#intuitionism

[chrisengel]

"...Lacan's invocations of intuitionism were intended to highlight the constructive nature of the symbolic order of meaning and discourse only. They were not meant as an endorsement of the underlying ontology. .... ..the intuitionist preclusion of actual infinity is not relevant to the meaning of Lacan's concept of the pas-tout" Russel Grigg: Lacan, Language and Philosophy 2008 - as discussed by Amy Swiffen Int J Semiot Law 2012 25 289-292 "From an intuitionist perspective to claim something with certain properties exists is to claim that an object with those properties can be constructed. Put differently, the truth of a statement is taken as equivalent to the mathematician being able to intuit the statement. ... Thus, for intuitionism, infinity is only potential"

[st-just]

Spending my formative years in a variety of deeply idiosyncratic internet hothouses during the Bush administration was very good for me I think, purely because it means I'm permanently immunized to arguments that start 'well I don't actually have a good argument for why this is wrong, but y'know any normal person feels disgust and revulsion thinking about it and that has to have some weight doesn't it?''

tell me you would have voted to re-criminalize sodomy without saying so, I guess.

[blurredblu]

I don't get why ppl think of Sonic as a beacon of good morality and having a strong moral code... like. He doesn't. He's optimistic, built different, and full of love for his friends, but he's not like shadow or knuckles or someone with a palpably strong sense of moral duty or duty, period, that he consciously enforces in whatever cases possible. He's literally just a silly and special little guy

[bredforloyalty]

like i don't agree that purity and therefore feelings of disgust should factor into the moral workings of adults and i don't quite agree with haidt's umm allusions to conservatism being less individualistic and centered around the rights and the good of the group but i do think it's helpful to think of morality on his terms specifically when it comes to conservatives and how they think and how they make moral judgments

[moribundphilosophy]

In this episode Jacob speaks to Philosopher Michael Huemer on his book Ethical Intuitionism. They speak about what intuitions are; and it's relationship with ethics. They also speak about competing models of ethics. 

[tanadrin]

Cheating is pretty straightforward in a zero sum game. If you’re breaking the rules to gain an advantage you are likely cheating someone else *out* of something. The intuitions around that work similarly to intuitions around theft, I think.

Cheating in a non-zero-sum context (most, but notably not all cheating in school) is a little different. You may be fraudulently obtaining credentials you did not earn, and you may be devaluing those credentials a little but the harms, such as they are, are very diffuse. It’s unlikely you can point to an individual cheater and say “you specifically have fucked someone over.”

Cheating in romantic relationships is intuitionally very weird to me, because potentially there are no harms! It really is a case of “what you don’t know can’t hurt you.” The harm unique to cheating romantically exists necessarily only alongside the knowledge that the cheating has occurred. If you get away with it, in some very real sense, you have done no harm. But of course most people would still strongly feel that a wrong has been committed, and not only that, but that if you want to redress the wrong you must begin by coming clean—and thus realizing a harm that until that point has only been theoretical.

I think that’s interesting! Conceptually we kinda group all these things together even though they are very different. And intuitions around some of these things don’t map neatly to intuitions around others.

[smuckles]

Hello ily I just wanted to know how being aroace and a dyke works together I think I'm not queer enough to intuitionally know that yet also ily

hiii!

i knew i was a dyke before i knew i was aroace. i've been a dyke since i was like 11. back then, i figured i did experience romantic/sexual attraction to women, and it's basically forged in my mind that i am a lesbian. i do still experience attraction towards women- even as a trans man, it cannot be considered straight because lesbian is my soul. it is not particularly romantic or sexual (or it is! who knows! i sure don't!) but it is love! i love women very much in a very dyke way and my aroace and transmale identity are not stopping that.

tldr; butch lesbian dyke is part of my soul and no lack of romantic or sexual attraction is gonna stop that

[tawakkull]

ISLAM 101: Spirituality in Islam: Part 238

Ma’rifa (Knowledge of God)

Ma’rifa is a special knowledge that is acquired through reflection, sincere endeavor, using one’s conscience and inquiring into one’s inner world. It is different from (scientific) knowledge (‘ilm). (Scientific) knowledge is acquisition reached through study, investigation, analysis, and synthesis, while ma’rifais the substance of knowledge attained through reflection, intuition, and inner perception. The opposite of (scientific) knowledge is ignorance, while the opposite of ma’rifa is denial.

Knowledge means comprehending or encompassing something thoroughly, while ma’rifa means familiarity with or recognition of something-that something may be the Divine Being- in some of its aspects. For this reason, the One of Unity is called the All-Knowing (‘Alim), but He has never been called the One having familiarity with something (‘Arif). In addition, the exacting scholars of truth view ma’rifa, which also means information, talent, and skill, as the culture acquired by conscience or one’s conscious nature. It has other meanings such as the ability to feel something with the spiritual faculty that humanity has been endowed with, the image of something known in the mind, and the knowledge kept in the memory which gains strength through repetition. From another perspective, it is consciousness, perception, and sufficient information which helps distinguish one thing from another. Ma’rifacan be summed up as having concise knowledge about something or someone through their acts or works and attributes-knowledge which can be developed and detailed.

In order that one can be among those who have knowledge of God and who are regarded by God as being one of such people, one should know God and the ways that lead to Him, recognizing the obstacles on the way, and knowing how to overcome these obstacles. One should also have enough will-power to apply what one knows. One who has true knowledge of God is a perfect human being who knows the Unique One, Who is the Eternally-Besought-of-All, with His Acts, Names and Attributes, and is a person in whose everyday life this knowledge shows itself. He or she is also one who always keeps the heart purified and pursues sincerity and purity of intention, who can remain free of negative moral qualities as far as possible, overcoming whatever dark emerges from the spirit and threatens to darken one’s horizon, and thereby demonstrating loyalty to the All-Protector. Such a one can bear everything that befalls on God’s way to obtain His approval, and invites others to the way of the Prophets, which shows itself through God’s confirmation in every step, and whose lights he or she always feels with pleasure.

There is another approach to the meaning of ma’rifa, namely the ability to perceive something as exactly what it is in itself, in its quiddity, distinct from any and all things not directly connected with it. According to this approach, knowledge of God is knowing the Divine Being with His Essential and Positive Attributes beyond all conceptions of modality. This is different from comprehending, perceiving and establishing other things, and is based on perception and the feeling of conscience. This feeling and perception should not be confused with modern intuitionism. The Divine Being is beyond all concepts and cannot be comprehended, perceived or scientifically known, although a certain knowledge or familiarity can be acquired of Him through His acts, Names and Attributes.

The acknowledgment that The inability to perceive Him is the true perception, excellently expresses the inability of anything limited to perceive Him and the imperceptibility of the One Who is Infinite. The same meaning is exquisitely expressed in the saying, We are unable to know You, O Known One, as knowing You truly requires.

It is only God Whose existence is absolute, and the greatest truth is acknowledging His Existence and Oneness. The first step in acquiring knowledge of Him is the attainment of belief, being a Muslim, and excellence-worshipping Him as if seeing Him. In realizing such a blessed aim, one should continue one’s traveling to the True Source of all gifts and blessings without turning to anything else as a source. One should be able to feel a new joy of reunion in every gift and blessing with which one is favored, and as the final point, gain familiarity with the mysteries of His Names and Attributes, and, if possible, of His Being.

This consideration is expressed as follows in Lutfiya Wahbi:

Try your hardest and be one who has ma’rifa of Him, One favored with knowledge of Him! For the All-Loving One declared, “so that I may be known;”[1] Knowing God is the ultimate cause for the creation of the two worlds; And knowing God is the adornment of humanity. Those devoid of knowledge of Him are low in rank. Knowing Him is a spiritual kingdom, And Knowing Him is a Divine gift and blessing. ………………………………………………………… When you, O moving spirit, receive this gift and blessing; The two worlds will be yours.

The following words, which are narrated in books concerning Sufism as a hadith qudsi-a saying, the meaning of which is from God and the wording of which was inspired in the Messenger-are the gist or kernel of all explanations concerning knowledge of God:

O humankind! One who knows his self also knows Me; one who knows Me seeks Me, and one who seeks Me certainly finds Me. One who finds Me attains all his aspirations and expectations, and prefers none over Me. O humankind! Be humble that you can have knowledge of Me; accustom yourself to hunger so that you can see Me; be sincere in your devotion to Me so that you can reach Me. O humankind! I am the Lord; one who knows his self also knows Me; one who renounces his self finds Me. In order to know Me, renounce your own self. A heart which has not flourished and been perfected is blind.

Knowledge of God sometimes becomes a source of wonder and astonishment for an initiate, as has been said, “One who knows the Truth becomes dumbfounded and tonguetied.” But it sometimes becomes a means of expression for the traveler to the Truth, as has been said, “One who knows the Truth finds his voice.” The voice finds its overflowing expression in one’s excitement and speech and echoes in one’s ears. Although opposites, both the saying of Muhammad Parisa,[2] “There is none who knows the Divine Being other than Himself,” and the saying, “I know none else save God,” are true.

There is none other than Him who has a true, substantial existence, and there are no true acts other than those performed by Him. Other beings have a relative existence when compared with Him, and other acts are also relative. Whatever takes place in the cycle of causality is of a relative nature. For this reason, knowledge of God is when an initiate melts away in the light of the Truth and gains a second, true existence. This may be viewed as self-annihilation in God and subsistence with Him. I think the author of al-Minhaj stresses this fact in these verses:

If you can see with the lights of certainty, Then do not see one who knows and the One Known differently. Fuduli[3] expresses this depth of knowledge of God as follows: One who knows God is not one who knows the wisdom of the world with what is in it, One who knows God is he who does not know what the world is with what is in it.

Sufis have made other descriptions concerning knowledge of God. According to these descriptions, knowledge of God is knowing the truth of the Divine Names and Attributes, grasping the phenomenon of the manifestations in existence and the discovery of the existential mystery, deeply perceiving the truth of existence with its originality and shadows, and understanding and representing in life the truth of religion according to the Will of the Desired One, Who is the final goal of those who set out to reach Him. Each of these descriptions requires a voluminous work to explain and is therefore beyond the scope of this study. We will only cite here some verses from Diyaiya (“The Book of Light”) which point to some dimensions of the subject matter:

The third chapter is about knowledge of God, O valiant young one; To describe it the wheel of speech is unable to work. ………………………………………………………………………………. There is no scribe nor a pen to write about it; One cannot get his tongue around it to express it. ……………………………………………………………………………… The mirror of reason is veiled from understanding it; The ability of perception has nothing to say in it; Only the bird of imagination can fly toward it; There is no example that we can coin to explain it. …………………………………………………………………………….. Here the gift comes only from God; This is a light-diffusing, sacred rank. ……………………………………………………………………………. The whole of creation is immersed in this realm, Which is more spacious than all the worlds. ……………………………………………………………………………. There is no true existent save He Who is the One, Perceiving this is the real vision; Do not interpret this vision in another way, or else, It will mean unbelief and heresy, O one with body of light. It is not the eyes in the head which have this vision; The All-Loving One is all-free from vision by these eyes. The innermost faculty-secret-discerns this truth, When you find this faculty in you, you can understand it. Human scientific knowledge and perception have nothing to say; The merit is in wonder and helplessness in this field. Perception of one’s helplessness is perception of the Truth; Listen to what Abu Bakr, the truthful one, says concerning it.[4]

The rank of knowledge of God (ma’rifa) is a rank of wonder, utter astonishment, and awe. It is possible to see this in almost all the reflections of the scholars of Sufism on knowledge of God. Some of them see it in direct proportion to the excess of the feeling of awe and have concluded that the deeper one is in knowledge of God, the deeper one’s feeling of awe is. Others regard knowledge of God as being the base of serenity and peacefulness and emphasize that inner peace and self-possession increase in proportion to the depth of knowledge of God. Still others consider knowledge of God as the heart’s attainment of friendship with God and the initiate’s following a way to nearness to God. The approach of Shibli[5] opens new windows on the knowledge of God. According to him, it means that an initiate has an essential relation with none save God, making no complaints when burning with His love, is a sincere, obedient and faithful servant of God who avoids any claims of superiority, and one who worries about his or her end. A person with true knowledge of God and who has a strong connection with the sources of this knowledge, one who has taken refuge in the guidance of the spirit and meaning of the Prophethood, and who has built sound relations with the truths that lie beyond human horizons, cannot feel any essential interest in transitory things nor does lower him or herself to feel attachment to other than the Lord. The Qur’an alludes to this highest point in (35:28), Only the knowledgeable among His servants have true reverence for God, reminding the traveler of the relation between knowledge and awe or reverence of God. The greatest of those who have knowledge of God, upon him be peace and blessings, said concerning the same point: I am greater than you in knowledge of God, and more intense in fearing Him.[6]

In the books on Sufism, in which the intellect guided by Revelation is operative, and which contain numerous gems of wisdom concerning the “garment of piety” of those who have true knowledge of God, with Whom their hearts are deeply connected, we can find many gems concerning knowledge of God. The following are only a few of them:

In the view of one favored with knowledge of God, the world with its material aspect becomes so small that it seems no greater than a cup. The souls that have gained profundity in knowledge of God expand to the extent that it is as if they have no limits. Those who taste the pleasure of knowledge of God, which is regarded as the sweetest of all honey, pursue no other wealth than nearness to the Truth. The richness of the honeycomb of knowledge of God in the heart is one of the most essential sources of love and zeal. An initiate burns with the zeal of reunion in proportion to how much this source overflows its banks, which he or she sees as the price of the favors received. The following points which differentiate those who have a sound knowledge of God from others are important. The former have no selfish expectations from whatever good they do, never think of competition for either material or spiritual ranks nor feel jealous of anybody. They do not see themselves as being greater than anyone else, nor do they moan because of missed opportunities, anymore than they feel arrogant because of their accomplishments. Even if they were granted the kingdom of the Prophet Solomon, they would only seek God’s company, regarding it as futile to turn to other things. They feel no relation with beings other than the Almighty with respect to their worldly existence and corporeal self, and know that one moment of God’s friendship is worth the entire world. They consider being with God among people as a victory that has been granted to their will-power, and see the Divine Will reflected in the face of their determination, recognizing the help of the Lord in the result of their endeavor, alongside many other instances of wisdom and God’s extraordinary gifts. They observe the manifestations of the Divine Oneness in the multiplicity of the creation, and thereby they grasp how a drop is transformed into an ocean, and a particle into the sun. They witness in their conscience how nothingness or non-existence is a fertile land, to be planted with existence and live drowned in ecstasies and intoxication.

Self-possession, steadfastness, seriousness, profundity, and resolution are the clearest and most important signs of perfect knowledge of God. Those who have this degree of knowledge live under the shower of the manifestations of God’s friendship and company. No sign of any flaws can be seen in their inner or outer world, nor is any laxity witnessed in their behaviors. They never show impertinence or conceit, even when favored with the most abundant gifts. On the contrary, they always act in a self-possessed manner, trying to lead a self-disciplined, spiritual life.

Obviously, everyone cannot have the same degree of knowledge of God. Some travel on the horizon of perceiving the Attributes essential to the Divine Being and the favors that accompany His acts. They observe and avail themselves of His proofs that are found within themselves and in the outer world, with the result that their love of truth and their relation with the Greatest of Truths are witnessed in their manners. They travel between the Divine acts, Names and Attributes and are thrilled with the different melodies of belief, knowledge of God, love, attraction and the feeling of being attracted by God to Himself. They feel in their conscience the reflections of the Divine acts or operations in the universe and pursue more and more the pleasure entailed in observing ever new colors and aspects. This is a way bequeathed by the Prophets and it is a way that can be followed by everyone. One who travels along this way of objective truth travels toward the Truth under the arches of His compliments.

On this path there are others who feel all the dimensions in existence ending in one dimension, who feel that everything is annihilated in God. It is as if they have reached a point where the lights and manifestations of the Divine Being and Attributes come together and annihilate their very being in the Divine Being, attaining a new existence with the Self-Subsistence of Him Who is the All-Knowing and the Ever-Existent.

While those belonging to the former group travel in the realm of the Divine Attributes and Qualities, others have already directed themselves to the Source of these Attributes and Qualities. Therefore, their observations and sensations are not aimed at either the Attributes exclusively in such a way as to veil the Being in their minds or spirits, nor at the Being exclusively in such a way as to suggest the denial of the Attributes. For this reason, such an approach has been regarded as the way of the perfected and most advanced, and the main path that is followed by those who travel to the greatest nearness to God.

The Book, the Sunna, reason, and the Divine system in creation and human primordial nature bear witness to the truth of this way along which God’s works of art show themselves brightly. Initiates who have firmly established their feet on this path witness at every step that God witnesses His Existence and Oneness, and they cannot help but utter, God bears witness that surely there is no deity but He (3:18). They hear in their conscience the confirmations of angels and those possessed of knowledge as a reflection of God’s witnessing, and continue to utter: and the angels and those possessed of knowledge (also bear witness to the same truth) (3: 18). Then, they see that all means and causes that are not essential to His Being having vanished, and they are able to be at perfect rest and to find perfect peace.

There are others who have such abundant knowledge of God that proofs of God are no longer needed in their world; all the things that witness Him are humbled in the face of their being in the Presence of the True Witness; all the means tremble with the shame of making distant whatever is near, and all the heralds are silent and busy with correcting the words that they have uttered. At this point, where everything is seen by the conscious nature as witnessing Him beyond all concepts of modality, the eyes are dazzled by the brightest manifestations of the Face, and all other identities save His are lost. Those who have reached this point see that the True Source of existence and knowledge surrounds everything from all sides, tasting the pleasure of perceiving every being’s perception of Him according to their level, and feeling that everything is annihilated in Him. They sense the way in which the manifestations of the Divine Names are combined with those of the Being, Attributes and Acts. The conscience is saved from any feeling of dependence on causality and reaches the horizon of Surely we belong to God (as His creatures and servants), and surely to Him we are bound to return (2:156). But this never means, as some have assumed, “absolute annihilation” or “union with God.”

Our Lord! Grant us from Your Presence a special mercy and arrange for us in our affairs what is right and for our good! And may Your peace and blessings be upon our master Muhammad, by whom the mysteries came to light and the lights shone brightly upon his pure Companions.

[1] Here there is a reference to the Qur’anic verse, I have not created the jinn and humanity but to worship Me (51:56). To worship Me has usually been interpreted as “so that I may be known and worshipped.” (Trans.) [2] Muhammad Parisa (d., 822/1419) was a great scholar and saint from Bukhara. He passed away in Madina. Among his books al-Fusul al-Sitta (Six Chapters) is famous. (Trans.) [3] Mehmed Fuduli (1490-1556). The greatest poet of the Turkish literature. He lived in Iraq. His Diwan, (“Collection of Poems”), Layla wu Majnun (“Layla and Majnun”), and Hadiqat al-Su’ada (“The Garden of the Holy Ones”) are some of his other well-known books. (Trans.) [4] The writer refers to Abu Bakr’s saying: “The inability to perceive Him is the true perception.” (Trans.) [5] Abu Bakr al-Shibli, of Khorasan by origin but born in Baghdad or Samarra, son of a court official and himself promoted in the imperial service, as Governor of Demavend. However, giving up governorship, he joined the circle of Junayd al-Baghdadi, and became one of the leading figures in Islamic Sufism. He died in 846 at the age of 87. (Trans.) [6] Al-Sahawi, al-Maqasid al-Hasana, 21.

[xerxeswitch]

hello! I’m new to witchcraft and one of the first things I wanna do is make a protection/luck charm. I have a rope necklace with a little glass vial on it and I was wondering what some good things to put in a protection or luck charm would be?

I have some epsom salt, rose quartz, amethyst, turquoise(I think it is), and shark teeth along with some others. Also what types of sigil should I use and how would you recommend I do it? Thank you so so much for helping me out!! I wish you much fortune in your journey <3

I apologize for such a late reply! Things has been hectic and I've been working with my spirit Family intensely along with other personal projects. (Have been away from Tumblr in a bit too) --- Well, I would say go with your intuition on what does good with your energy. Not all protection-famous ingredients work with the type of energy you may or may not have! So far, your choices are pretty solid. (Especially the shark teeth!) But some good suggestions for protection/reflection from me: -Horehound herbs -Angelica Roots -St. John's Wort -Obsidian -Black Tourmaline -Shungite --- As for sigils...to be honest, I use a decal sigil of Archangel Michael for a vanity mirror if you are okay with working with angels. But 95% of the time, I create my own sigils. I use the technique where you write your intentions clearly on a parcel. I take out the vowels and any repeating letters, and use those letters left over to create and manipulate them into shapes intuitionally to create a sigil. For example: "I aim to protect my loved ones." Take out any vowels and any repeating letters --- left over: M T P R C Y L V D S. And you create these letters into shapes. Get creative! This is the method I personally use but you don't have to. Just a suggestion of course. I just like it handmade because it felt more effective and personal for what I'm going for that collides with my energy directly. Hope this helps! If you have any other questions about this still, don't hesitate! I'll try to get back at a timely manner... ---

[psychotrenny]

I know the phrase "we're not making it out of this are we" get's thrown around a lot but it's all I can think about whenever I see people unironically say shit like "ACAB includes Fandom Cops". Like you cunts don't get it do you?

Apparently the police aren't bad because of their intuitionally enshrined role as the violent defenders of capitalism and white supremacy and all the associated injustices. Nor are they bad because of their existence as an armed organisation separate from and put in power over the people. Nope. Cops are Bastards because they're like telling you what to do and really harshing the vibe man. Anyone who gets in the way of your vision of absolute unrestricted personal freedom is a cop when you really think about it. No matter how petty it might be. Like seriously you cunts have no idea. As far as you're concerned politics is all just aesthetics and feelings and vibes. No relation to material reality whatsoever

[abyrondeans]

“Experimental Song #96″

I just put “Experimental Song #96″ on my website byrondeans.com, in the “MY WORKS” section.  I’ve been feeling the “slow mind” from thinking fast and slow a lot, intuitionally.  That, somehow, seems to connect to the geopolitical situation in the world, and that in turn connects to fast-paced music and drinking caffeine in the afternoon, and short: the moral of the story is they excite and then they specialise in being calm and using the slow mind on the subject.

I don’t know if my song helps with the excitement problem: that would be one major issue with writing with the help of muse like Lana and Stevie Nicks.  But I have to get paid.  So I guess maybe I don’t have a choice.  Then again, Uncle John’s Band is about knowing the fire from the ice.  It all reduces to science, like my, Rita Bettis or the Wallace brothers’s winning science fair projects, and often isn’t very complicated,

In terms of the slow mind users I just mentioned, I’d say The Killing Fields does a good commentary on them: the whole thing changes once their bombed.  That’s when they can’t use the slow mind.  That will excite the mind.

[chrisengel]

Intuitionist totality is a fundamental concept in intuitionist mathematics that sharply contrasts with the classical approach. While classical mathematics embraces the law of the excluded middle—the principle that every statement is either true or false—intuitionism demands a more constructive framework. A set is deemed totally defined within intuitionism only when a concrete method exists to determine membership for any given element. This necessitates a specific procedure to prove whether an element belongs to a set or not. Intuitionism is profoundly skeptical of potential infinity, requiring that all set elements be individually specified or constructed. This constructive approach has profound implications for fields like analysis, logic, and set theory. As L.E.J. Brouwer, a pioneer of intuitionism, asserted, "The real numbers are not to be thought of as given in advance, but rather as continually becoming." This quote encapsulates the intuitionist view of mathematics as a dynamic process of construction. In contrast, David Hilbert, while critical of intuitionism, acknowledged its significance, stating, "Intuitionism is a serious attempt to establish mathematics on a new foundation."

[macla539ac]

Intuitionism is dumb shit

[the-chomsky-hash]

B. In other words, we are dealing with two modalities [vis.,

philosophy of experience, sense, subject (Sarte, Merleau-Ponty)

philosophy of knowledge, intuitionism, rationality, concept (Cavailles, Bachelard and Canguilhem)

] according to which phenomenology was taken up in France, when quite late - around 1930 - it finally began to be, if not known, at least recognized.

1. Contemporary philosophy in France began in those years.

a. The lectures on transcendental phenomenology delivered in 1929 by Husserl (translated

by Gabrielle Peiffer and Emmanuel Levinas as Meditations cartesiennes, Paris, Colin, 1931

and by Dorion Cairns as Cartesian Meditations, The Hague, Nijhoff, 1960

) marked the moment: phenomenology entered France through that text.

b. But it allowed of two readings:

i. one, in the direction of a philosophy of the subject - and this was Sartre's article on the "Transcendance de L'Ego" (1935)

ii. another, which went back to the founding principles of Husserl's thought:

– [on one hand, taking up]

those of formalism and intuitionism

those of the theory of science

– [on the other hand,] in 1938 Cavailles's two theses:

on the axiomatic method [and thus a logical pluralism]

the [historical] formation of [a mathematics:] set theory

– Michel Foucault, Introduction (part I: Introduction), The Normal and the Pathologic by Georges Canguilhem, 1966, translated by Carolyn R. Fawcett in collaboration with Robert S. Cohen, 1978

[beautifullyscarred423]

The healing ❤️‍🩹 journey is intimately , intuitionally and intentionally intimidating.

Most people think that it’s just a journey of learning and knowing oneself.

However it’s also a journey of acceptance.

The acceptance and Innerstanding of all aspects of ourselves. The negatives most importantly.. with keeping the intention in mind of being able to healthily receive and accept that in others.

[omegaphilosophia]

Theories of The Philosophy of Mathematics

The philosophy of mathematics is a branch of philosophy concerned with the nature of mathematical objects, structures, and reasoning. It investigates foundational questions about the nature of mathematical objects, the methods of mathematical proof and reasoning, and the relationship between mathematics and the rest of human knowledge. Some central questions in the philosophy of mathematics include: What are mathematical objects, and how do we know they exist? Are mathematical objects discovered or invented? Are mathematical truths dependent on human thought and language, or are they independent of us? What is the relationship between mathematics and logic? What is the nature of mathematical reasoning, and how is it justified? The philosophy of mathematics is closely connected to other branches of philosophy, such as epistemology, ontology, and the philosophy of science.

Some theories in the philosophy of mathematics include:

Platonism: Platonism is the view that mathematical entities, such as numbers, sets, and geometric shapes, exist independently of human thought or experience. According to Platonism, mathematical objects are abstract, non-physical entities that have an objective reality and are discovered, rather than invented, by mathematicians. Platonism holds that mathematical entities exist in a realm that is separate from the physical world, which is known as the "Platonic realm" or the "realm of forms." This realm is eternal, immutable, and perfect, and contains all possible mathematical objects.

Intuitionism: Intuitionism is a school of thought in the philosophy of mathematics that emphasizes the role of intuition and mental constructions in mathematical reasoning. Intuitionists reject the idea that mathematical objects have an independent existence, and instead view mathematics as a human activity that involves constructing and manipulating mental objects. According to intuitionism, mathematical truth is a matter of intuition and constructive proof, and mathematical objects are not necessarily abstract objects, but rather constructions of the mind.

Formalism: Formalism is the view that mathematics is a formal system of symbols and rules, and that mathematical statements have meaning only within this system. According to formalists, mathematical objects and concepts do not exist independently of the language and symbols used to describe them, and mathematical truth is a matter of following the rules of the system. It suggests that mathematical truths are derived purely from the manipulation of symbols rather than from any external or metaphysical reality.

Logicism: Logicism is the view that mathematics is a branch of logic, and that mathematical concepts and truths can be reduced to logical concepts and truths. According to this view, mathematical objects and concepts are reducible to logical concepts, and mathematical statements can be proved using logical deduction. Logicists believe that the foundations of mathematics can be derived from the basic principles of logic and proven using logical reasoning.

Constructivism: Constructivism is a philosophy of mathematics that emphasizes the role of human construction, invention, and intuition in mathematics. It holds that mathematical entities such as numbers and geometrical shapes are not discovered, but rather invented or constructed by human beings. According to constructivists, mathematical knowledge is not objective and independent of human thought, but is instead a product of human activity. They reject the idea that mathematical concepts exist independently of human minds or that they are discovered through some sort of intuition or perception. Instead, they view mathematical concepts as constructions that are based on rules, conventions, and human activity.

Structuralism: This theory holds that mathematical objects are defined by their place in a mathematical structure, rather than by their intrinsic properties. Structuralism focuses on the structure of mathematical systems, rather than on the specific objects or concepts that make up those systems. Structuralists believe that mathematical objects and concepts only exist in relation to the broader structure of the mathematical system in which they are used. They argue that understanding the relationships between mathematical objects and concepts is more important than understanding the objects and concepts themselves. In this sense, structuralism can be seen as a response to the formalist and logicist approaches to the philosophy of mathematics, which focus on the logical and axiomatic foundations of mathematics, and the platonist approach, which emphasizes the existence of mathematical objects as abstract entities.

Predicativism: Predicativism is a position that rejects certain types of definitions of mathematical objects as being too impredicative, or circular. The predicativist holds that only those concepts and objects can be used in mathematical reasoning that can be defined without reference to any objects that are "higher" in the hierarchy of mathematical objects. For example, a predicative definition of the set of natural numbers might be that it includes the number 0 and any number that can be obtained by adding 1 to a previously defined number. However, a definition that refers to all subsets of the natural numbers would be impredicative, as it involves reference to a set that is higher in the hierarchy than the set being defined.

Empiricism: Empiricism is the position that mathematical knowledge is ultimately based on empirical experience. This view holds that mathematical concepts are abstracted from concrete empirical situations, and that mathematical propositions are ultimately tested by observation and experiment. According to this view, mathematical objects and concepts do not have an independent existence, but are instead constructed by the mind based on sensory experience.

Nominalism: Nominalism is the position that mathematical objects and concepts do not have an independent existence, but are mere names or labels that we use to describe certain patterns or regularities in the world. According to this view, mathematical propositions are not statements about a separate realm of mathematical objects, but rather are descriptions of empirical regularities.

Conventionalism: Conventionalism is the position that mathematical propositions and concepts are not discovered, but rather are constructed by convention or agreement. According to this view, mathematical objects and concepts are not discovered through empirical observation, but are instead invented by mathematicians and accepted by the mathematical community based on their usefulness and coherence. Conventionalists hold that there is no objective truth about mathematical concepts and propositions, but rather that they are true only by convention or agreement.

Fictionalism: Fictionalism is a philosophical position in the philosophy of mathematics that takes mathematical theories to be useful fictions. According to this view, mathematical objects and theories do not really exist, but are simply invented or imagined by mathematicians in order to provide a useful framework for describing and explaining the world. Fictionalists believe that mathematical statements are not true or false in the same way that empirical statements are, but are instead evaluated based on their usefulness in certain contexts.

Mathematical realism: Mathematical realism is the philosophical position that mathematical objects, such as numbers, sets, and geometric figures, exist independently of human thought or perception. According to this view, mathematical entities are discovered rather than invented by humans, and they have a reality and existence that is independent of any physical or mental instantiation. Mathematical realism holds that mathematical objects and theories are true in a robust sense, and that they provide objective and reliable knowledge about the world. This position is contrasted with mathematical nominalism, which denies the existence of mathematical objects as independent entities, and mathematical fictionalism, which holds that mathematical theories are useful fictions rather than true descriptions of reality.

Mathematical anti-realism: Mathematical anti-realism is the view in philosophy of mathematics that denies the existence of mathematical objects, such as numbers, sets, and functions. Anti-realists hold that mathematical statements do not refer to independently existing entities, but instead are only useful fictions or products of human thought and language. Some anti-realists hold that mathematics is purely a human invention, while others believe that mathematical concepts and theories are simply tools that are useful for solving practical problems and making predictions, but do not have any truth value beyond their practical applications.