7 Philosophical Preliminaries

7 Philosophical Preliminaries
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7.1   Metapreliminaries 7.1.1   Why a chapter of preliminaries?
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This chapter explains some general features of my philosophical outlook,
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Readers sympathetic to empiricism will tend to reject the rest of this book.
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7.1.2   Modern empiricism
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it is impossible to attain any substantive knowledge of the world except on the basis of observation.
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rationalism holds that there is some substantive knowledge about the world that is not based on observation;
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pure reason.
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an extreme form of empiricism, logical positivism,
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literally meaningless,
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wide swathes of human intellectual endeavor meaningless, including such fields as metaphysics, theology, and ethics.
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if any scientific theory entails the existence of observationally undetectable facts, that theory must be either false or meaningless.
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empiricists have generally treated their philosophy more like an a priori axiom than like an empirical hypothesis.
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assumed as self-evident,
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Peter van Inwagen describes an ideology of ‘scientism’, consisting in ‘an exaggerated respect for science
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all knowledge must be like scientific knowledge,
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all books not containing mathematics or science should be burned,
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7.1.3   The significance of empiricism
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Positivistic assumptions were crucial in motivating Einstein’s Theory of Relativity, the Copenhagen Interpretation of quantum mechanics, and the formalist approach to mathematics,
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Today, even those who would explicitly disavow positivism tend to accept positivist-inspired theories without knowing their provenance.
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some very broad philosophical viewpoints, such as ‘naturalism’.
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Empiricism and positivism set the agenda
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the leading philosophical tradition in the English-speaking world.
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7.2   Phenomenal conservatism
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Phenomenal conservatism holds that undefeated appearances are a source of justification (perhaps the only source of justification) for belief.
Note:GNOSEOLOGIA DEL SENSO COMUNE...PRINCIPIO DI CREDULITÀ

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An appearance is a broad type of mental state, distinct from and normally prior
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including sensory experiences, memory experiences, and rational intuitions.
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When I look out the window, it seems to me that there is a squirrel in the tree (visual appearance); I seem to recall falling off my motorcycle a few times in college (memory appearance); it seems to me that the shortest path between any two points must be a straight line (rational intuition); it seems to me that, given that cows have four stomachs, it follows that cows have more than one stomach (inferential appearance).
Note:ES DI APPARENZE RAZIONALI

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There is no rational basis for discriminating fundamentally among species of appearances. What makes sensory experiences a source of justification is the same thing that makes memories and intuitions a source of justification:
Note:IL PRIMATO DEI SENSI NN HA SENSO....MEMORIA E INTUIZIONE

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It is, for example, arbitrary to hold that sensory experiences may be presumed reliable but that intuitions should not be.
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phenomenal conservatism is not the thesis that all appearances are true.
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how things initially appear is the rational starting point:
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unless contrary evidence
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7.3   Synthetic a priori knowledge
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7.3.1   The question of the synthetic, a priori

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•Empirical knowledge is knowledge whose justification depends essentially on observations
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•A priori knowledge is knowledge that is not empirical.
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•An analytic statement is, roughly, one whose denial is a contradiction.
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synthetic statement is one that is not analytic, that is, its denial is consistent.
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is there any synthetic, a priori knowledge?
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can there be a sentence whose denial is not contradictory, but nevertheless we can see it to be true in a way that does not depend on observation for its justification?
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7.3.2   The answer
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No object is completely purple and also completely orange.
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For any two moments in time, one is earlier than the other.
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it is better to be happy than to be miserable.
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If x is inside y, and y is inside z, then x is inside z.
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The appearance of white is more similar to the appearance of yellow than to that of any other chromatic color.
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No action can cause an effect to occur before the action itself occurs.
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The number three exists.
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There could have been only seven planets in the solar system.
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The probability that either it is raining or it isn’t is 1.
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numbers, spatial properties, colors, ethical value, decision theory, time, causation, probability, possibility,
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Take a famous epistemological thought experiment: suppose that I am a disembodied brain being kept alive by scientists in a vat of nutrients; my brain is being artificially stimulated to create the illusion of a physical world, and so on. In this case, all of my observations are false. Nevertheless, even if this scenario is true, I still know that no object is completely purple and completely orange.
Note:PERCHÈ PARLIAMO DI APRIORI?

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produce the definitions of the relevant terms in the statement, substitute the definitions for the terms they define, then, from the denial of the resulting statement, derive a sentence of the form ‘A and not A’.
Note:COSA FARE X DIMOSTRARE L ANALITICITÁ

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Take the sentence, ‘No object is completely purple and also completely orange.’ The project of showing this to be analytic is stymied at the first stage by the fact that there is no verbal definition of either ‘purple’ or ‘orange’. (There is only an ‘ostensive definition’, that is, these terms have to be explained by pointing to examples of the relevant colors.)
Note:IMPOSSIBILE NEL NS CASO

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‘Something is completely purple and also completely orange’, has the same logical form as ‘Something is completely furry and also completely happy’, which is not a contradiction.
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7.3.3   How much synthetic a priori knowledge is there?
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they are willing to accept analytic a priori knowledge, but not synthetic a priori knowledge.
Note:L EMPIRISMO CADE O VINCE QUI... LA CONOSC ANALITICA È MNIMIZZATA COME NN SOSTANZIALE (SOLO LINGUISTICA) PER SALVARE LA LGICA

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What is the source of our synthetic a priori knowledge? The best answer to this is rational intuition, and the best explanation for our justification for relying on rational intuition is phenomenal conservatism.
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Rational intuition is not relevantly different from observation, reasoning, or memory for present purposes; all of these are simply different species of appearances,
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we have good reason for seeking multiple justifications for a given conclusion; if it is possible to support a conclusion through both observation and intuition, this is preferable to supporting it through only one of these means.
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7.4   Metaphysical possibility
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7.4.1   The meaning of ‘possible’ and related terms
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a proposition is possible if it could be true
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A proposition is necessary if it could not be (and could not have been) false;
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A proposition is contingent if it is neither necessary nor impossible; that is, it could be true and could be false.
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‘logical possibility’ and ‘metaphysical possibility’.
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A proposition is said to be logically possible provided only that it is not contradictory.
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Metaphysical possibility is undefinable;
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7.4.2   Metaphysical possibility is broader than physical possibility
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even things that conflict with the laws of nature may nonetheless be in some sense ‘possible’,
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laws of nature could have been different.
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‘It could have turned out that we lived in a perfectly Newtonian
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7.4.3   Metaphysical possibility as conceivability?
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To say that something is metaphysically possible is something close to saying that it is coherently conceivable.
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conceivable’ just means ‘possible to conceive’,
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a proposition might be impossible for human beings to conceive solely because of some cognitive defect or limitation on our part.
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conceivability by an ideal observer,
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7.4.4   Metaphysical possibility and science fiction
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The notion of metaphysical possibility can also be illuminated by considering the limitations of fictional stories.
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in Star Trek, people travel faster than the speed of light all the time.
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aspects of stories are rejected by alert fans as ‘not making sense’. Time travel stories sometimes evoke this kind of criticism,
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on the ‘branching timelines’ theory, when a person ‘goes back’ to some earlier time t, what actually happens is that a new branch of the universe is generated
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there is a certain very broad sort of possibility that ought to constrain stories, such that if a story is impossible in this broad sense, it is thereby defective.
Note:IL PUNTO DI QS DISCUSSIONE....C È UN IMPOSSIBILITÀ CHE VA OLTRE LE LEGGI DELLA FISICA....IMPO METAFISICA

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critics are claiming that the time travel stories are metaphysically impossible.
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7.4.5   Metaphysical possibility as a priori knowability?
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Metaphysical possibility is closely tied to the notion of a priori knowledge.
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Thus, we know a priori that pentagons have five sides, and it is metaphysically necessary that pentagons have five sides; we know a priori that no object is completely purple and completely orange, and it is metaphysically necessary that no object is completely purple and completely orange.
Note:ESEMPI...VALE SIA X L ANALITICO CHE X IL SINTETICO

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7.4.6   Logical vs. metaphysical possibility
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The synthetic a priori truths are metaphysically necessary, yet their denial is not contradictory
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The synthetic, necessary, a priori truths that I have been defending are anathema to empiricists.
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7.4.7   False signs of possibility: Analogies and mathematical systems
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No one should believe that a proposition is metaphysically possible merely because it is logically possible.
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Mathematical systems in modern times are constrained by nothing other than mere consistency
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the fact that one can develop a coherent mathematical system in which one talks about ‘infinite numbers’ such as ℵ0, does not show that any such numbers exist or could exist.
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the argument by analogy: A is possible, and there is an analogy to be drawn between A and B; therefore, B is possible. This is usually fallacious, particularly when the analogy is based upon mere similarity of mathematical structure.
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it is possible to travel in either direction along a spatial dimension, and there is an analogy to be drawn between the temporal dimension and a spatial dimension
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7.5   Possibility and paradox
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I argue that most of the paradoxes of the infinite involve scenarios that are logically possible but metaphysically impossible.
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I hold that there are many more necessary truths than are standardly recognized by philosophers, scientists, and mathematicians;
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I think there are many fewer possibilities than are commonly recognized.
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For an empiricist, nothing can be ruled out a priori unless it is actually a contradiction
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Even though empiricism is less popular than it once was, contemporary philosophy retains a significant resistance to synthetic necessary truths.
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Suppose we want to know whether some proposition P is metaphysically necessary, impossible, or contingent. Many think that the presumption should be that P is contingent,
Note:BURDEN OF PROOF...UN PORTATO DELL EMPIRISMO

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If, however, metaphysical possibility is distinct from logical possibility, and if there are many things that are logically contingent yet metaphysically necessary or impossible, then it is unclear why there should be any such burden of proof.
Note:L'IMPOSSIBILITA' METAFISICA CI TOGLIE MOLTI IMBARAZZI... MOLTI PARADOSSI POSSONO ESSERE LIQUIDATI

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7.6   A realist view of mathematics
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the nature of mathematics.
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a body of a priori knowledge, some of it analytic and some synthetic.
Note:OPINIONE....COS È LA MATEMATICA....ANALITICA L INFERENZA...SINTETICA L ESISTENZA. ES: IL NUMERO 3 ESOSTE (GIUDIZIO SINTETICO A PRIORI)

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properties of and relations between certain kinds of universals.
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It is, however, necessary that there could be things exemplifying the property.
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Arithmetic studies the properties and relationships of numbers, where numbers are properties that groups of things (whether physical or non-physical) can exemplify – for example, whenever there are two of anything, the property of twoness is exemplified.
Note:ESEMPIO...REALTA' CHE EMERGONO DA ESEMPI SEMPRE PRESENTI...IMMANENTISMO

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This view of mathematics (which is a form of mathematical Platonism) always seemed to me completely natural, so much so that I have never seriously entertained any other view. Nevertheless, the view is quite controversial in contemporary philosophy of mathematics.
Note:L'IMMANENTISMO MATEMATICO LA VIA PIU' NATURALE

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Some philosophers and mathematicians believe, instead, that mathematics is essentially a conventional symbol-manipulation game:
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mathematicians invent a series of symbols,
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the whole system is pure invention,
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That view of mathematics, known as ‘formalism’, is motivated by empiricism. The empiricists of the twentieth century were loath to admit that there was any a priori knowledge of objective reality,
Note:FORMALISMO NOMINALISTA.... UN PORTATO DELL EMPIRISMO PER LIMITARE L APRIORISMO

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Some empiricists turned to the formalist philosophy of mathematics to rescue them from what would otherwise be a striking collection of counterexamples to their epistemological theory.
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