Per Martin Löf: How did 'judgement' come to be a term of logic ?

Paris - Savoirs ENS 14.10.2011
Transcription of the lecture: pml.flu.cas.cz...
What is logic? Is it the study of the process of inference or reasoning, called demonstration in mathematics, by means of which we justify our judgements? Or is it the study of the logical and set-theoretical concepts, like proposition, truth and consequence on the one hand, and set, element and function on the other, that make their appearance in the contents of our judgements? This is the fundamental question whether logic is in essence, or by nature, epistemological or ontological. The answer is presumably that it is both, which is to say that, within logic, one can distinguish between two parts, or two layers, the one epistemological and the other ontological. But there remains the question of the order of priority between these two layers: Which comes first? Is epistemology prior to ontology, or is it the other way round? Bolzano, whose logic in four volumes, called Wissenschaftslehre, has the most clear architectonic structure of all logics that have so far been written, treated of the ontological notions of proposition, truth and logical consequence (Ableitbarkeit) in the first two volumes of his Wissenschaftslehre, relegating the epistemology to the third volume. Thus he let ontology take priority over epistemology. Although the line of demarcation between the two was drawn in exactly the right place by Bolzano, my own work on constructive type theory has forced me to the conclusion that the order of priority between ontology and epistemology is nevertheless the reverse of the order in which they are treated in the Wissenschaftslehre. The epistemological notions of judgement and inference have to be in place already when you begin to deal with propositions, truth and consequence, as well as with other purely ontological notions, like the set-theoretical ones.
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Nagel Lectures 2013 (by Per Martin Löf)
• Per Martin-Löf - Nagel...

[@Urdatorn]

Fascinating anecdote about the tension between grammarians and logicians in Baghdad! This talk is a great "condiment" to the awesome "ON THE MEANINGS OF THE LOGICAL CONSTANTS AND THE JUSTIFICATIONS OF THE LOGICAL LAWS".

[@VasuJaganath]

All his lectures are masterpieces!

[@gaulindidier5995]

He's what I picture when I think of a Druid.

[@drewduncan5774]

huge compliment on druids

[@vittoriobeghelli3561]

Thank you for the upload!

[@Mephistel]

I can't believe someone just cracked open a can of soda right next to the mic during the talk.

[@halian.vilela]

What a fantastic investigation!!

[@LogicFoundationsMathematics]

Complete transcription of the lecture: pml.flu.cas.cz/uploads/PML-Paris14Oct11.pdf

[@Urdatorn]

Important answer at 1:17:18

[@fbkintanar]

Great talk.

[@dubbelkastrull]

1:12:21 Husserl, Intention, arabic Manna
1:23:17 Arabic qadiya figgetence between saying and...?

[@hulk9231]

Please i'm working on constructive type theory and i really need more explanations about it if you cen helpme

[@annaclarafenyo8185]

The key point is that you can program proofs just like you write software. The main idea is the so-called "Howard Curry correspondence" (it's really the Brouwer-Hayting-Kolmogoroff interpretation of intuitionistic logic). The idea is to interpret every logical connective as a type in a programming language, and ACTUAL type! Like "functions taking these kinds of objects to those kind of objects", then inhabiting these types with specific examples. The best reference is the book on Homotopy Type Theory, nothing in the CS literature is good.

[@thomasp.1828]

"compressed style of aristoteles leads commentators to insert words" very interesting

[@canelonism]

[@dadsonworldwide3238]

In America id imagine this occurs early 1900s when higher ed starts hiding pragmatic philosophy in their basements .lol
If I heard someone day logistical conclusion I'd eqaute they used a 3 step process. But this isn't always the case as I'm forced to remind myself.
My search I've found judgement only follows many other excersizes .
Athens adopts this alphabetical exodus language model and is unpacking successful social behaviors of the past like
Prayer is reformulating every possible question that can be asked about a system .
Classical American founders use this
Prayer logic
Obviously Europe is deep in cursed rationalism, we are teaching less ons of past knowledge.
Again Classical founders say yes to
This deduction or subtracting rationalism of the day. But says not so fast and adds the right to invoke common sense philosophy where here the inherentance or blessing is the conclusion & judgements occur.
As you see prayer logic Cursed rationalism Blessed common sense you also find standardized weights and measure .
A more Egyptian,1st temple mosaic, platonic tripartite 3 way Transfer of data in company with objective ,subjective and idealogical understanding..
Ancient worlds curses and blessings or addition & subtraction still need the first steps of prayer and logic to occur.

[@gotellthem2099]

For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life John 3:16😆