1 What-is-Grounding

Knowing what-is-grounding means knowing what-is [A] grounded truth. Knowing what-is [A] grounded truth, however, is knowing precisely what-is grounding [A] truth. “Knowledge is not enough, we have to apply it; wanting is not enough, there has to be an action.”1 Knowing what-is-grounding is knowing precisely what-is grounding [A] twofold truth [A=dv]. What-is-known-to-be-true-of-grounding is [A] concept and/or relation. What-is-grounding [A=dv] is inter-disciplinary—methodologically foregrounding [A] frameworks. Hypothesizing [A=dv] concept-relation further requires the following linguistic, mathematical, physical, metaphysical, and logical distinctions: (I) Linguistics—although odd in appearance, grounds [A] reflexive semantic structure. Linguistics also requires hypothesized concept-relation [A=dv] grounds [A] methodology inter-disciplined in transparency. Transitively, the transparent and reflexive intuitions are therefore grounded directly in mathematical axioms. (II) Mathematics—transitive through Leibniz Law [LL], “equality, congruence, and/or parallelism,”—grounds logical and metaphysical possibility, either affirmation and/or negation, either [A] and/or [Not A]. 2 (III) Physics—velocity, force, and/or acceleration—actually grounding [A] spatiotemporal dimension in continuum in the methodology of physics derives from mathematical axioms like metaphysics and logic, but the instruments calculating physical calculi relate to grounding [A] hypothesized concept-relation [Adv] by the scale and reality of physical time and space. (IV) Metaphysics—necessary and/or possible, heterogeneous and/or homogenous, particular and/or general, spatial and/or temporal, intrinsic and/or extrinsic, in the actual world and/or possible worlds, within the horizons of existence and/or of non-existence, by concept and/or relation— grounds hypothesis [Adv]. (V) Logic—impeccably constructing [A] rigid mathematical stockade—is stated in symbolic terms; i.e., “(X), (∃X), ∼, ⋅, v, ⊃, ≡, =, (E!X).”3

Grounding is [A] and/or [Not A] truth.

~A

Grounding [A] and/or [Not A] affirms and/or negates [A] truth.

~ (A (~ A))

1 [p. 93]; Goethe, Johann Wolfgang. Maxims and Reflections. London: Penguin Books; 1998. 2 [p. 66]; Dantzig, et al.; 1954. 3 [p. 2]; Gödel, Kurt. The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. Princeton, NJ: Princeton University Press; 1940.

2 That [A] is necessarily true implies [A] is possible.

(□A) ⊃ (◊A)

If it is necessary that [A] is true then [Not A] is necessarily false.

□A ~ □ (A ~A)

Rather if it is possible that [A] is true then [Not A] is also possibly true.

◊A ~ ◊ (A ~A)

It is possible [A] and/or [Not A] is true if and only if it is necessarily possible that [A] is true.

□ (◊àA)

It is [A] is possible then it is necessarily possible that [A] is true.

◊Aà□◊A

If it is true that [A] is necessary then it is necessarily true that [A] grounds necessary truth.

□Aà□□A

If [A] is necessarily grounding truth then [A] is actually true.

Aà□

If [A] is actually true it is necessary that [A] equals itself.

□ (A=A)

Leibniz says, “nothing is necessary whose contrary is possible,” the concept of grounding as a relation presents [A] negation as a grounding relation.4 Consider Frege’s laws of compound negation in pre-supposing [A] and [B] in [A=B].

1. “A is true, B is true; therefore (A and B) is true.” 2. “Not (A and B) is true; A is true; therefore B is false.” 3. “A is false; B is false; therefore (Neither A nor B) is true.” 4. “(A and B) is true; A is false; therefore B is true.” 5. “(Not A) and B is true; (not (not B)) and (not A) is true; therefore B and (not A) is true.” 6. “Not ((not A) and B) is true.” 5

4 [p. 14]; Leibniz, Gottfried Wilhelm. Discourse on Metaphysics and other Essays. Indianapolis, IN: Hackett; 1991. 5 [pp. 60-73];Frege, Gottlob. Logical Investigations. New Haven, CT: Yale University Press; 1977.

3 Quine says grounding is a “non-causal type of dependence.”6 ‘No entity without identity,’ says Quine.7 His “method is to extract existence commitments from our best theory” and this approach is “to say what grounds what.”8 Quine affirms [A=A] grounds hypothesized concept-relation [Adv] as “one axiom of identity” deriving from: 9

(x)(x=x)

Axiomatic necessity is necessarily as mathematical “definitions, postulates, or axioms.”10 Kant says “knowledge which reason gains from concepts,” and “construction of concepts” is [A] mathematically grounding [ad infinitum].11 Consider Rosembloom’s reference to axioms in canonical form [L1]:

1. A3 = [ o=o ] 2. A4 = [ 1=1 ] 3. A5 = [ a=a ] 4. A6 = [ f=f ] 5. A7 = [ (=( ] 6. A8 = [ )=) ] 7. A9 = [ ⊃=⊃] 8. A10 = [ ~=~]

Logically grounding [A] necessity or possibility formally stated as (□àA) v (◊àA), mathematically presupposes [A] logical grounding in evidencing axiomatic heritage to [L1]: [A5], [A7], [A8], [A10]. The concept of proof initates (~A). Logic refers to [A] inherited proof grounded transitively in mathematical axiom, “A sentence q is said to be true if there is a proof of q. The language whose construction is embodies in the preceding definitions will be call [L1].”12

[A=A] [B=B][C=C]

[A=B] [B=C] [A=C]

“The principle of transitivity consists in the statement that if two things are in some way equivalent to a third they are equivalent to each other.”13

[A=B=C]

Carnap says, “the empirical examination of a physical theory given in the form of a calculus” is grounding.14 [Adv] is affirmed by Carnap’s mathematical positivism because [A] identity is 6 [p. 1]; Clark, Michael. J., and Liggins, David. “Recent Work on Grounding.” Analysis, V.0.No.0, pp. 1-12; 2012. 7 [p. 339] McDaniel et el; 2012. 8 [pp. 348, 351]; Schaffer, Jonathan. “On what grounds what.” In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. 347-383; 2009.9 [p. 121]; Quine, et al; 1966. 10 [p. 322]; Dantzig, Tobias. Number, The Language of Science. New York, NY: The Free Press; 1954. 11 [p. 577]; Kant, Immanuel. Critique of Pure Reason. London: Penguin Classics; 2007. 12 [p. 94]; Rosenbloom, Paul. C. The Elements of Mathematical Logic. Mineola, NY: Dover Publications; 1950. 13 [p. 323]; Dantzig; et al; 1954.

4 dependent actual grounding: “The axioms and theorems of a geometrical calculus are translated into descriptive, factual propositions of interpreted physics; they form a theory which we may call physical geometry, because it is a branch of physics, in contradistinction to mathematical geometry i.e., the geometrical calculus.”15 In grounding the geometrical calculus of mathematics in physics most essentially direct in postulating actual concept-relation, Carnap’s position fortifies the potentiality of grounding consistent with [A] hypothesized grounding concept-relation [Adv]. Number properties—commutative, associative, distributive—compare generally to the universal character of mathematics grounding transitivity. “The operations of arithmetic are based on the tacit assumption that we can always pass from any number to its successor, and this is the essence of the ordinal concept.”16

A + B = B + A.

(A + B) + C = A+ (B + C).

A(B + C) = AB + AC. Dantzig says, “The abstract operations of algebra, which deal with objects that have purposely been stripped of their physical content, could not occur to minds which were so intensely interested in the objects themselves.” “The symbol is not a mere formality; it is the very essence of algebra.”17 This generalized structure transcendent in all the physical science appears to draw the axioms into transitive identities by a scientific approach, on the one hand, at such an elementary mode of arithmetic, while on the other hand, the complexity of the issue at hand reveals a matter of qualitative intransitivity in the character of the mathematical language itself. 18 What-is-grounding—hypothetically—is concept-relation [A=dv]: first, [Ad] determining-concept and second, [Av] velocity-relation, constituting reflexive, transparent, and transitive properties. Grounding [A] concept-relation constituent of essential properties, [Av Ad ], includes [Ad], conceptually determining, and [Av], relating velocity. In [WP1, WP2, …] possible worlds and/or [WA] actual world, quantifier [∃x] supervenes [A] necessary truth, [A=A], as possibility of truth [A=dv]. [A] is transitive to hypothesized grounding, [A=dv], if and only if “the properties of the logical symbols are presupposed to be known” in grounding [=dv].19 According to temporality of possible time worlds [T1, T2, …], Gallois refers to a trans-temporal mode of Leibniz Law grounding [A] identity in a congruency with [A=dv]. “The

14 [p. 67]; Carnap, Rudolf. Foundations of Logic and Mathematics. Chicago, IL: University of Chicago Press; 1985. 15 [pp. 52-53]; Carnap, et al; 1985. 16 [p. 9]; Dantzig, et al; 1954. 17 [p. 80]; Dantzig, et al; 1954. 18 [pp. 58-59]; Dantzig, et al.; 1954. 19 [p. 1]; Gödel, Kurt, et. al.; 1940.

5 persistence of an incontestable physical object can pose a problem of diachronic identity only if that object is capable of changing its parts.”20

[LL]: {“Transt: (x)(y)(z)(t)[(at t: x = y & at t: y = z) à at t: x = z]}.”21

Velocity-relation [Av] foregrounds [A] “definition of the path” only [A] concept rendered externally in the frameworks of metaphyisics in philosophies such as ethics, psychology, and even political science. 22

[d = vt].23 Einstein says “it is possible to describe the position of a point (at rest) by means of three numbers (coordinates) [x,y,z], and that there is an indefinite number of points in the neighborhood of this one, the position of which can be described by co-ordinates [x,y,z], of the first point.” Inertia between gravitational restriction and necessary requisition of accelerated force spatiotemporally foregrounds possibility. Inertial mass requires accelerating from inner-to-outer beyond [A] point of rest. Potentiating velocity property [Av] in motion relates determining property [Ad], grounding [A] from [Adv]. Consider his equations of force:

[Force = (Inertial Mass) x (Acceleration)]

[Force = (Gravitational Mass) x (Intensity of the Gravitational Field)].

[Acceleration = ((Gravitational Mass) / (Inertial Mass)) x (Intensity of the Gravitational Field)].

Heidegger’s understanding of temporality in metaphysics in part speaks from Brentano’s thoughts on continua in relation to velocity [Av]: “If time itself could pass now more quickly, now more slowly, then this formula would lose all determinateness.”24 Brentano remarks on the inversion of the physics velocity equation into:

[v=s/t]. Heidegger says “ground’ or ‘reason’ means: possibility, basis, and proof.”25 His take on Leibniz is that: “the [principium rationis] exists because, if it did not, there would be beings which would necessarily be without reason. For Leibniz, this means that there would be truths which resisted resolution into relations of identity; there would be truths, that is, which would necessarily run counter to the ‘nature’ of truth in general. Because this is impossible, because there is such a thing as truth, there is also such a thing as the [principium rationis].”26

20 [p. 196]; Gallois, André, et al.; 1998.21 [p. 70]; Gallois, André. Occasions of Identity: A study in the metaphysics of persistence, change, and sameness. Oxford: Clarendon Press; 1998. 22 [p. 28];” Heidegger, Martin. Nature, history, State, 1933-1934. London: Bloomsbury Academic; 2013. 23 [p. 52]; Einstein, Albert. Relativity: The Special and the General Theory. New York: Penguin Books; 2006. 24 [p. 52]; Brentano, Franz. Philosophical Investigations on Space, Time, and the Continuum. London: Croom Helm; 1988. 25 [p. 109]; Heidegger, Martin. The Essence of Reasons. Evanston, IL: Northwestern University Press; 1969.26 [p. 17]; Heidegger, et. al; 1969.

6 Heidegger’s temporal grounding is [singulare tantum].27 He affirms [A] grounding identity hypothesis: “The usual formulation of the principle of identity reads: [A = A]. The principle of identity is considered the highest principle of thought.”28 Heidegger considers practical errors in mathematically grounding: “The [µαθηµατα], the mathematical, is that ‘about’ things which we really already know. Therefore we do not first get it out of things, but, in a certain way, we bring it already with us. For this we can now understand why, for instance, number is something mathematical.”29 Heidegger’s mentor professor, Rickert, similarly considers mathematical grounding: “actually, they take one as far away as possible from the world of real things and events, for the latter are never homogenous, and everything that can be ‘individualized’ mathematically is, like every purely quantitative, unreal when considered in itself.”30 What is the character of truth that grounds [A] in active existence? Heidegger continues by elaborating on this presupposed identify that “Being belongs with thinking to an identity whose active essence stems from that letting belong together which we call the appropriation.”31 Although Heidegger’s phenomenology fails to address a solution mathematically, his attempt to challenge the concept of grounding is consistent with another of his mentors, Husserl: “The science concerned with what is radical must from every point of view be radical itself in its procedure.”32 Past, present, and future modalities ground beings in what Heidegger calls constant “being-becoming.”33 McDaniel presents Heidegger’s metaphysics in between sets “[S1]” and “[S2]” as “ready-to-hand” and “ready-at-hand,” signifying Heidegger’s differentiation of essential properties: “in order to understand the kind of being had by some set of objects [S1], we need to first understand the kind of being had by some set of objects [S2], and then understand the kind of being had by those in [S1] in terms of the kind of being had by those in [S2], even though every one of the members of [S2] depends on the existence of some of member of [S1].34 In grasping Heidegger’s ontological focus it is necessary to notice the temporal foregrounding: “that which essences from earlier on determines itself from our future.”35 Consider his concept of grounding in relation to utilized axioms in [A=A]: “As axiomatic, the mathematical project is the anticipation of the essence of things, of bodies; thus the basic blueprint of the structure of every thing and its relation to every other thing is sketched in advance.”36

27 [pp. 71-72]; Heidegger, et al.; 1969. 28[p. 23]; Heidegger, Martin. Identity and Difference. New York, NY: Harper & Row Publishers; 1969. 29 [p. 276]; Heidegger, Martin. Basic Writings: From Being and time (1927) to the Task of Thinking (1964). New York, NY: Harper Perennial Modern Thought; 2008. 30[p. 121]; Rickert, Heinrich. Science and History, a Critique of Positivist Epistemology. Toronto, Canada: D. Van Nostrand Company; 1962. 31 [p. 39]; Heidegger, et al.; 1969. 32 [p. 146]; Husserl, Edmund. Phenomenology and the Crisis of Philosophy. New York, NY: Harper & Row, New York; 1965. 33 Heidegger, Martin. Mindfulness. London: Continuum; 2006. 34 [pp. 354-355]; McDaniel, Kris. Heidegger's Metaphysics of Material Beings. Philosophy and Phenomenological Research, V.87: No.2, pp. 332-357; 2012. 35[p. 97]; Heidegger, Martin. Logic as the Question Concerning the Essence of Language. Albany: State University of New York Press; 2009..36[p. 292]; Heidegger, et al; 2008.

7 Heidegger identifies the singular foundations of the axiom utilized in hypothesizing [A] grounding as [Adv], prior to its mathematical transformation. Fichte’s thoughts on grounding are consistent with Heidegger in terms of the essential foreground of [A] being: “You yourself are this thing; you placed before yourself and projected out of yourself by the inmost ground of your being, your finitude; and everything you see outside of you is always yourself.”37 Heidegger is consistent with nothingness as a grounding relation despite his criticism of mathematics, claiming, “from the nothing all beings as beings come to be,” [ex nihilo omne ens qua ens fit].38 Hypothesizing concept-relation relates to Aristotle’s grounding: “Their root problem is that they posit Forms that are universal and at the same time Forms that are separable and therefore particular.”39 Aristotle grounds according to [πρωτη αρχη], “primary position of grounding.”40 For Aristotle, actuality is both [ενεργεια], the processed realization of energy, as well as [εντελεχεια], actuality as substance.41 “The possession of a potentiality just is the possession of a potentiality to act, and such a potentiality is not unconditional but depends on the obtaining of propitious circumstances, which include the satisfaction of a [ceteris paribus] condition. The [cetera], that is, are made [paria] by the very contents of the definition.”42 Aristotle’s active grounding, in relation to hypothesized [Ad] concept-determining property, is consistent with the defined necessity determining grounding from [A] primary position to potentiated grounds [Adv]. “For the same perceiving as well as being.”43 Parmenides summarizes [A] concept-relation of grounding consistent with [Adv]. If [Adv] potentiates active spatiotemporal form, then grounding necessarily always foregrounds. In this regard, [A] possibility axiomatically and a potentiality practically provides not only a necessity in the form of [A] identity, it requires that [A] grounding is actual. In other words, [A] determining-velocity grounding active beings and quantifying their demands directly understands what-is grounding [A] existence. Grounding is [A] foregrounded existence. Foregrounded existence is the active ability through time and space. In other words, hypothesized concept-relation is the necessity of velocity determined in understanding transparency in the grounding of all transitive identities: direct intuition. Funny enough, if grounding truth actually moves, determining-velocity [Adv] affirms that Heraclitus was correct when he said, “Lightning steers all.” 44

Reference • Aristotle. The Metaphysics. New York, NY: Penguin Classics; 2004. • Blanché, Robert. Axiomatics. New York, NY: Free Press of Glencoe; 1962.

37 [p. 50]; Fichte, Johann G. The Vocation of Man. Indianapolis, IN: Hackett Publishing Company; 1987. 38[p. 108]; Heidegger, et. al; 2008. 39 [p. 424],{µ.9}; Aristotle, et al.; 2004.40 [p. 60]; Heidegger, et al.; 1969. 41 [lv-lvii]; Aristotle, et al.; 2004. 42 [p. 264],{θ.5}; Aristotle. The Metaphysics. New York, NY: Penguin Classics; 2004. 43 [p. 27]; Parmenides Fragment, “το γαρ αυτο νοειν εστιν τε και ειναι”; Heidegger, et al.; 1969. 44 [p. 21];“τα δε παντα οιακιζει κεραυνος.” Gadamer, Hans-Georg. The Beginning of Knowledge. New York, NY: Continuum; 2002.

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