takers for science and maths studies?
(Incidentally I now call "universals" an intermediate level of "object" - of beholding - between "primary" and "secondary objects".)
The authors won't admit to pushing "internalism", which seems to be about inference yet it is stated that it is free of "semantics".
My own instincts lie in semiotics, phenomenology, and the kind of reasoning (which I have been calling "inference") which I find in Jevons, Thouless, or books cowritten by Fosl.
To my mind "semantics" as a word means the exact opposite to its apparent specialised meaning in "formal logic".
Would I be right in thinking that cross checking "logic" by actual inference is likely to produce fairly reliable results because it is often not too vast in scale to fall greatly foul of Godel's incompleteness theorem?
Do professional "formal logic" practitioners think the general public wouldn't be interested and that a strange notation has to be denoted the sole entry point (and to what we might ask)? Do they think it wouldn't be good to simultaneously paraphrase as they go along, not only to inspire newcomers, but as a cross check for themselves?
I know abstracts are abstract, but they are still kinds of things. When I read string theory books or recursion books, there are lovely pictures of the topology I was always so fond of as an infant (with no-one to help me then), but not in "logic" books, where they would be equally appropriate.
Why do authorities underestimate the intelligence and flair of outsiders and then complain there aren't enough takers for science and maths studies?
(Incidentally I now call "universals" an intermediate level of "object" - of beholding - between "primary" and "secondary objects".)
Comments (10)
I made to myself this question plenty of times. I do not understand why they are so sticky in their arguments either. Probably they feel anxious if they new generations can take their positions or something. This is one of the objects I really missed in our modern education system: flexibility and the aim to motivate the outsiders. I feel that the ancient principle of "the disciple can surpass the master" is tumbling down. You are speaking about maths and science but somehow this applies to all academic areas.
Do you think this should be more attractive or eye catching?
What are you calling "internalist"? Just curious.
2
And Spencer Brown had a similar leaning with his laws of form - https://en.wikipedia.org/wiki/Laws_of_Form
Louis Kauffman has written a number of fine papers that give a historical overview of this more visual tradition in logic - https://www.ingentaconnect.com/content/imp/chk/2011/00000018/F0020001/art00004
Is that the kind of thing you are looking for?
Still intrigued. All I get from Google is a jewellers in Tunbridge Wells.
- Vaananen J and T Wang, 'Internal categoricity in arithmetic and set theory' in Notre Dame Journal of Formal Logic, 56.1, pp 121-34
- Potter M, Set theory and its philosophy, Oxford 2004
Depending how close to or far from Dedekind one wanted to get (apparently).
I haven't looked those two pieces of literature cited up yet, I am looking for icing and marzipan in Button & Walsh like the dutiful child confronted with the canonical but fearsome Christmas "cake".
I am determined to fight my way into this field: they can't wall me out!
Another book sometimes referenced by Button & Walsh is Hrbacek K and T Jech, Introduction to set theory, 3 rd ed, Dekker 1999.
I don't want to get hold of Potter or Hrbacek only then to be told I still need a degree in maths before I start. Do any readers have experience of those two texts? I suppose periodical articles tend to be very technical and I don't know how to get hold of them?
If you want entertaining logic, Raymond Smullyan is hard to beat.
Here's one to whet your appetite: http://www.logic-books.info/sites/default/files/lady-or-the-tiger-and-other-logic-puzzles.pdf
- that many of the answers will remain incomplete or even almost completely unknown, due to too few clues
- that you often have to change the sequence in which you attend to issues, and not deal with them in the order someone told you to (I think I'll suggest that on the theism thread)
- the sentiments in the epilogue