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elloft.bsky.social
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@elloft.bsky.social
94 followers 24 following 1.9K posts
Philosophy|Mathematics (Logic)|Pedagogy|Linguistics|Psychology|Aesthetics|Data Science|Web Dev|Poetry

This is kind of just a notebook
Tags are mostly for muting

Je comprends le français 🇫🇷
Ich verstehe ein bisschen Deutsch 🇩🇪
Ενδιαφερόμενος για ελληνικά 🇬🇷
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elloft.bsky.social
p113 \textsc{$\Z_n$ is a group of order $n$}

What doesn’t seem right here is that $\Z_n$ is the target domain. Typically, target domains are \textit{more} abstract than their sources, yet, here, they even explicitly describe A, B, *, etc. in the source as “abstract.”

lol, lmao
ADDITION MODULO 3 AS A COMMUTATIVE GROUP WITH THREE ELEMENTS Source Domain ALGEBRA: GROUPS Target Domain MODULAR ARITHMETIC The commutative group with 3 elements → The essence of addition modulo 3 The set (I, A, B) of abstract elements → → The set (0, 1, 2) of numbers The abstract binary operation * → The addition operation + The algebraic-identity element I → The arithmetic-identity element 0 The abstract element A → The number 1 The abstract element B → The number 2 Abstract closure law → Arithmetic closure law Abstract associative law → Arithmetic associative law Abstract commutative law → Arithmetic commutative law Abstract identity: There is an element I, such that X * I = X. Arithmetic identity: There is an → element 0, such that X + 0 - X. Abstract inverse: For each X, * Table Arithmetic inverse: For each X, there is a Y such that X * Y - I. → there is a Y such that X + Y - 0. → + Table
October 29, 2025 at 9:31 PM
elloft.bsky.social
Speaking of falling in and out of love with one’s target languages, according to the last date written in my #Greek notebook, I stopped studying #ελληνικά right before I made my Bluesky account. Oops…😅

#langsky
A page from a notebook with Greek notes written on it and the date 1/17/2025 in the top-right corner
October 28, 2025 at 2:02 AM
elloft.bsky.social
I’m perplexed by these passages from Lectures on the Philosophy of Mathematics by Joel David #Hamkins. I feel there’s something to be said about them, but I can’t quite put my finger on what it is. One could ramble about Wittgenstein, aesthetics, Lean, levels… #mathsky #philsky #logic
p175 of Lectures on the Philosophy of Mathematics by Joel David Hamkins p176 of Lectures on the Philosophy of Mathematics by Joel David Hamkins p177 of Lectures on the Philosophy of Mathematics by Joel David Hamkins
October 26, 2025 at 1:21 AM
elloft.bsky.social
p65 \& p68 Numbers as objects and the conceptual foundation of number theory
ARITHMETIC IS OBJECT CONSTRUCTION Source Domain ОBJECT CONSTRUCTION Target Domain ARITHMETIC Objects (consisting of ultimate parts of unit size) → Numbers The smallest whole object → The unit (one) The size of the object → The size of the number Bigger → Greater Smaller → Less Acts of object construction → Arithmetic operations A constructed object → The result of an arithmetic operation A whole object → A whole number Putting objects together with other objects to form larger objects → Addition Taking smaller objects from larger objects to form other objects → Subtraction Whole objects are composites of their parts, put together by certain operations. —> Whole numbers are composites of their parts, put together by certain operations. It is this metaphorical entailment that gives rise to the field of number theory, the study of which numbers can be decomposed into other numbers and operations on them.
October 24, 2025 at 6:41 AM
elloft.bsky.social
p64 \& p67 Artificial metaphors for zero.

Cf. the invention/discovery problem. Cf. the problem of whether nothing is a thing or not.
THE ZERO COLLECTION METAPHOR The lack of objects to form a collection → The empty collection As in the case of the object-collection metaphor, a special additional metaphor is needed to conceptualize zero. Since the lack of an object is not an object, it should not, strictly speaking, correspond to a number. The zero object metaphor is thus an artificial metaphor. THE ZERO OBJECT METAPHOR The Lack of a Whole Object → Zero
October 24, 2025 at 6:23 AM
elloft.bsky.social
p55 \textsc{arithmetic is object collection}.
ARITHMETIC IS OBJECT COLLECTION Source Domain ОBJЕСТ COLLECTION → Target Domain ARITHMETIC Collections of objects of the same size → Numbers The size of the collection → The size of the number Bigger → Greater Smaller → Less The smallest collection → The unit (One) Putting collections together → Addition Taking a smaller collection from a larger collection → Subtraction
October 24, 2025 at 5:50 AM
elloft.bsky.social
N.B. \textsc{categories are containers}. (p43-44)
CATEGORIES ARE CONTAINERS Source Domain CONTAINERS Target Domain CATEGORIES Bounded regions in space → Categories Objects inside the bounded regions → Category members One bounded region inside another → A subcategory of a larger category Source Domain CONTAINER SCHEMA INFERENCES Excluded Middle Every object X is either in Container schema A or out of Container schema A. Modus Ponens Given two Container schemas A and B and an object X, if A is in B and X is in A, then X is in B. Hypothetical Syllogism Given three Container schemas A, B, and C, if A is in B and B is in C, then A is in C. Modus Tollens Given two Container schemas A and B and an object Y, if A is in B and Y is outside B, then Y is outside A. → → → Target Domain CATEGORY INFERENCES Excluded Middle Every entity X is either in category A or out of category A. Modus Ponens Given two categories A and B and an entity X, if A is in B and X is in A, then X is in B. Hypothetical Syllogism Given three categories A, B and C, if A is in B and B is in C, then A is in C. Modus Tollens Given two categories A and B and an entity Y, if A is in B and Y is outside B, then Y is outside A.
October 22, 2025 at 9:34 PM
elloft.bsky.social
Notes on Where Mathematics Comes From by #Lakoff and Nuñez

#mathsky #cogsci #philsky
The Romance of Mathematics In the course of our research, we ran up against a mythology that stood in the way of developing an adequate cognitive science of mathematics. It is a kind of "romance" of mathematics, a mythology that goes something like this. • Mathematics is abstract and disembodied-yet it is real. • Mathematics has an objective existence, providing structure to this universe and any possible universe, independent of and transcending the existence of human beings or any beings at all. • Human mathematics is just a part of abstract, transcendent mathematics. • Hence, mathematical proof allows us to discover transcendent truths of the universe. • Mathematics is part of the physical universe and provides rational structure to it. There are Fibonacci series in flowers, logarithmic spirals in snails, fractals in mountain ranges, parabolas in home runs, and π in the spherical shape of stars and planets and bubbles. • Mathematics even characterizes logic, and hence structures reason it-self-any form of reason by any possible being. • To learn mathematics is therefore to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe. • Because mathematics is disembodied and reason is a form of mathematical logic, reason itself is disembodied. Hence, machines can, in principle, think.
October 19, 2025 at 1:58 PM
elloft.bsky.social
Still don’t feel very good.

Also sort of wishing I hadn’t given all my nice drawing pens and pencils away haha, oops
Doodle of a head sticking out of a tall mound next to a short, bare tree and some stones Doodle of a fluffy-looking creature with a short tail, many short legs, and a long neck Ink drawing of a silhouette of a spider with an egg sac Doodle of a head with what appears to be a tired expression and hair that looks like a bunch of little rectangles. His neck and shoulders are very crudely outlined.
October 7, 2025 at 9:55 PM
elloft.bsky.social
I’ve been feeling really down lately, so I started flipping through my high school sketchbooks to take my mind off things. It has certainly been amusing.
An abstract black and white doodle of a guy who appears to be baring his teeth and swinging his fist A black and white doodle of a landscape with pointy mountains A black and white doodle of a face An abstract black and white doodle
October 7, 2025 at 12:27 AM
elloft.bsky.social
The results are so pretty, but getting to those results is rather cumbersome.
LaTeX TikZ drawing of four octants O1-O4 drawn on axes M, U, and P_c
October 5, 2025 at 8:38 PM
elloft.bsky.social
Get a desk that you can write on. It’s super fun. 10/10 would recommend
A desk with a sheet of clear, hard plastic laid over it and with expo marker writing on the plastic
September 22, 2025 at 12:39 AM
elloft.bsky.social
I don’t recall us interacting, but I think I liked one of your #mathsky posts

Regardless, Russell’s real table is in Ch1 of his book The Problems of Philosophy. For the rest, I’m sort of thinking in terms of Zoltán Kövecses’ book Metaphor: a Practical Introduction.
September 15, 2025 at 11:58 PM
elloft.bsky.social
Wow. What a great diagram. Very helpful. Thanks, Kövecses.
A circle with an outline of a submarine and an arrow pointing to another circle with a rudimentary drawing of a submarine sandwich.
September 14, 2025 at 12:26 AM
elloft.bsky.social
Hm, these days I'm more likely to call it a linguistic paradox because it hinges on the ambiguity of the word 'then,' but I suppose this isn't far off from our most recent thoughts on the if-feeling. I just didn't know about metaphor theory when I wrote this.
44. When we say “If P , then Q,” we are really talking about a se- quence of sensations. That is what the if-feeling is. “Here are the sensations invoked by P , get ready for the sensations invoked by Q.” It is the feeling of what is eventual. It occurs in the listener as a result of our tone of voice, but also as a result of the listener’s own deduction of whatever con- clusions correspond to the hypothesis P . 45. This is the psychological paradox that envelopes all a priori rea- soning. In the land of logic where nothing happens, the only thing that anyone ever feels is what is eventual.
September 13, 2025 at 1:31 AM
elloft.bsky.social
(13.7, p52) For future reference.
7. The system of notation must make it possible for the analyst to provide a record that he himself can understand, after a lapse of time, and that can be communicated to others without serious loss of meaning. Difficult as it may be to fulfil this ambition its achievement would not be enough. For development of psycho-analysis a notation must be found that records psycho-analytic work, as mathematical notation records facts, but just as mathematical notation records facts and provides a means for calculation as well, so the ideal psycho-analytic notation must provide a means for working on the problem that the notation has enabled the analyst to record.
September 7, 2025 at 8:13 PM
elloft.bsky.social
I always forget to look for these unless I’m reading news titles. Oh well.

Nevertheless, A GOVERNMENT (AGENCY) is A COMPANY/BUSINESS.
Trump signs executive order rebranding Defense Department as Department of War 16 hours ago NBC News
September 6, 2025 at 2:44 PM
elloft.bsky.social
damn…
A LaTeX item in an enumerate environment formatted as 3.2.302
September 3, 2025 at 6:07 AM
elloft.bsky.social
A bit metaphorical and personified, but I'm fairly satisfied with the result. #poetrysky
plucked from a pool of soul, whatever that may be, this frame emerges around its own content and unknowingly makes land-, or rather timemarks of its decades and pushes attributes that make it whole above the lip and behind where we see; this array of sublingual stuff admits it knows neither what a true self takes nor depth of information made into an essential identity, which fortifies this entity, but if he doesn't learn this self into the pool of soul, remelt @elloft.bsky.social (Bluesky) September 2, 2025
September 3, 2025 at 2:23 AM
elloft.bsky.social
I recall §58 from Wittgenstein’s Philosophical Investigations, but I can’t quite put my finger on what I want to say here, if anything at all.
58. "I want to restrict the term 'name' to what cannot occur in the combination 'X exists'. — And so one cannot say 'Red exists', because if there were no red, it could not be spoken of at all." - More correctly: If "X exists" amounts to no more than "X" has a meaning - then it is not a sentence which treats of X, but a sentence about our use of language, that is, about the use of the word "X". Philosophical Investigations (page) 33e It looks to us as if we were saying something about the nature of red in saying that the words "Red exists" do not make sense. Namely, that red exists 'in and of itself'. The same idea - that this is a metaphysical statement about red - finds expression again when we say such a "indestructible" thing as that red is timeless, and perhaps still more strongly in the word But what we really want is simply to take "Red exists" as the state-ment: the word "red" has a meaning. Or, perhaps more correctly, "Red does not exist" as "'Red' has no meaning" ' Only we do not want to say that that expression says this, but that this is what it would have to be saying if it made sense - that the expression actually contradicts itself in the attempt 29 to say that just because red exists in and of itself'. Whereas the only contradiction lies in something like this: the sentence looks as if it were about the colour, while it is supposed to be saying something about the use of the word "red". - In reality, how-ever, we quite readily say that a particular colour exists, and that is as much as to say that something exists that has that colour. And the first expression is no less accurate than the second; particularly where what has the colour' is not a physical object.
September 2, 2025 at 6:26 PM
elloft.bsky.social
(p207)
preliminary. As a medium, color is a go-between for the values weak and dispersed in ordinary experiences and the new concentrated perception occasioned by a painting. A phonographic disk is a vehicle of an effect and nothing more. The music which issues from it is also a vehicle but is something more; it is a vehicle which becomes one with what it carries; it coalesces with what it con-veys. Physically, a brush and the movement of the hand in applying color to canvas are external to a painting. Not so artistically. Brushstrokes are an integral part of the esthetic effect of a painting when it is perceived. Some philosophers have put forth the idea that esthetic effect or beauty is a kind of ethereal essence which, in accommodation to flesh, is compelled to use external sensuous material as a vehicle. The doctrine implies that were not the soul imprisoned in the body, pictures would exist without colors, music without sounds, and literature without words. Except, however, for critics who tell us how they feel without telling or knowing in terms of media used why they feel as they do, and except for persons who identify gush with appreciation, media and esthetic effect are completely fused.
August 29, 2025 at 2:04 AM
elloft.bsky.social
(p206) Same issue with alt text
going to jail or to hell, makes conduct unlovely. It is as anesthetic as is going to the dentist's chair so as to avoid a lasting injury. When the Greeks identified the good and beautiful in actions, they revealed, in their feeling of grace and proportion in right conduct. a perception of fusion of means and ends. The adventures of a pirate have at least a romantic attraction lacking in the painful acquisitions of him who stays within the law merely because he thinks it pays better in the end to do so. A large part of popular revulsion against utilitarianism in moral theory is because of its exaggeration of sheer calculation. "Decorum" and "propriety" which once had a favorable, because esthetic, meaning are taking on a disparaging signification because they are understood to denote a primness or smugness assumed because of desire for an external end. In all ranges of experience, externality of means defines the mechanical. Much of what is termed spiritual is also unes-thetic. But the unesthetic quality is because the things denoted by the word also exemplify separation of means and end; the "ideal" is so cut off from the realities, by which alone it can be striven for, that it is vapid. The "spiritual" gets a local habitation and achieves the solidity of form required for esthetic quality only when it is embodied in a sense of actual things. Even angels have to be provided in imagination with bodies and wings. I have referred more than once to the esthetic quality that may inhere in scientific work. To the layman the material of the scientist is usually forbidding. To the inquirer there exists a fulfiling and consummatory quality, for conclusions sum up and perfect the conditions that lead up to them. Moreover, they have at times an elegant and even austere form…
August 29, 2025 at 2:03 AM
elloft.bsky.social
(p205) too much text to fit everything in alt text. Oh well. See directly below.
in them. There are ends which are merely welcome cessations and there are ends that are fulfilments of what went before. The toil of a laborer is too often only an antecedent to the wage he receives, as consumption of gasoline is merely a means to transportation. The means cease to act when the "end" is reached; one would be glad, as a rule, to get the result without having to employ the means. They are but a scaffolding. Such external or mere means, as we properly term them, are usually of such a sort that others can be substituted for them; the particular ones employed are determined by some extraneous con-sideration, like cheapness. But the moment we say "media," we refer to means that are incorporated in the outcome. Even bricks and mortar become a part of the house they are employed to build; they are not mere means to its erection. Colors are the painting; tones are the music. A picture painted with water colors has a quality different from that painted with oil. Esthetic effects belong intrinsically to their medium; when another medium is substituted, we have a stunt rather than an object of art. Even when substitution is practiced with the utmost virtuosity or for any reason outside the kind of end desired, the product is mechanical or a tawdry sham-like boards painted to resemble stone in the construction of a cathedral, for stone is integral not just physically, but to the esthetic effect. The difference between external and intrinsic operations runs through all the affairs of life. One student studies to pass an examination, to get promotion. To another, the means, the activity of learning, is completely one with what results from it. The consequence, instruction, illumination, is one with the process. Sometimes we journey to get somewhere else because we have business at the latter point and would gladly, were it possible, cut out the traveling. At other times we journey for the delight of moving about and seeing what we see. Means and end coalesce…
August 29, 2025 at 2:03 AM
elloft.bsky.social
Remarks on Meter in Poetry:
(p162)
Emotional energy continues to work but now does real work; it accomplishes something. It evokes, assembles, accepts, and rejects memories, images, observations, and works them into a whole toned throughout by the same immediate emotional feeling. Thereby is presented an object that is unified and distinguished throughout. The resistance offered to immediate expression of emotion is precisely that which compels it to assume rhythmic form. This, indeed, is Coleridge's explanation of meter in verse. Its origin, he says, he "would trace to the balance in the mind effected by that spontaneous effort which strives to hold in check the workings of passion.... This salutary antagonism is assisted by the very state which it counteracts, and this balance of antagonists becomes organized into meter by a supervening act of will or judg ment, consciously and for the foreseen purpose of pleasure." There is "an interpenetration of passion and of will, of spontaneous impulse and voluntary purpose." Meter thus "tends to increase the vivacity and susceptibility of both the general feelings and the attention. This effect it produces by the continued excitement of surprise and the quick reciprocations of curiosity gratified and re-excited, which are too slight indeed to be at any one moment objects of distinct consciousness, yet become considerable in their aggregate influence."
August 16, 2025 at 1:39 PM
elloft.bsky.social
On the other hand, this second definition is somewhat interesting as well. Imagine if, in mathematics, someone asked whether a proposition ψ is true or not, and one responded by stating a completely different proposition φ that indirectly implies either ψ or \neg ψ, but without giving a “proof.”
implicate Dictionary verb 1. show (someone) to be involved in a crime. "police claims implicated him in many more killings" 2. convey (a meaning or intention) indirectly through what one says, rather than stating it explicitly; imply. "by saying that coffee would keep her awake, Mary implicated that she didn't want any"
August 5, 2025 at 3:55 AM