"Modern civilisation has a number of extremely delicate and highly interconnected components whose graceful degradation is effectively impossible."

It is "much easier to break things than to build them up. The government administrations of Britain, France and Germany for example, were set up at a time in the nineteenth century when the rising middle classes demanded a properly functioning state[…]. It took perhaps a generation for professional, neutral public services to fully emerge."

"Forty years of globalised neoliberalism have broken our societies, our economies and our political systems, and we no longer have the ability to put them back together."

https://braveneweurope.com/aurelien-the-end

Fig 3: In DIA, complexity skyrockets. No problem for CHIMERYS!
→ CHIMERYS delivers high ID rates with better FDR control than other solutions
→ More informative fragment utilization yields more reliable #quantification
It handles #DIA data in a spectrum-centric fashion.
4/7

@matthewconroy Great work. Keep going. I'm was inspired. Just spent the morning working with Claude LLM to code a terminal based app that works with the RWGPS api

https://github.com/alxtrnr/eddington_number

#CognitivePsychology #JDM #DecisionMaking #RiskCommunication #probability #uncertainty #ProbabilityPhrases #VerbalPhrases #norwegian #quantification #FramingEffect

@the_etrain
Chief, is there a scale for how biting a side-eye is when throwing shade?
Seems to me this could be as important to calibrate as Scoville units in spicy hot takes.
#HotTakes, #Shade, #Measurement, #Quantification, #Scales, #SocialInteraction, #TuckersBalls

Peirce's 1885 “Algebra of Logic” • Discussion 2
• https://inquiryintoinquiry.com/2024/04/03/peirces-1885-algebra-of-logic-discussion-2/

Re: FB | Daniel Everett

One thing I've been trying to understand for a very long time is the changes in Peirce's writing about math and logic from 1865 to 1885. If there's anything I've learned from reading Peirce in the often dim light of intellectual history it is to be wary of progressivist assumptions — but unlike many of his other fans I apply that caution also within the body of his own work. Long story short, from 1865 to 1885 I see progress on several fronts but also bits of backsliding from his more prescient early insights. So it's a puzzle … and it will take more study to ravel out the reasons why.

Resources for reconciling Peirce's two accounts —
1. The 1870 account of logical involution
2. The 1885 account of universal quantification

Peirce's 1870 “Logic of Relatives” • Selection 12 • The Sign of Involution
• https://inquiryintoinquiry.com/2014/06/09/peirces-1870-logic-of-relatives-selection-12/
Comments —
(1) https://inquiryintoinquiry.com/2014/06/10/peirces-1870-logic-of-relatives-comment-12-1/
(2) https://inquiryintoinquiry.com/2014/06/11/peirces-1870-logic-of-relatives-comment-12-2/
(3) https://inquiryintoinquiry.com/2014/06/12/peirces-1870-logic-of-relatives-comment-12-3/
(4) https://inquiryintoinquiry.com/2014/06/14/peirces-1870-logic-of-relatives-comment-12-4/
(5) https://inquiryintoinquiry.com/2014/06/15/peirces-1870-logic-of-relatives-comment-12-5/

Peirce's 1885 “Algebra of Logic” • Selections
(1) https://inquiryintoinquiry.com/2024/03/24/peirces-1885-algebra-of-logic-selection-1/
(2) https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-selection-2/
(3) https://inquiryintoinquiry.com/2024/03/30/peirces-1885-algebra-of-logic-selection-3/
(4) https://inquiryintoinquiry.com/2024/04/01/peirces-1885-algebra-of-logic-selection-4/

Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
• https://www.jstor.org/stable/2369451

#Peirce #Logic #AlgebraOfLogic #LogicOfRelatives #RelationTheory #CategoryTheory
#Semiotics #PredicateCalculus #Quantification #LogicalInvolution #ComputerScience

Peirce's 1885 “Algebra of Logic” • Selection 3
• https://inquiryintoinquiry.com/2024/03/30/peirces-1885-algebra-of-logic-selection-3/

❝On the Algebra of Logic❞
❝A Contribution to the Philosophy of Notation❞

❝§1. Three Kinds Of Signs❞ (cont.)

❝For instance, take the syllogistic formula,
\[\begin{array}{clcl}\text{All}&M&\text{is}&P\\&S&\text{is}&M\\\therefore&S&\text{is}&P.\end{array}\]

❝This is really a diagram of the relations of \(S,\) \(M,\) and \(P.\) The fact that the middle term occurs in the two premisses is actually exhibited, and this must be done or the notation will be of no value.

❝As for algebra, the very idea of the art is that it presents formulæ which can be manipulated, and that by observing the effects of such manipulation we find properties not to be otherwise discerned. In such manipulation, we are guided by previous discoveries which are embodied in general formulæ. These are patterns which we have the right to imitate in our procedure, and are the icons par excellence of algebra. The letters of applied algebra are usually tokens, but the \(x, y, z,\) etc. of a general formula, such as

\[ (x + y)z = xz + yz, \]

❝are blanks to be filled up with tokens, they are indices of tokens. Such a formula might, it is true, be replaced by an abstractly stated rule (say that multiplication is distributive); but no application could be made of such an abstract statement without translating it into a sensible image.❞ (3.363).

#Peirce #Logic #AlgebraOfLogic #RelationTheory
#Semiotics #Icon #Index #Symbol #Quantification

Peirce's 1885 “Algebra of Logic” • Selection 2.3
• https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-selection-2/

❝On the Algebra of Logic❞
❝A Contribution to the Philosophy of Notation❞

❝§1. Three Kinds Of Signs❞ (cont.)

❝With these two kinds of signs alone any proposition can be expressed; but it cannot be reasoned upon, for reasoning consists in the observation that where certain relations subsist certain others are found, and it accordingly requires the exhibition of the relations reasoned with in an icon.

❝It has long been a puzzle how it could be that, on the one hand, mathematics is purely deductive in its nature, and draws its conclusions apodictically, while on the other hand, it presents as rich and apparently unending a series of surprising discoveries as any observational science.

❝Various have been the attempts to solve the paradox by breaking down one or other of these assertions, but without success. The truth, however, appears to be that all deductive reasoning, even simple syllogism, involves an element of observation; namely, deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts.❞ (3.363).

#Peirce #Logic #AlgebraOfLogic #RelationTheory
#Semiotics #Icon #Index #Symbol #Quantification

Peirce's 1885 “Algebra of Logic” • Selection 2.2
• https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-selection-2/

❝On the Algebra of Logic❞
❝A Contribution to the Philosophy of Notation❞

❝§1. Three Kinds Of Signs❞ (cont.)

❝But tokens alone do not state what is the subject of discourse; and this can, in fact, not be described in general terms; it can only be indicated. The actual world cannot be distinguished from a world of imagination by any description. Hence the need of pronouns and indices, and the more complicated the subject the greater the need of them.

❝The introduction of indices into the algebra of logic is the greatest merit of Mr. Mitchell's system. He writes F_1 to mean that the proposition F is true of every object in the universe, and F_u to mean that the same is true of some object. This distinction can only be made in some such way as this. Indices are also required to show in what manner other signs are connected together.❞ (3.363).

#Peirce #Logic #AlgebraOfLogic #RelationTheory
#Semiotics #Icon #Index #Symbol #Quantification

Peirce's 1885 “Algebra of Logic” • Selection 2.1
• https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-selection-2/

❝On the Algebra of Logic❞
❝A Contribution to the Philosophy of Notation❞

❝§1. Three Kinds Of Signs❞ (cont.)

❝I have taken pains to make my distinction of icons, indices, and tokens clear, in order to enunciate this proposition: in a perfect system of logical notation signs of these several kinds must all be employed. Without tokens there would be no generality in the statements, for they are the only general signs; and generality is essential to reasoning. Take, for example, the circles by which Euler represents the relations of terms. They well fulfill the function of icons, but their want of generality and their incompetence to express propositions must have been felt by everybody who has used them. Mr. Venn has, therefore, been led to add shading to them; and this shading is a conventional sign of the nature of a token. In algebra, the letters, both quantitative and functional, are of this nature.❞ (3.363).

#Peirce #Logic #AlgebraOfLogic #RelationTheory
#Semiotics #Icon #Index #Symbol #Quantification