Numbers and Arithmetic



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Edmund Husserl is a critical figure in the development of philosophy in the twentieth century. His invocation of the transcendental ego and “consciousness as such” (the result of the first or epoche reduction) is part of a quest for the ultimate basis of reality in subjectivity.

Numbers and Arithmetic

What makes an arithmetic formula true?


Invented a method in philosophy for determining the foundation of all knowledge: something itself certain, necessary, without doubt, absolutely provable.  Like arithmetic.
Close to J.S. Mill: empirical basis of mathematics.
Studied mathematics Phd (1883)

Studied philosophy with Franz Brentano (1884-86) Psychology from and Empirical Standpoint [1874]


Philosophy of Arithmetic (1891) psychological foundation of arithmetic.  Criticized for underlying psychologism by Gottlob Frege

On the concept of number: 1887
Unity, multiplicity, combining
Example: a rose  whole and parts. Synthesized and non-synthesized unity “Each part thrown into relief by a distinct act of noticing
Discussion of number.  Totality or multiplicity is nothing other than something or other and…

Concept of collective combinations  and “something”


Mathematical > develop a theory of inferential systems.  Science > system of propositions interconnected by set of inferential relations.
Background and Context

Husserl concerned with a lack of firm foundation of human knowledge (sciences, logic, mathematics); certainty


Opposed to trends of his time:

Relativism (Nietzche as most radical) refused to believe truth exists apart from particular perspectives

Skepticism insisted that truth was unknowable or could not know that we knew it. (Hume)

Historicism: truth relative to historical or cultural epoch

Positivism: all truth must be known on the basis of the facts, but this ignores the role of the mind in knowledge and eliminates the idea of “necessary” truths
Decartes: Certainty through universal doubt, from which Cogito ergo sum is the absolute necessary first principle and everything else derived from this point
Locke-: conception of the mind: cartesian certainty of subjective experience: two movements: in looking at a pen, first from pen to sense organ, second from sense to mind’s eye/image creation/representation - not possible to know if what is in mind’s eye accurately matches object

Primary quality: ex. Solidity, adheres in pen, necessary for experience

Secondary quality: ex. Color (yellowness not essential part of pen, yellow may be different, particular to mind)

Passive, Tabula Rasa


Hume: experiences can be broken down but much of what we know can’t be derived from our sense experiences
Kant: transcendental idealism/self, synthetic unity of apperception: some things in the world provided by the mind > ideal and necessary for the mind to experience anything: Idealism>some features of the world depend on a priori before experience: structures in the mind.  synthesis of sensory and conceptual forms of objects-as-known)

(certainty ; find a way of justifying first principles, rules of mind necessary for any belief).  

The truths of philosophy are those basic rules of the mind that underlie and make possible all empirical knowledge of the world.  Retreat to mind.

Logical Investigations (1900) and critique of Naturalism
Naturalist focuses simply on Object:  but mistake to bracket out Object and focus only on Subject. Study the link/hyphen in S-O:I know something:”know” is the hyphen.
“Philosophy as a Rigorous Science” - critique of naturalism

19th century naturalism: everything reducible tol state of nature.

Mill: all mathematics based on empirical observations:  comes from experiment and observation
Problem: experimental is faulty, therefore if mathematics is based on empiricism, then mathematics and logic is also faulty.  However, 2+3=5 regardless.  Strips certainty out: progress but mathematics and logical judgements undermined: mathematics ultimately due to psychology but that due to physical laws, thus all sciences ultimately based on psychology.  Frege also warned against psychologism: all judgements made due /reducible to psychological properties of the mind..  Ex. aliens and mathematics, assume universal, but alien psychology….logic reducible to natural properties.  However, logic not just descriptive of our states but normative: how we should think.  Extends beyond the argument.  Wants to defend transcendental basis as being rigorous, beyond argument.
Naturalism thesis: that everything belongs to the world of nature and can be studied by the methods appropriate to studying that world.

Logic as governed by naturalistic laws.

Problem.  Naturalism sees everything as physical nature: brings assumptions that philosopher does not: doesn’t know what it means to be natural while the psychologist presumes it.  Consciousness as feature of nature: reduction:

Natural science: presupposition that nature is a unity of spatio-temporal being

-observe and collect ‘data” then rigorously use to identify distinct laws and results of testing inductively
Husserl - “an idealist who sets up and justifies theories which deny precisely what he presupposes in his idealistic war of acting, whether it be in constructing theories of , in justifying and recommending values or practical norms...absurdity remains hidden from him because he naturalizes reason.”
Logical Investigations, Vol 1 - “Psychology models itself on a form of naturalism where psychology-the empirical science-concerns itself with determination of basic events of consciousness...those events are thought of , nevertheless, as belonging to nature, that is , belonging human or brute consciousness that for their part have an unquestioned and co-apprehended with human brute organism.  To eliminate the relationship to nature would deprive the psychical of its character as an objectively and temporally determinable fact of nature (80)
Refutes premises of psychologism: error of collapsing normative / regulative discipline of logic down on to the merely descriptive discipline of psychology.  Mental operations such as combination would be source of their own regulation.  “Should” becomes “is”, facticity of customary thinking
Phenomenology and crisis of Philosophy  contains essays “Philosophy as rigorous science” and “Crisis of European science and transcendental phenomenology”
The foundation for all knowledge was the transcendental ego, in parallel to Descartes (Cartesian Meditations) 1928.  Focus on consciousness as such, or subjectivity but reject Descartes systematic doubt and insist that knowledge can be established through an investigation of consciousness = Phenomenology

Phenomenological Method (Ideas 1, 1913)

Intentionality- directedness of experience towards things in the world, property of consciousness that is of or about something. Reflective act, active act

From medieval term meaning “conscious external reference which mind has in knowing something”.


Our experience represents (intends) things only through particular concepts, ideas, images, etc.  these make up the meaning or content of a given experience and are distinct from the things they present or mean.
Phenomena: strict empiricist, what appears before the mind are sensory data or qualia.

Strict rationalist, what appears before the mind are ideas, rationally formed.


Experience mediated by worldview. Framework already there: ex walk into a church, what we see comports to existing schema: aware already of what we see.   Some pure transcendental and also experiences from past compound and unify experience.
Franz Brentano “Psychology from an Empirical Standpoint”, phenomena are what occur in the mind: mental phenomena are acts of consciousness or their contents and physical phenomena are objects of external perception, existing “intentionally” in acts of consciousness.  Distinguished descriptive psychology from genetic psychology.  Where genetic psychology seeks the causes of various types of mental phenomena, descriptive psychology defines and classifies the various types of mental phenomena.  Every act of consciousness is directed toward some object and only mental phenomena are so directed.
Ideas 1, study the complex of consciousness and correlated phenomena.  Noesis meaning to perceive, think, intend, the intentional process.  The Ideal content is noema, an ideal meaning and the object “as” intended, the object-as-it appears
What is true is on basis to what is evident to us.  Truth is given to consciousness through intuition (nous, intellectual intuition) . World constituted (Kant)  by consciousness itself.  Frame world though our experience.  Result is necessary, not contingent, truth.
Conflict between “realism” (world as it is) and “idealism” (world as result of our own ideas), question bypassed by Husserl.
Instead, he give us a Concept of world as appears to us that can be analyzed in terms of structures, how does it take on the structures it has, become available to us.  Simply a description of the way the world appears.  
Ex. look at a bowl.  Sense in which we simply see it, given through our senses, but also seen from a perspective, not one at at time.  See “As” with a backside, not just the perspective from the front.  Descriptive of complex concepts through which we see, built in to the experience.  What we see not simply given to us, but a whole host of presuppositions that make it much richer than the simply given.
Phenomenological reduction- way of phenomenological investigation.  

Epoche (greek “suspension) where one “brackets” out the natural world, including the concept of causal relations.  Common sense understanding of what we see (stimulus to sense organs, 2 world point of view, infer an object on the outside)  must get rid of this naturalistic notion of mind as a result of nature.  Instead see the bowl regardless of what is causing it.  (contrast berkley and idea planted by god, or hologram, matrix, dream) .  Yet there is a sense that the bowl in my hallucination is the same bowl, regardless) .  Doesn’t make any difference in my description of the bowl and scene of the bowl.  Instead Reduce experience to consciousness as such as the transcendental ego.  Just describe what that is all about.  leaves the “natural attitude
Meanings generally and propositions in particular exist independently of their actually functioning as intentional content. Thus, true propositions such as the Pythagorean theorem can be discovered.

Bracketing: suspending judgement:

Not doubting existence of objects when bracketing: concern is why we do not have good grounding for their very essence/foundations of knowledge



Bracketing of variables between particular bits of knowledge/consciousness: particulars and theories are bracketed.
Eidetic reduction (Plato's “eidos” form or idea) - goal is discovery of essences (meanings that are immanent in consciousness) . pure consciousness is “going back to the things themselves”  back to the experience, basic intuitions, essential structures of those intuitions through which we can understand what knowledge is all about.  Back to mind and consciousness, based on rules and essences and isolate those .  Just look at consciousness and not at the world .  Ex essential experience of a bowl: a thing with back side, with mass, with space.  Essential for any material object whatsoever.
Philosophy does not have object, but consciousness can be its object

Lebenswelt / life world
I know what I know as part of my overall worldview/Lebenswelt (life world): wants “I” of lived world rather than I of some abstract theoretical world: I know of a pre-scientific, theoretical consciousness.
Intersubjectivity: how share knowledge with others?  Lebenswelt (“life world”) is meaningful world of shared human experience.  Dimension of human practice.  Mathematical paradigm too limited.
Lifeworld: meaningful world of shared human experience(empathetic, pragmatic), weaker bracketing, intersubjective experience, attribute intentional acts to other subjects
Influence
Students of his went beyond the “I know” to the entire activity of “I” in the lived world (Heidegger) in a pre theoretical basis
Historical movement of Phenomenology launched in first half of the 20th century by Edmund Husserl, Martin Heidegger, Maurice Merleau-Ponty, Jen-Paul Sartre.
Heidegger takes phenomenology to practice


Method developed, but others to use the method

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